Currency Option Trading Strategies as an Alternative Tool ... · Vol. 15 No. 2 Currency Option...

Currency Option Trading Strategies as anAlternative Tool for Central Bank Foreign

Exchange Interventions∗

Helena Glebocki Keefea and Erick W. Rengifob

aFairfield UniversitybFordham University

Many emerging markets’ central banks are concerned withexcessive volatility in foreign exchange rates and intervene tosmooth volatility. This paper proposes a specific option trad-ing strategy as an alternative central bank tool to aid for-eign currency intervention, where dynamic delta hedging ofthe net portfolio position guides the central bank’s interven-tion in the spot market. We term this trading strategy the “W”spread, and show that the exchange rate can be stabilized andvolatility lowered with this market-driven approach to foreignexchange intervention.

JEL Codes: F31, G15.

1. Introduction

Many emerging markets’ central banks are concerned with excessivevolatility in foreign exchange rates and wish to exert some controlover the direction and speed with which the value of their currency

∗The authors would like to thank the Global Association for Risk Profession-als for their support in the funding of this research, as well as the participants ofthe First Annual Meeting of the Peruvian Society of Economists and members ofthe Peruvian Central Bank. The usual disclaimers apply. Author contact: Keefe:Department of Economics, Fairfield University, Fairfield, CT 06824 (USA), (203)254-4000, e-mail: [email protected]. Rengifo: Department of Economics andthe Center for International Policy Studies (CIPS), Fordham University, 441 EastFordham Road, Dealy Hall, Office E513, Bronx, NY 10458. Phone: 718-817-4061,Fax: 718-817 3518.

179

180 International Journal of Central Banking June 2019

changes. Historically, intervention methods have relied on the pur-chase and sale of foreign currency directly in the spot market.1 Thispaper proposes a specific option trading strategy as an alterna-tive central bank tool to aid foreign currency intervention, wheredynamic delta hedging of the net portfolio position guides the cen-tral bank’s intervention in the spot market.2 The main objective ofthe central bank in adopting this type of an intervention strategy isto limit exchange rate volatility with an intervention position that isdriven by market forces. It is important to note that no interventionstrategy can overcome the effects of structural changes that causeexchange rate movements, but this strategy can dampen the effectsof sudden exchange rate shocks and lower volatility. Because thestrategy responds to market conditions, rather than subjective inter-ventions determined by policymakers, it may be more effective inresponding to shocks than discretionary spot market interventions.

We use the Colombian central bank’s experience with volatilityoptions as a benchmark3 and analyze an option trading strategy thatwe term the “W” spread, where the central bank holds a portfolio oftwo long calls, two long puts, one short call, and one short put.4 Theproposed intervention happens on two fronts. First, on a daily basis,the spot market purchase/sale of USD will be determined by theresponsiveness of the option price to a change in the daily exchangerate—or the option’s delta. Second, at maturity, the central bankas well as the market participants can use the proceeds from theoption execution to buy/sell USD on the spot market that onceagain complements the central bank’s goal of stabilizing exchange

1More recently, central banks in Brazil, India, Mexico, and Turkey havebeen intervening through the derivatives market. See Domanski, Kohlscheen, andMoreno (2016) and Nedeljkovic and Saborowski (2017).

2We tested a variety of traditional strategies first that did not reach theintended goal of lowering volatility through both daily interventions and atexercise. Results are available upon request.

3Colombia is one of the only economies known to have used currency optionsas a means for curbing exchange rate volatility. This strategy has been found tobe successful in reaching the stated goals of smoothing the volatility (Keefe andRengifo 2015).

4In all cases, the options are in U.S. dollars (USD). For example, in a longcall position, the central bank has the right to buy USD from the issuer of theoption. In a short call position, the central bank has the obligation to sell USDto the owner of the option.

Vol. 15 No. 2 Currency Option Trading Strategies 181

rate movements. Our results show that since the spot market inter-ventions are now driven by the delta of the option, the central banklowers volatility with a clear, market-driven position.

The remaining sections of the paper are structured as follows.Section 2 provides a review of the literature. Section 3 describesthe W-spread option trading strategy and argues why this strategyis an improvement on others already used in the market. Section 4presents the analytical approach and methodology. Section 5 reportsthe results by testing the W-spread strategy with a simulated seriesof the Colombian peso–U.S. dollar exchange rate (COPUSD). Herewe price options contracts at various strike prices and analyze theoutcome of dynamically delta hedging the net portfolio position andits effect on exchange rate movements. Section 6 concludes.

2. Literature Review

There is limited literature on the use of currency options by centralbanks for the purpose of exchange rate intervention. In the past,the proposition for emerging market central banks to use currencyoptions has been more of a theoretical exercise. This may be partlydue to the relatively shallow and underdeveloped derivatives mar-kets in these economies. Despite the recent growth in demand forforeign exchange derivatives in emerging economies, they representonly a fraction of the global derivatives market. Emerging marketsmake up only 4.4 percent of the daily over-the-counter (OTC) trad-ing of foreign exchange derivatives according to data collected by theBank for International Settlements (BIS).5 Yet, there is demand forthese financial products. Turnover in foreign exchange derivativesfor emerging market economies has increased by over 300 percentfrom 2001 to 2013.

Furthermore, options made up only 6 percent of the total foreignexchange derivatives market traded in emerging economies as of 2010(Mihaljek and Packer 2010). Adoption of options-based interventiontools by central banks may aid further development of these mar-kets. Local traders as well as export/import businesses would have a

5This excludes the top four derivatives trading centers of Hong Kong, Singa-pore, Korea, and Brazil, which make up over 90 percent of the total emergingmarket derivatives trading (Mihaljek and Packer 2010).


new hedging instrument readily available to them. Caballero (2003)contends that emerging markets need instruments for hedging andinsurance purposes against capital flow reversals, specifically, andthe exchange rate volatility that they may cause. In comparing Aus-tralia and Chile, Caballero illustrates how emerging markets requireinsurance to assist in the response to crises and shocks that wouldmatch the effectiveness of policy responses in advanced economies.

There have been a number of arguments for the adoption ofa derivatives-based intervention strategy. Wiseman (1999) arguesthat governments should commit themselves to frequent and regu-lar auctions of short-dated physically delivered currency options asa mechanism to stabilize exchange rates. Since almost all centralbank authorities would like to reduce exchange rate volatility, with-out pushing it all the way to zero, official auctions would encourageprivate banks to buy options and exercise them when profitable.Dynamic delta hedging on the part of the trader can substitute foractively pursuing the same position in the market.

Zapatero and Reverter (2003) consider the intervention strate-gies of central banks when directly intervening in the spot marketusing foreign exchange reserves compared with intervention with theuse of options. With the counterparty investment bank hedging itsposition, the options intervention method performs better than tra-ditional spot market intervention using foreign exchange reserves.The currency stabilization occurs through the hedging activities ofthe investment bank in the bond market to offset its currency optionsposition with the central bank.

Keefe and Rengifo (2015) analyze the success of volatility optionsused by the Colombian central bank to mitigate deviations of theexchange rate from the twenty-day moving average. In 85 percent to90 percent of options executed, the value of the COPUSD revertedtowards the trend, thereby successfully minimizing the volatility.After abandoning the strategy in 2009, the Colombian central bankhas once again instituted the use of volatility options as of October2015.

A fundamental assumption in our strategy is the use of dynamicdelta hedging to guide the open-market intervention position ofcentral banks. According to Breuer (1999), if market makers holdnet long positions, their dynamic delta-hedging behavior can lowervolatility. When the owners of an option contract sell USD in the


spot market to hedge their positions when the domestic currency isdepreciating against the dollar, and purchase USD when the domes-tic currency is appreciating against the dollar, this will help sta-bilize exchange rates. Furthermore, the transparency with whichthe central bank auctions option contracts to market participantsmay introduce stability and additional hedging instruments into themarket (Archer 2005). Garber (1994) and Malz (1995) also studythe effects of hedging on currency stabilization. By influencing mar-ket liquidity and expectations, the use of currency options by centralbanks can be effective in stabilizing the exchange rate and controllingvolatility.

Testing the effectiveness of foreign exchange interventions hasbeen complicated, since the size, frequency, and duration of inter-vention may vary drastically within and between countries. Themost thorough analysis of intervention effectiveness to date hasbeen conducted by Fratzscher et al. (2015) by studying foreignexchange intervention in thirty-three countries. They find that for-eign exchange intervention is widely used by a number of countries,and that it is an effective policy to smooth and stabilize exchangerates.

Daude, Levy Yeyati, and Nagengast (2014) review the effective-ness of traditional foreign exchange intervention in emerging marketeconomies, specifically with the reassessment of this tool in the wakeof the global financial crisis. The authors find that the most effectiveinterventions are those that are used as a countercyclical macroeco-nomic tool, smoothing out short-run volatility and currency swings.Interventions can slow appreciation, and are most effective when thecurrency is already overvalued. Their effectiveness decreases underconditions of greater capital account openness (Adler and Tovar2011).

Leon and Williams (2012) concur that foreign exchange inter-vention via either purchase or sale of foreign currency is effective ifthe goal is to keep the exchange rate within a targeted range. Theinterventions are an appropriate policy tool in emerging economieslooking to control imported inflation while maintaining competitive-ness. Egbert (2007) finds that interventions in emerging Europeaneconomies were successful in curbing appreciation pressure, whileGuinigundo (2013) shows that by using spot market interventionsas the main tool for intervention, the central bank of the Philippines


was able to curb exchange rate volatility without adhering to a spe-cific level of the exchange rate. The results in this paper supportthat finding. Akinci et al. (2006) also found that purchase-basedinterventions were successful in curbing appreciation.

Our research contributes to the literature on both the potentialuse of currency options by central banks and the potential effective-ness of such tools in curbing exchange rate volatility. By proposinga novel trading strategy that allows the central bank to operate inboth the spot and derivatives market, we explore a new approachto the question of how central banks in emerging market economiescan effectively intervene in currency markets to reach their objectiveof smoothing exchange rate volatility.

3. W-Spread Strategy

The W-spread strategy has two key components. First, in the optionsmarket, the central bank portfolio position consists of two long calls,one short call, two long puts, and one short put, where the underly-ing asset is the U.S. dollar (USD). With this portfolio combination ofcalls and puts, the exercise of the options at maturity contributes tothe intervention objectives of the central bank. Second, the dynamicdelta hedging of this portfolio on a daily basis determines the centralbank’s daily spot market purchase/sale of USD in a way that onceagain complements its intervention objectives.6 The use of optionscreates a stronger signaling channel between the policymakers andmarket participants because those following the market will have aclear understanding of the actions of the central bank. The optiondelta and the delta hedging inform both market participants and thecentral bank of intervention positions and act as an announcementvia the market.

Although the central bank will incur costs in the form of premi-ums paid for buying the long options and payoffs paid when the short

6The combination of long and short positions as well as call and put optionsis the crucial element of this strategy. By holding both sides of the market, thecentral bank limits the opportunity for market manipulation, and the interven-tion is driven by the responsiveness of the options’ market price to changes inthe exchange rate. With this strategy, the intervention position of the centralbank in the spot market is now driven by the delta of the option and thereforeis determined by market forces.


Figure 1. W-Call Spread

Notes: The W-call spread presents a position with limited risks but unlimitedgains in case of depreciation beyond K3. It consists of one short call with strikeprice K2, one long call with strike price K1, and one long call with strike priceK3. The middle strike price (K2) for the short position is determined as K1+K3

2 .

option positions are exercised, central banks will also receive posi-tive payoffs when the long options are exercised plus the premiumsreceived from the sales of options. As will be presented in section 5,the potential costs of the strategy are offset by the potential gains,making the strategy a near-zero net expected returns/losses.

3.1 Details of W-Spread Strategy

To understand the W-spread strategy, consider first the call sideand the put side separately.7 Figure 1 depicts the W-call spread,which consists of two long call positions with a strike price of K1and K3, and one short position with a strike price of K2. The middlestrike price for the short position is determined as K1+K3

2 . For theW-call spread strategy, as the spot exchange rate value depreciatesbeyond K3, the central bank gains S − K2 at maturity, as seen intable 1. The gains continue to increase as the spot exchange rate,S, increases (local currency depreciates). On the other hand, if S

7The underlying asset for all options is the U.S. dollar, and all option contractsare European and therefore cannot be exercised until maturity.


Table 1. W-Call Spread Payoffs

Calls

Long Call Short Call Long Call(K1) (K2) (K3) Total

S ≤ K1 0 0 0 0K1 ≤ S < K2 S − K1 0 0 S − K1K2 ≤ S < K3 S − K1 –(S − K2) 0 K2 − K1S ≥ K3 S − K1 –(S − K2) S − K3 S − K2

Note: This table presents the payoffs that would be paid by the issuer of the shortcall and received by the owner of the long calls.

appreciates beyond K1, all call options will expire without beingexercised and the losses will be limited to the premiums paid on thelong call options.

The net cost to the central bank will be the premium paid onthe long call options plus the payoff on the short call option if itis exercised. As can be seen, the losses are limited to the premiumpaid on the long options, but the gains are unlimited if the currencydepreciates beyond K3. It would be counterintuitive for the centralbank to attempt to move the market into a deep depreciation, aswe assume that the goals of the central bank to maintain stabilityprevail over any objective to maximize gains.

The W-put spread presented in figure 2 consists of two long putpositions with strike prices at K1 and K3, and one short put witha strike price of K2. The middle strike price for the short positionis determined as K1+K3

2 . Once again, the strategy offers unlimitedgains and limited losses in payoffs. As the currency value appreci-ates beyond K1, the central bank obtains a payoff of K2 −S, as seenin table 2, which increases as the spot exchange rate, S, continuesdecreasing (local currency appreciates). On the other hand, if theexchange rate depreciates beyond K3, all put options expire with-out being exercised and the only losses the central bank faces arethose of the long put option premiums.

As can be seen in both W-call spread and W-put spread strate-gies, the risks are limited and the gains unlimited if the exchangerate moves beyond the strike price K3 for the W-call spread and K1


Figure 2. W-Put Spread

Notes: The W-put spread presents a position with limited risks and limitedgains. It consists of one short put with the strike price K2, one long put withstrike price K1, and one long put with strike price K3. The middle strike price(K2) for the short position is determined as K1+K3

2 .

Table 2. W-Put Spread Payoffs

Puts

Long Put Short Put Long put(K1) (K2) (K3) Total

S < K1 K1 − S –(K2 − S) K3 − S K2 − SK1 ≤ S < K2 0 –(K2 − S) K3 − S K3 − K2K2 ≤ S < K3 0 0 K3 − S K3 − SS ≥ K3 0 0 0 0

Note: This table presents the payoffs that would be paid by the issuer of the shortput and received by the owner of a long put.

for the W-put spread. Combining both spreads creates the W-spreadstrategy, depicted in figure 3. In a neutral W-spread strategy, thereis an equal distribution of funds into the W-call spread and W-putspread strategy, depicted by the graph on the left in figure 3.8 The

8We refer to the even split in W-puts/W-calls in the W-spread strategy as“neutral” because the weight of the delta hedging (purchase or sale of USD)based on appreciation or depreciation will be equal between the W-put spreadsand W-call spreads.


Figure 3. W-Spread Strategy

Notes: The W-spreads with calls and puts presents a position with limited risksand unlimited gains. It consists of combining the W-call spread with the W-putspread. In a neutral position, the W-put/W-call spread ratio is 1, depicted in theleft graph. In a call-biased W-strategy, the W-put/W-call spread ratio is 0.25,depicted in the middle graph. In a put-biased W-strategy, the W-put/W-callspread ratio is 4, depicted in the right graph.

neutral strategy is used as the characteristic example to explain howthe strategy functions. In reality, if the central bank is observingpersistent movement of the exchange rate or strong expectations ofappreciation or depreciation of the currency, it can and should enacta biased strategy.

In a biased strategy, the portfolio is weighted heavier with eitherW-calls or W-puts, as is illustrated in figure 3 and figure 4. In anappreciationary scenario, the central bank adjusts its strategy toreflect the actual or expected appreciation of the domestic currency.More traders would be seeking put options, which for the long posi-tion provide protection against further appreciation and on the shortside allow them to bet the appreciation will be curbed (workingin favor of the central bank’s goals). In a put-biased strategy, thecentral bank holds a relatively larger concentration of W-puts toW-calls in the portfolio. If 10,000 contracts are traded as part ofthe intervention strategy, 80 percent of the contracts would be allo-cated towards W-put spreads, and the remaining 20 percent towardsW-calls. The W-put/W-call ratio would be 4. The net dynamic delta-hedging activity of the central bank leading up to maturity will forcethe central bank to buy USD on the spot market, thereby counteringthe appreciation pressure more strongly than in a neutral position


Figure 4. Distribution of W-Spread

Notes: In a neutral position, the W-put/W-call spread ratio is 1. In a call-biasedW-strategy, the W-put/W-call spread ratio is 0.25, and would be enacted underconditions of strong depreciation. In a put-biased W-strategy, the W-put/W-callspread ratio is 4, and would be enacted under conditions of strong appreciation.

(the explanation for how the hedging works will be provided in detailbelow).

Conversely, under conditions of depreciation of the local cur-rency, a portfolio weighted heavier with W-calls than W-puts wouldbe appropriate. In this scenario, more market participants are seek-ing out call options in general. For the long position, the call options


would protect against losses associated with further depreciation ofthe currency, whereas market participants holding short positionsare betting that the depreciation will be curbed before maturity(again, an action that would complement the goals of the centralbank in this scenario). The net dynamic delta-hedging activity ofthe central bank leading up to maturity will force the central bankto sell USD on the spot market, thereby countering the depreciationpressure more strongly than in a neutral position. The biased strate-gies can be employed in conditions when there are expectations ofstrong or persistent depreciation (ratio smaller than 1) or appreci-ation (ratio larger than 1), so that the central bank is essentially“doubling up” on its effort to combat the deviations of the exchangerate.

It is important to note that the weights associated with the cen-tral bank’s portfolio may be adjusted continuously to reflect marketconditions. There is nothing precluding the central bank from wait-ing until maturity to issue a new set of options. Nor must the datebe fixed to thirty days, which is a relatively short time span thatallows adjustment as is deemed necessary. If the central bank beginsin a neutral strategy, but more calls are transacted than puts, bydefault it is now holding a W-call-biased strategy. Therefore, theadjustment can be either overt, based on the weights assigned bythe central bank, or dictated by demand from market participants.In either case, the weights, and thereby the intervention, adjusts toreflect market realities.

Table 3 details the payoffs associated with the W-strategy. Inthe top panel of table 3, the payoffs at maturity for the neutralW-spread strategy are presented, showing the position of the cen-tral bank when all contracts have expired or have been exercised.The lower two panels of table 3 show the payoffs for a call-biasedand put-biased W-spread strategy. As can be seen, the W-spreadstrategy yields the potential for unlimited gains with limited risk.When the exchange rate at maturity, S, moves beyond strike pricesK1 or K3, this results in payoffs greater than zero which increase asS is farther from the strike prices. When the exchange rate at matu-rity is between strike prices K1 or K3, the payoffs for the centralbank are still positive even though limited in size. The same holdstrue for the biased strategies, as can be seen in the lower panels oftable 3.


Tab

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W-S

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adStr

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yPay

offs

Calls

Puts

Long

Call

Short

Call

Long

Call

Long

Put

Short

Put

Long

Put

(K1)

(K2)

(K3)

Tota

l(K

1)

(K2)

(K3)

Tota

lN

et

W-P

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W-C

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ead

=1

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K1

00

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K1

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–(K

2−

S)

K3

−S

K2

−S

K2

−S

>0

K1

≤S

<K

2S

−K

10

0S

−K

10

–(K

2−

S)

K3

−S

K3

−K

2S

−2K

1+

K2

K2

≤S

<K

3S

−K

1–(

S−

K2)

0K

2−

K1

00

K3

−S

K3

−S

3K2

−2K

1−

S

S≥

K3

S−

K1

–(S

−K

2)

S−

K3

S−

K2

00

00

S−

K2

>0

W-P

ut/

W-C

allSpr

ead

=0.

25

S<

K1

00

00

K1

−S

–(K

2−

S)

K3

−S

K2

−S

K2

−S

>0

K1

≤S

<K

24(

S−

K1)

00

4(S

−K

1)

0–(

K2

−S)

K3

−S

K3

−K

24S

−5K

1+

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K2

≤S

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34(

S−

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–4(S

−K

2)

04(

K2

−K

1)

00

K3

−S

K3

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6K2

−5K

1−

S

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K3

4(S

−K

1)

–4(S

−K

2)

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3)

4(S

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2)

00

00

4(S

−K

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>0

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=4

S<

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00

00

4(K

1−

S)

–4(K

2−

S)

4(K

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S)

4(K

2−

S)

4(K

2−

S)

>0

K1

≤S

<K

2S

−K

10

0S

−K

10

–4(K

2−

S)

4(K

3−

S)

4(K

3−

K2)

S−

5K1

+4K

2

K2

≤S

<K

3S

−K

1–(

S−

K2)

0K

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00

4(K

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S)

4(K

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9K2

−5K

1−

4SS

≥K

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1–(

S−

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(S−

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00

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table

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The costs the central bank faces include the premium it mustpay to hold the long option positions and the payoffs it must pay forthe short positions when the contracts are exercised. Table 3 takesinto account the net payoffs, and therefore already accounts for thecost of paying the short position payoffs. Theoretically, the accu-mulated delta-hedging transactions until maturity, measured by thecumulative financial costs incurred, equal the options’ premiums.9

Moreover, the net payoffs obtained in any of the W-spread strategiescover the costs associated with premiums paid by the central banks.This is particularly true for deep in-the-money or out-of-the-moneyfinal exchange rates. On average, by pairing the W-spread strat-egy with dynamic delta hedging, the central bank is able to coverits hedging costs with the net payoffs, creating a position where infact the central bank does not face compounding gains or losses,presenting another positive advantage for central banks to incorpo-rate dynamic delta hedging as part of the options-based interventionstrategy. We show this in several simulations presented in section 5.

3.2 Details of Dynamic Delta Hedging

The W-spread strategy’s dynamic delta hedging informs the cen-tral bank of the correct size of USD to purchase or sell on the spotmarket in order to cover its option positions. With dynamic deltahedging, the central bank can reduce volatility by providing (reduc-ing) liquidity and by clearly signaling its intentions to all marketparticipants. Since the delta of the option captures the responsive-ness of the option value to changes in the spot exchange rates andbecause these changes can be estimated on a daily basis, hedgingbased on the delta of the option provides the central bank with amarket-driven strategy to guide its spot market interventions.

The delta of the option is the derivative of the option price withrespect to the spot exchange rate and can be presented as follows(DeRosa 2011, Chen 1998):

δcall = e−r∗τΦ(x + σ√

2) (1)

δput = e−r∗τ(Φ(x + σ

√2) − 1

), (2)

9For example, see Hull (2012, chapter 7).


where

x =lnSt

K +(r − r∗ + σ2

2

)τ

σ√

2

and 0 ≤ δcall ≤ 1 for call deltas and −1 ≤ δput ≤ 0 for put deltas.The delta of the option is influenced by the daily spot exchange

rate (S), the foreign interest rate (r∗), the domestic interest rate(r), the strike price (K), and volatility (σ). Therefore, as the centralbank responds to changes in the deltas of the options in its portfolio,it is responding in essence to changes in each of these variables.

To understand how the hedging of the W-spread strategy con-tributes to the intervention goals of central banks, we must firstconsider what occurs during the hedge. Dynamically delta hedginga long call on USD when the local currency depreciates implies thatthe owner of the option sells USD in the domestic spot market.10

By doing so, the supply of USD in the spot market rises, therebyintroducing appreciation pressures that counter the depreciation ofthe local currency. Similarly, by dynamically delta hedging a long-put position as the local currency depreciates, the owner of the longput sells USD in the domestic spot market to offset his position atmaturity of the option contract. The offsetting spot market posi-tions contribute to appreciation pressure that counters the depreci-ation of the local currency (COP, for example). These scenarios aresummarized in table 4.

In the W-spread strategy, the central bank hedges the net port-folio position (recall that the W-spread strategy is made of two longcalls, one short call, two long puts, and one short put). Therefore,whether it is buying or selling USD depends on the aggregated deltasof each of the six options in the portfolio. As we demonstrate in thefollowing section, the W-spread strategy is designed specifically sothat the buying/selling of the foreign currency through the hedgecontributes to countering the deviations of the exchange rate.

10The long call gives the owner the option to buy USD at the strike price at agiven future time. For these owners, depreciation benefits them since their payoffis given by max(S–K,0). Thus, at any time during the life of the option, theyshould (short) sell whenever St > K and buy whenever St < K. Of course, thisimplies first that the owner is comfortable performing periodic delta hedges andthat the financial costs associated with it are adequately considered.


Table 4. Impact of Dynamic Delta Hedging on ExchangeRate Movements

Dynamic Delta-Hedging Position

Calls Puts

Long Short Long Short

Depreciation Short-Sell USD Buy USD Short-Sell USD Buy USDCounters Exacerbates Counters Exacerbates

Appreciation Buy USD Short-Sell USD Buy USD Short-Sell USDCounters Exacerbates Counters Exacerbates

Note: This table presents the overall daily dynamic delta-hedging outcomes underconditions of depreciation or appreciation for short and long positions for calls andputs.

3.3 Dynamics of the W-Spread Strategy

As presented previously in figure 4, the mix of W-call and W-putspreads in the central bank’s portfolio may be altered to reflect theexpectations of the persistent exchange rate movements. First, if thecentral bank wants to hold a position that does not signal expecta-tions of depreciation or appreciation, they can evenly distribute theirportfolio between the W-call spread and W-put spread (W-put/W-call spread ratio equal to 1). By doing so, their daily interventionsvia the delta-hedging position are equally large for an appreciationor depreciation of their currency.

On the other hand, if there are expectations of persistent appre-ciation or depreciation (not driven by fundamentals), accompaniedby high volatility in the market, the central bank can choose tohold a biased W-spread portfolio to signal a stronger interventionin response to the persistent and not fundamentals-driven appreci-ation or depreciation, as discussed above. For example, with persis-tent depreciation, the central bank can hold a call-biased W-spread.Under this strategy and on a daily basis, the central bank’s deltahedging in the spot market implies a net sale of USD that is greaterthan under the neutral W-spread strategy (W-put/W-call spreadratio equal to 1). Through the sales of USD on the spot market,the central bank counteracts the persistent depreciation and con-tributes to decreasing volatility by providing greater liquidity into


the market. With persistent appreciation, the central bank can holda put-biased W-spread. Under this strategy and on a daily basis,the central bank’s delta-hedging interventions in the spot marketimply a net purchase of USD which is greater than under the neu-tral W-spread strategy. Through the purchase of USD on the spotmarket, the central bank counteracts the persistent appreciation byabsorbing excess liquidity of USD into the market.

For every option the central bank holds or issues, there is anoffsetting position by a market participant that has purchased orsold the option. The risk associated with the offsetting positions ofmarket participants is derived from the delta hedging of short posi-tions, which may exacerbate the movements in the exchange rate.Delta hedging of the long position complements the goals of the cen-tral bank.11 Since options act as a risk-management tool for manycorporations and traders, market participants can choose to hedgeall, part, or none of their net portfolio positions. In many cases,the option itself acts as a hedge against other positions the marketparticipants are holding. Since hedging can be costly, not all mar-ket participants hedge their entire portfolio position. Additionally, inderivatives markets not all the participants are willing, interested, orcapable of delta hedging their positions on a daily basis. The desireto hedge depends on the nature of the business under consideration(trading, international trade—exporters and importers, among oth-ers) and their knowledge of the derivatives markets. In the appendix,three potential scenarios are presented where the offsetting marketpositions are hedged 100 percent, 50 percent, and 10 percent, whilethe central bank hedges 100 percent of both long and short positions.If the cumulative offsetting market positions are hedged by less than100 percent, then the central bank’s dynamic delta-hedging positionprovides an intervention strategy that is conducive to its goals ofstabilizing exchange rate movements.

We focus on the W-spread in this paper after testing variousother traditional strategies. We develop the W-spread because thecentral element which drives the day-to-day intervention is the deltahedging conducted by the central bank. This element, along withthe option value, acts to influence the exchange rate both through

11Examples are shown in the appendix.


the volume transacted and through the signaling channel, where theanticipation of central bank intervention in reaction to exchange ratemovements influences the position of traders. The hedging of otherstrategies traditionally considered for central bank usage, such asshort calls or short puts, along with other trading strategies, suchas the short straddle or short strangle, exacerbate the exchange ratemovements the central bank is attempting to curb.12

Dynamic delta hedging is a critical element of any option tradingstrategy adopted by policymakers to mitigate losses and avoid theexcessive buildup or drawdown of foreign exchange reserves. By thenature of the hedge, the equivalent volume of foreign or domesticcurrency that will be transacted at maturity will already by accu-mulated through the delta hedge. Therefore, the intervention doesnot create a need to alter the level of foreign exchange reserves in themedium term. Through the delta hedging, the reserves will returnto the original pre-intervention level at exercise.

The W-spread strategy also has a number of important byprod-ucts associated with it. By using options to guide its interventions,the central bank is creating or deepening the options market whilestrengthening the institutional framework that previously either didnot exist or was very shallow, as is the case in many emerging mar-ket economies.13 By operating in the options market, the centralbank is assisting in creating a deeper risk trading platform for theprivate sector. Additionally, the greater information flow betweenmarket participants and policymakers that occurs when the centralbank participates in options contracts will strengthen the respon-siveness of the central bank to market conditions and thereby allowpolicymakers to act more effectively in ensuring that optimal marketconditions are in place. Central banks in emerging markets can alsoget valuable information from traders’ behavior and expectationsthat can be implied from these markets. In this way, intervention

12More detailed explanation and intervention impact analysis using thesestrategies is available upon request.

13Note that the creation and support of these markets has sizable economicvalue. The beneficiaries of derivatives markets include FX traders, exporters andimporters, and any other economic agent wanting to hedge foreign exchange risk.Therefore, by contributing to the creation of these risk markets, central banksare advancing financial market development, which is important for economicgrowth.


via the options market provides a two-way information platformthat can convey useful information for all participants.

4. Methodology

In testing the W-spread strategy, the goal is to understand whetherat maturity and with daily dynamic delta hedging the central bankis able to mitigate exchange rate volatility. We focus on the follow-ing conditions: persistent depreciation, depreciation with a shock,persistent appreciation, appreciation with a shock, and volatility inthe exchange rate with no specific trend.

First, we simulate the W-spread strategy with no impact onexchange rates to illustrate how the dynamic delta-hedging ele-ment reacts to exchange rate movements. Then, we incorporate theimpact of the daily interventions on the exchange rate to analyzehow the intervention lowers volatility. We use a random genera-tion of exchange rates within set bounds such as deviations between(–0.10%, +0.10%); (–0.25%, + 0.25%); (–0.50%, +0.50%); (–0.50%,+0.10%); (–0.50%, +0.25%); (–0.10%, +0.25%); (–0.10%, +0.50%);(–0.25%, +0.50%) of the COPUSD with starting values between1995 and 2010 and an average daily change of +/– 0.12 percent.We also include a “shock” in the second series of simulations withintervention impact analysis. The shock size was a deviation in theexchange rate by between +/– 1.25 percent and +/– 5.0 percent.This shock reflects a drastic increase/decrease in the COPUSD valueto mirror a time of distress in the markets.

Using a simulated series of the COPUSD, we calculate the optiondeltas, from which we establish daily USD purchases/sales. Thevolume of purchases/sales through the delta hedge determines theintervention position of the central bank on the spot market.

To start, we use the following strike prices in the results presentedbelow:

K1,0 = 0.9975 ∗ S0

K3,0 = 1.0025 ∗ S0

K2,0 =K1,0 + K3,0

2,


where S0 represents the spot market exchange rate one day beforeissuance of the W-spread strategy and the strike prices are very closeto at-the-money position. After the volatility and strike prices aredetermined, we estimate the call and put deltas using the Garman-Kohlhagen model as per equations (1) and (2) including Colombia’srisk-free interest rate, the U.S. risk-free interest rate, and the simu-lated exchange rate series. The time to maturity for all contracts isthirty days.

For our analysis, the portfolio consists of 10,000 contracts, witheach contract worth USD 10,000. The total value of these contractsis then USD 100 million. It is simple to alter the contract size andtotal number of contracts transacted, and we have tested the impactof such changes on the W-spread strategy.14 In accordance with thedescriptions presented in section 3, we simulate the use of a neutralW-spread strategy (W-put/W-call spread equal to 1), a call-biasedW-spread (W-put/W-call spread less than 1), and a put-biasedW-spread (W-put/W-call spread greater than 1). With a neutralstrategy, there is an even distribution between W-puts and W-calls,with 5,000 contracts in each (W-put/W-call spread equal to 1). Inthe call-biased W-spread, there are 8,000 contracts allocated to theW-call spread and 2,000 contracts allocated to the W-put spread(W-put/W-call spread equal to 0.25). In the put-biased W-spread,there are 2,000 contracts allocated to the W-call spread and 8,000contracts allocated to the W-put spread (W-put/W-call spread equalto 4).

4.1 Daily Transactions

In the dynamic delta hedge, the central bank purchases/sells USDdaily based on the delta of the option. Therefore, we calculate totalUSD purchased or sold on a daily basis, the daily interest cost, anddaily cumulative value transacted.

The USD transacted on the spot market on day t for option i iscalculated as the difference between the option delta on day t andt − 1 multiplied by the option contract size. For one contract, theUSD transacted (SpotDeltat,i) based on the dynamic delta hedgewill be

14Results are available upon request.


SpotDeltat,i = (δt,i − δt−1,i) ∗ X, (3)

where X represents USD per contract or the contract size, which isUSD 10,000 in this analysis, and δt,i represents the delta of optioni on day t. Recall that in the W-spread strategy, we have two longcalls and one short call (W-call spread) as well as two long puts andone short put (W-put spread), thus i = 1 . . . 6. For example, δ15,sp

represents the delta of the short put on day 15.The total net USD transacted via the dynamic delta hedge is

calculated as

DailySpotDeltat =6∑

i=1

(SpotDeltat,i ∗ Qi). (4)

Again, SpotDeltat,i represents the delta hedge for one contract andQi represents the number of contracts issued per type of options

i with6∑

i=1Qi = 10,000. Each type of option has its contract size

that can vary. For our analysis, we assume equal contract size acrossoptions unless otherwise stated. Moving forward, we will refer to thetotal W-spread strategy option value of USD 100 million as Y, whereY = Q∗X (the number of contracts multiplied by the contract size).

The cumulative value of the daily transactions (DailyCVt) att = 1 equals the total USD transacted on the spot market. Fort > 1, the cumulative daily transactions are calculated as

DailyCVt = DailyCVt−1 + IntCt−1 + DailySpotDeltat. (5)

The daily cumulative USD transacted includes the potential cost forthe central bank to conduct the hedge in the form of the interestcosts (IntCt). The interest costs paid to obtain (or borrow) USD15

at time t are determined as

IntCt =(e

r365 − 1

)DailyCVt−1, (6)

where r represents the domestic interest rate, which for our simula-tions is the Colombian interbank lending rate.

15In this paper we consider this cost even though central banks normally donot have this cost, since they can borrow from their international reserves. Weare taking a more conservative stance here.


4.2 End-of-Period Transactions

To present the total accumulated USD transacted at maturity (T ),we calculate the end-of-period USD transacted (EOPV TT ) as

EOPV TT = DailyCVT + NetPayoffsT , (7)

where DailyCVT is the cumulative USD transacted at maturity, i.e.,T = 30. As seen in the previous equation, EOPV TT depends on theaccumulated value of the USD from the dynamic delta hedge andthe net payoffs.

Net payoffs can be divided into long payoffs, which are revenuesfor the central bank, and short payoffs, which are costs for the centralbank. The net payoffs at maturity are presented in table 5, show-ing the resulting payoffs for the W-spread strategy at all possibleoutcomes for the exchange rate at maturity, S30.

Table 6 presents a summary of calculations of costs and gainsassociated with the W-spread strategy and dynamic delta hedgingat maturity. It includes the accumulated USD transacted throughdelta hedging, the interest costs, the net payoffs for both the longand short positions, and the long and short premiums. The premi-ums of each contract will be paid by the central bank in the longpositions and received by the central bank in the short positions.The net gains of the W-spread strategy are represented as

NetGainsT = (LongPayoff T + ShortPremiumT ) − (IntCT

+ ShortPayoff T + LongPremiumT ). (8)

We refer to NetGainsT as the profit/cost of the W-spread strategy,since it is possible that the central bank can profit from the strategy.Specifically, the gains of the W-spread strategy in the form of longpayoffs and short premiums could outweigh the costs, as they dounder conditions of persistent depreciation or appreciation that wepresent in section 5.

The analysis of the daily position of the central bank along withthe position at maturity with respect to the amount of USD trans-acted, the payoffs, and the costs of the strategy will provide insightinto the ability of the central bank to employ the W-spread strategyto smooth drastic exchange rate movements and reach its interven-tion goals. It is important to consider both the daily and at-maturity


Tab

le5.

Pay

offs

with

W-S

pre

adSeg

men

tation

End

ofPer

iod

(T=

30)

Defi

nit

ion

ofF

S<

K1

F2(K

1+

K3

−K

2−

S)

W-P

ut/W

-Cal

lSp

read

=1

F1

=0.

5∗Y

3;F

2=

0.5∗

Y3

K1

<S

≤K

2F

1(S

−K

1)+

F2(K

3−

K2)

W-P

ut/W

-Cal

lSp

read

=4

F1

=0.

2∗Y

3;F

2=

0.8∗

Y3

K2

<S

≤K

3F

1(K

2−

K1)+

F2(K

3−

S)

W-P

ut/W

-Cal

lSp

read

=0.

25F

1=

0.8∗

Y3

;F

2=

0.2∗

Y3

S≥

K3

F1(S

+K

2−

K1

−K

3)

Note

s:T

his

tabl

epr

esen

tsth

epa

yoff

stru

ctur

eba

sed

onth

eW

-spr

ead

stra

tegy

segm

enta

tion

.Yre

pres

ents

the

tota

lUSD

tran

sact

ed,

whi

chis

the

cont

ract

size

(USD

10,0

00)

mul

tipl

ied

byth

eto

talnu

mber

ofco

ntra

cts

(10,

000)

.


Table 6. Summary of Cost Calculations at Maturity

End of Period (T = 30)

W-Spread Strategy

End-of-Period USD DailyCVT + NetPayoffsT

TransactedInterest Cost IntCT = (e

r365 − 1)DailyCVT−1

Long Payoff4∑

j=1

[max(ST − K1, 0) ∗ Yj + max(K1 − ST , 0) ∗ Yj ]

+4∑

j=1

[max(ST − K3, 0) ∗ Yj + max(K3 − ST , 0) ∗ Yj ]

Short Payoff −2∑

j=1

[(max(ST − K2, 0) + max(K2 − ST , 0)] ∗ Yj)

Long Premium −4∑

j=1

(LongOptionPricei) ∗ Yj

Short Premium2∑

j=1

(ShortOptionPricei) ∗ Yj

Profit/Cost of Option (LongPayoff + ShortPremium)Strategy −IntCT + ShortPayoff + LongPremium)

Share of Total Profit/Y or Cost/Y

Notes: Y represents the contract size, which is USD 10,000 multiplied by the total num-ber of contracts, or 10,000. The payoff structure will depend on the segmentation of theW-spread strategy and the distribution of W-puts to W-call spreads, as seen in table 5.

positions with respect to the four possible scenarios: S30 < K1;K1 ≤ S30 < K2; K2 ≤ S30 < K3; and S30 ≥ K3. The simulationsin the following section provide clear insight into all four possibleoutcomes.

4.3 Intervention Impact Analysis

To determine how the W-strategy may affect exchange rate volatil-ity, we simulate the COPUSD movements under the following condi-tions: persistent depreciation, depreciation with a shock, persistentappreciation, appreciation with a shock, and volatility with no settrend. For the simulations we use a linear price impact function,16

16We thank the referee for suggesting to include this analysis in the paper.


where the change in the exchange rate is a function of the volumetransacted. It is important to note that data on volume (amount ofdollars bought per intervention) of central banks’ intervention is notavailable, and thus we rely on a statistical method to derive possiblelinear impact functions.

To estimate the linear approximation of the price impact func-tion, the moving average over thirty days of the COPUSD from 2010to 2013 is used, yielding 1,370 observations. The changes in thethirty-day moving average are then calculated and classified intoappreciation (–1) or depreciation (1) of the COPUSD. The confi-dence intervals are then computed, per side, using a 95 percent con-fidence level. In this way, we determine the upper and lower limitsfor the exchange rate movements when the Colombia peso appreci-ates or depreciates. We use the lower and upper limits as the limitsof the price impact functions, thereby assuming that the interven-tions have a lower (upper) impact on the exchange rate equal to thelower (upper) limit of the confidence intervals. For this simulation weassume that the lowest purchased (sold) amount of USD correspondsto USD 1 million up to USD 100 million. This yields a linear pricechange based on the volume transacted, from USD 1 million to USD100 million, giving an approximation of how the COPUSD reacts toa given quantity (volume) purchase/sale of USD. Finally, we use asimple OLS estimation to determine the coefficients which will allowus to estimate the price impact that will be used to determine theapproximate impact of the quantity bought or sold as mandated bythe delta-hedging strategy. The impact of volume on the currencyexchange is then modeled as

P = α + βV + μ, (9)

where P represents the exchange rate change, α represents the coeffi-cient for the price impact, β represents the coefficient correspondingto the impact of volume on the exchange rate, and V represents vol-ume transacted. μ represents the iid error term. The OLS regressionis run separately for appreciation and depreciation values, since theimpact of intervention may differ under each.

With this information we start the simulation to determinethe impact of acting according to the delta hedge based on theW-strategy presented in the paper. We do this by simulating random


values of the COPUSD to reflect the conditions mentioned before.To compare our results, we keep the original random exchange rates,i.e., values of the exchange rate without intervention (FX ). We cal-culate the delta based on the changes of FX from day 0 to day 1.The delta will determine the volume of USD purchased/sold (V ) asexplained above. Once we have calculated the volume transacted,we determine the impact on this such that

FXnew = (α̂ + β̂V ) + FX, (10)

where FXnew represents the new COPUSD value based on the priceimpact, V is the volume transacted in the spot market based ondelta hedging, and FX represents the COPUSD generated withoutintervention impact. We continue to calculate the deltas now basedon FXnew for the next day and continue estimating the value ofCOPUSD with the intervention impact based on the delta hedging.This simple linear approximation allows us to test how the deltahedging based on the W-strategy can affect the exchange rate. Oncewe have these numbers (FX without intervention and FXnew withvolume impact on the exchange rates), we calculate the standarddeviations and compare the effect of the intervention on volatil-ity. We use the same approach to calculate the effect of a neutralW-strategy compared with a biased W-strategy to determinewhether the biased strategy described in section 3.1 is more effectivein lowering volatility.

5. Results

In presenting the results of the W-spread strategy analysis, we beginwith a general perspective on the outcomes at maturity consideringthe key components of the strategy—the option exercise and thedaily hedging. Then, we present the results of the simulations underscenarios of persistent depreciation and persistent appreciation withno impact, and finally the simulations accounting for the impact ofthe daily dynamic delta hedging.


The possible outcomes at maturity are presented in table 7 interms of option exercise, share of W-spread strategy exercised, andthe net amount of USD transacted based on where the spot exchangerate at maturity lands in relation to each strike price. The fourscenarios depicted align with the scenarios discussed in table 5 insection 4.

Consider the first scenario, where S30 is less than strike price K1(or an appreciation of the local currency). In this scenario, the cen-tral bank sells USD at a higher price than S30 through the long putpositions that are exercised at K1 and K3. Under a neutral W-spreadstrategy, the central bank sells USD 16.6 million, meaning that it hasan equivalent of USD 16.6 million in local currency (16.6 × S30) thatcan be used to buy USD to counter appreciation pressure. Also, bybuying USD from the owners of the put positions at K2, the centralbank helps to decrease the selling pressure in the spot market. Thisis true because the owners of the short puts of the W-put spreadat K2 are selling USD to the central bank instead of to the market,which in turn relieves some of the selling pressure and, again, helpsto counteract the appreciation pressure on the local currency. More-over, if the owner of the W-put spread at K2 wants to make a profiton their purchase,17 they need to buy USD at S30 from the marketin such a way that achieves a positive payoff (K2 − S30 > 0), con-tributing with a buying pressure that counters appreciation. Finally,by exercising the central bank’s two long put positions, the offsettingshort put positions will have no incentive to sell USD in the spotmarket, since they bought USD from the central bank at a pricehigher than S30 based on the option contract. It would be unwisefor the traders holding the offsetting short put positions to turnaround and sell the USD purchased from the central bank throughthe option contract because this would lead to a scenario where theyare buying high and selling low. Therefore, the likelihood that theiractivity would increase selling pressure of USD in the local mar-ket is low. Note that this impact increases with higher appreciationexpectations where the W-put/W-call spread ratio moves from 1to 4.

17Note, the long put position at K2 is exercised when K2 > S30.


Tab

le7.

W-S

pre

adStr

ateg

yR

esults

atM

aturi

ty

W-P

ut/

W-C

all=

1W

-Put/

W-C

all=

4W

-Put/

W-C

all=

0.25

S30

<K

1

Sell

USD

atK

1(L

ong

Put

)−

0.5

Y 3−

0.8

Y 3−

0.2

Y 3

Sell

USD

atK

3(L

ong

Put

)−

0.5

Y 3−

0.8

Y 3−

0.2

Y 3

Buy

USD

atK

2(S

hort

Put

)0.

5Y 3

0.8

Y 30.

2Y 3

Net

Tra

nsac

ted

−0.

5Y 3

−0.

8Y 3

−0.

2Y 3

Net

Tra

nsac

ted

inU

SD−

16.6

mill

ion

−26

.6m

illio

n−

6.6

mill

ion

K1

≤S

30<

K2

Buy

USD

atK

1(L

ong

Cal

l)0.

5Y 3

0.2

Y 30.

8Y 3

Sell

USD

atK

3(L

ong

Put

)−

0.5

Y 3−

0.8

Y 3−

0.2

Y 3

Buy

USD

atK

2(S

hort

Put

)0.

5Y 3

0.8

Y 30.

2Y 3

Net

Tra

nsac

ted

0.5

Y 30.

2Y 3

0.8

Y 3

Net

Tra

nsac

ted

inU

SD16

.6m

illio

n6.

6.m

illio

n26

.6m

illio

n (con

tinu

ed)


Tab

le7.

(Con

tinued

)

W-P

ut/

W-C

all=

1W

-Put/

W-C

all=

4W

-Put/

W-C

all=

0.25

K2

≤S

30<

K3

Buy

USD

atK

1(L

ong

Cal

l)0.

5Y 3

0.2

Y 30.

8Y 3

Sell

USD

atK

3(L

ong

Put

)−

0.5

Y 3−

0.8

Y 3−

0.2

Y 3

Sell

USD

atK

2(S

hort

Cal

l)−

0.5

Y 3−

0.2

Y 3−

0.8

Y 3

Net

Tra

nsac

ted

−0.

5Y 3

−0.

8Y 3

−0.

2Y 3

Net

Tra

nsac

ted

inU

SD−

16.6

mill

ion

−26

.6m

illio

n−

6.6

mill

ion

S30

≥K

3

Buy

USD

atK

1(L

ong

Cal

l)0.

5Y 3

0.2

Y 30.

8Y 3

Buy

USD

atK

3(L

ong

Cal

l)0.

5Y 3

0.2

Y 30.

8Y 3

Sell

USD

atK

2(S

hort

Cal

l)−

0.5

Y 3−

0.2

Y 3−

0.8

Y 3

Net

Tra

nsac

ted

0.5

Y 30.

2Y 3

0.8

Y 3

Net

Tra

nsac

ted

inU

SD16

.6m

illio

n6.

6m

illio

n26

.6m

illio

n

Note

s:T

his

tabl

epr

esen

tsth

eac

tion

atm

atur

ity

with

the

W-s

prea

dst

rate

gyse

gmen

tation

base

don

the

rela

tion

ship

bet

wee

nth

esp

otex

chan

gera

teat

day

30(S

30)an

dth

eth

ree

stri

kepr

ices

(K1,K

2,K

3).

Yis

the

cont

ract

size

(USD

10,0

00)m

ultipl

ied

byth

eto

tal

num

ber

ofco

ntra

cts

(10,

000)

,th

eref

ore

Yeq

uals

USD

100

mill

ion.

Pos

itiv

eva

lues

repr

esen

tpu

rcha

ses

and

nega

tive

valu

esre

pres

ent

sells

.


If we analyze the last case (S30 ≥ K3), where there is depreciationof the local currency, the reverse action is be observed. Specifically,under the neutral W-spread strategy, the central bank buys USD16.6 million that can be sold to counter the depreciation pressure.Also, by selling USD to the owner of the call (long call) at K2,the central bank can help decrease the buying pressure in the spotmarket, again helping to counteract the depreciation of the localcurrency. This is true because the long call positions at K2 are buy-ing USD from the central bank rather than from the market, whichin turn relieves some of the buying pressure. Moreover, traders withthe long call position that want to cash their positive payoffs need tobuy USD in the spot market (S30 − K2 > 0). Finally, by exercisingthe central bank’s two long call positions, the offsetting short callpositions will have no incentive to buy USD in the spot market, sincethey sold USD to the central bank at a price lower than S30 basedon the option contract. It would be unwise for the traders holdingthe offsetting short call positions to turn around and buy USD onthe spot market, because this would lead to a scenario where theyare buying high and selling low. Therefore, the likelihood that theiractivity would increase buying pressure of USD in the local market islow. Note that this impact increases with higher depreciation expec-tations where the W-put/W-call spread ratio moves from 1 to 0.25.For the intermediate cases (K1 ≤ S30 < K2 and K2 ≤ S30 < K3)more discretion is necessary since there is no clear appreciation ordepreciation pressure.

5.1 Simulation with Persistent Depreciation

We begin with the simulated exchange rates series that presentspersistent depreciation in the COPUSD. In these simulations, theintervention impact function has not been included and the goal isto test whether the W-strategy aligns with the goals of the centralbank. Figure 5 illustrates the simulation. Figures 6 and 7 presentthe calculated dynamic delta-hedging position and daily cumula-tive USD transacted during a period of depreciation. In figure 6we present a neutral W-spread strategy where the ratio of W-putsto W-call spreads equals 1. In figure 7 we present a call-biasedW-strategy where the ratio of W-puts to W-call spreads is less than1. The daily USD transacted represents the actual amount of USD


Figure 5. Series of Simulated Exchange Rates for Periodswith Persistent Depreciation

Notes: Exchange rates are simulated using a uniform pseudo-random distribu-tion to represent periods of persistent and significant depreciation. The startingvalue of simulation is based on the ten-day average COPUSD exchange rates end-ing on October 20, 2012. Maximum depreciation in this simulation equals 1,922Colombian pesos per U.S. dollar, which is a 2.23 percent depreciation over thirtydays.

the central bank is buying or selling in the spot market based onthe net portfolio position and is determined by the deltas of eachoption contract in the portfolio. Positive values indicate net pur-chases, whereas negative values indicate net sales. The daily cumu-lative value transacted includes the interest costs and shares pur-chased/sold of the foreign currency in the spot market denominatedin local currency (COP).

There are three scenarios depicted in each figure. The first is aW-call spread strategy, where the central bank is holding (long) andissuing (short) call options. The second is a W-put spread strat-egy, where the central bank is holding (long) and issuing (short) putoptions. The last is a W-spread strategy that combines the W-calland W-put spreads. According to the W-call spread position delta,


Figure 6. Depreciation Dynamic Delta-Hedging Outcomes(W-put/W-call spread: 1)

Notes: The dynamic delta-hedging position is calculated for 100 series for athirty-day contract period. By construction, the simulated exchange rates aresteadily depreciating over the thirty-day period. The W-spread strategy pre-sented here is a neutral one since the W-put/W-call spread ratio is 1. As can beseen, holding a position in both a W-call spread and W-put spread strategy isthe least disruptive to the spot market.

the first-day initial spot market position is substantial, requiringthe central bank to sell approximately USD 30 million of foreigncurrency (USD) in the spot market. Throughout the period to matu-rity, the net call portfolio position will require the central bank tocontinue selling USD in the spot market to dynamically delta hedgeits options portfolio. By doing so, it in turn introduces a counter-acting pressure to the persistent depreciation of the simulated seriesbecause, all else equal, the consistent sale of USD by the centralbank should contribute to driving down the value of the foreign cur-rency relative to the local currency, leading to an appreciation of theColombian peso. Under a W-put spread position, the central bankinitially conducts a large purchase of USD in the spot market andsubsequently sells off its initial spot market position throughout the


Figure 7. Depreciation Dynamic Delta-Hedging Outcomes(W-put/W-call spread: 0.25)

Notes: The dynamic delta-hedging position is calculated for 100 series for athirty-day contract period. By construction, the simulated exchange rates aresteadily depreciating over the thirty-day period. The W-spread strategy presentedhere is a call-biased one since the W-put/W-call spread ratio is 0.25. As can beseen, holding a position in both a call and put strategy is the least disruptive tothe spot market.

period to maturity. In the first day, the central bank buys approxi-mately USD 18 million. Note that if the W-put spread is consideredindependently, the initial purchase may exert an undesired impacton the exchange rate. Specifically, it would contribute to the depre-ciation pressure observed in figure 5 by increasing the value of theforeign currency to local currency, leading to further depreciationof the Colombian peso. However, the net position of the W-spreadstrategy (third column of figures 6 and 7) show that the spot marketinterventions have the potential to counteract the depreciation pres-sure. Specifically, the net spot market transactions suggest a largesale of USD followed by small sales that in reality should help torelieve some of the depreciation pressure as the relative supply ofUSD to COP on the spot market increases, all else equal.


The cumulative value transacted is known and limited, as canbe seen in the bottom three graphs of figures 6 and 7. The cumu-lative value transacted takes into account the accumulation ofsales/purchases of USD to hedge the net portfolio position through-out the time to maturity as well as the interest costs associated withthe transactions. In the call-biased W-spread strategy, presented infigure 7, the central bank sells more USD on the initial day thanin the neutral strategy presented in figure 6, but does not notablychange the spot market position in the remaining days leading tomaturity. By changing the ratio of W-call spreads and W-puts inthe W-spread strategy, the central bank can alter its initial positionin the spot market in such a way that makes the initial interventionlarger, which may counter the persistent movement of the exchangerate more significantly upfront. The ratio can also signal to the mar-ket that the central bank is trying to more strongly counteract thedepreciation.

The total value transacted represents the accumulated dailydynamic delta-hedging transactions and interest costs throughoutthe contract period. Presented in table 8 is the outstanding positionof the central bank from its hedging operations and its options con-tracts, which includes the hedging costs, payoffs, and premiums asdescribed in table 6. Table 8 illustrates the average across all 100series and depicts the value of transactions for series when the port-folio position is neutral (W-put/W-call spread ratio is 1) as well asfor a call-biased portfolio (W-put/W-call spread ratio less than 1)during a period of depreciation.

As can be seen in table 8, the total cumulative interest costsare low considering that the total outstanding USD in option con-tracts is USD 100 million. The net value transacted throughout theoption contract is determined by the W-put/W-call spread ratio.18

Since only the W-call spreads are exercised when the spot marketprice depreciates above the strike price K3, the outstanding volumeof USD the central bank is obligated to transact is covered by thenet value collected from their long positions. The W-puts expire outof the money and will not be exercised, as the currency depreciates

18As a percentage of the total option value (USD 100 million), the net valuetransacted is only 0.52 percent and 1.14 percent for the neutral and call-biasedstrategies, respectively.


Tab

le8.

End-o

f-Per

iod

Dynam

icD

elta

Cos

ts,Pay

offs,

and

Pre

miu

ms

Ave

rage

Acr

oss

Ser

ies

(USD

)

W-P

ut/

W-C

all=

1St.

Dev

.W

-Put/

W-C

all=

0.25

St.

Dev

.

End

-of-Per

iod

USD

Tra

nsac

ted

−50

,108

,000

3,61

3−

80,1

88,0

003,

884

Inte

rest

Cos

t−

112,

200

3,61

3−

195,

360

3,88

4Lon

gPay

off2,

474,

600

5,27

13,

908,

700

8,52

4Sh

ort

Pay

off−

1,23

7,30

02,

636

−1,

954,

400

4,26

2Lon

gP

rem

ium

−65

9,16

01,

404

−81

2,58

01,

772

Shor

tP

rem

ium

314,

630

670

391,

340

853

Pro

fit/C

ost

ofO

ptio

nSt

rate

gy78

0,55

04,

938

1,33

7,70

06,

423

Shar

eof

Tot

al0.

78%

0.00

5%1.

34%

0.00

6%

Note

s:“E

nd-o

f-Per

iod

USD

Tra

nsac

ted”

repr

esen

tsth

ecu

mul

ativ

eva

lue

ofda

ilydy

nam

icde

lta

hedg

ing

and

inte

rest

cost

s.E

ach

cont

ract

size

isU

SD10

,000

and

ther

ear

e10

,000

cont

ract

sis

sued

.T

heta

ble

depi

cts

the

cost

sfo

rse

ries

whe

nth

epor

tfol

iopos

itio

nis

neut

ral(W

-put

/W-c

allsp

read

ratio

of1)

asw

ellas

for

aca

ll-bi

ased

por

tfol

io(W

-put

/W-c

allsp

read

ratio

of0.

25)

duri

nga

per

iod

ofde

prec

iation

.T

heca

lcul

atio

nsre

flect

thos

ede

scri

bed

inth

esu

mm

ary

tabl

e6.

The

nega

tive

valu

esre

flect

aco

stor

outlay

offu

nds

for

the

cent

ralba

nk,w

here

asth

epos

itiv

eva

lues

refle

ctfu

nds

acqu

ired

byth

ece

ntra

lba

nk.“P

rofit

/Cos

tof

Opt

ion

Stra

tegy

”is

the

sum

ofth

elo

ngpa

yoff

and

shor

tpr

emiu

mm

inus

the

sum

ofth

ene

tva

lue

tran

sact

ed,in

tere

stco

st,sh

ort

payo

ff,an

dlo

ngpr

emiu

m.


above K3.19 The initial purchase position on the first day for the W-puts is offset by the subsequent smaller sales throughout the contractperiod. Therefore, the central bank is only transacting on the spotmarket the amount needed to cover its option obligations. By doingso, it limits excessive reserve accumulation and purchases/sells USDaccording to the relationship between the exchange rate and optionprice, or the delta of the option.

5.2 Simulation with Persistent Appreciation

The next analysis tests the use of the W-spread strategy under sce-narios with persistent appreciation. Figure 8 illustrates the simula-tion. Figures 9 and 10 present the calculated dynamic delta-hedgingposition and the daily cumulative value transacted during a periodof persistent appreciation. Once again, three scenarios are presentedin each figure. If we consider only the W-call spread strategy, theinitial spot market position requires the central bank to sell approx-imately USD 30 million in day 1. This move contributes to localcurrency appreciation and, as such, can be potentially destabilizingto the market. However, after this initial selling and throughout theperiod to maturity, the net portfolio position requires the centralbank to buy USD in the spot market to dynamically delta hedgeits position. The daily purchases of USD may in turn introduce acounteracting pressure to the persistent appreciation by driving upthe value of USD relative to the domestic currency.

Considering the W-put spread alone, the central bank initiallyconducts a large purchase of USD in the spot market (approxi-mately USD 18 million) and continues purchasing USD throughoutthe period to maturity. By continually purchasing USD on the spotmarket, the hedging activity of the central bank alters the relativesupply of USD to COP in the spot market in a way that may intro-duce depreciation pressure to counter the persistent appreciation,

19It is important to note that the exercise of each of the puts or calls will bedetermined by whether the spot exchange rate at maturity is greater than orless than the corresponding strike price. In the scenario presented here, the spotexchange rate has depreciated above K3, which is 1,884.


Figure 8. Series of Simulated Exchange Rates for Periodswith Persistent Appreciation

Notes: Exchange rates are simulated using a uniform pseudo-random distribu-tion to represent periods of appreciation. The starting value of the simulation isbased on the ten-day average COPUSD exchange rates ending on October 20,2012. Maximum appreciation in this simulation is 1,824, which is a 2.97 percentappreciation over thirty days.

all else equal. Note that in the neutral W-spread strategy (thirdcolumn in figure 9), the central bank initially sells USD, but thencontinually purchases USD over the period to maturity. However,since the initial position is a sale of USD 12 million, it may be siz-able enough to contribute to the appreciation, and therefore counterthe goals of the central bank. In this case, by altering the W-put/W-call spread ratio more heavily towards the W-put spread, as seenin figure 10, the central bank can avoid this situation and now pur-chase USD 17 million in the spot market on the initial day of thecontract and continue to purchase USD throughout the period tomaturity (third column in figure 10). Altering the ratio not onlysignals to the market that the central bank is acting to curb theappreciation, but also that the spot market hedging position of the


Figure 9. Appreciation Dynamic Delta-Hedging Outcomes(W-put/W-call spread: 1)

Notes: The dynamic delta-hedging position is calculated for 100 series for athirty-day contract. The exchange rate is steadily appreciating over the period tomaturity. The W-put/W-call spread ratio is 1. As can be seen, holding a positionin both a W-call spread and W-put spread strategy is the least disruptive to thespot market.

central bank may drive up the relative price of USD to COP andact to counter the appreciation.

Table 9 depicts the value of transactions for series when the port-folio position is neutral (W-put/W-call spread ratio equal to 1) aswell as for a put-biased portfolio (W-put/W-call spread ratio equalto 4) during a period of appreciation. The calculations reflect thosedescribed in the summary table 6. Once again, the total cumulativeinterest costs are low considering that the total outstanding USD inoption contracts is USD 100 million (0.09 percent and 0.17 percentfor W-put/W-call spread ratios of 1 and 4, respectively). The netvalue transacted throughout the option contract is determined bythe W-put/W-call spread ratio. Since only the W-puts will be exer-cised when the spot market price appreciates below strike price K1,the outstanding amount of USD that the central bank is obligatedto transact is covered by the USD proceeding from its long position.


Figure 10. Appreciation Dynamic Delta-HedgingOutcomes (W-put/W-call spread: 4)

Notes: The dynamic delta-hedging position is calculated for 100 series for athirty-day contract. The exchange rate is steadily appreciating over the period tomaturity. The W-put/W-call spread ratio is 4. As can be seen, holding a positionin both a W-call spread and W-put spread strategy is the least disruptive to thespot market and contributes to countering the persistent appreciation simulatedin the market.

The W-call spreads expire out of the money and are not exercisedwhen the spot exchange rate at maturity falls below K1.20 The ini-tial purchase position on the first day for the W-call spreads is offsetby the subsequent smaller purchases throughout the contract period.Therefore, the central bank is only transacting on the spot marketthe amount needed to cover its option obligations in the W-spreadstrategy.

20It is important to note that the exercise of each of the puts or calls will bedetermined by whether the spot exchange rate at maturity is greater than orless than the corresponding strike price. In the scenarios presented here, the spotexchange rate has appreciated below K1, which is 1,875.


Tab

le9.

End-o

f-Per

iod

Dynam

icD

elta

Cos

ts,Pay

offs,

and

Pre

miu

ms

Ave

rage

Acr

oss

Ser

ies

(USD

)

W-P

ut/

W-C

all=

1St.

Dev

.W

-Put/

W-C

all=

4St.

Dev

.

End

-of-Per

iod

USD

Tra

nsac

ted

50,0

82,0

005,

910

80,1

64,0

005,

379

Inte

rest

Cos

t−

92,0

524,

942

−17

0,83

05,

379

Lon

gPay

off1,

791,

700

3,96

83,

480,

700

6,95

1Sh

ort

Pay

off−

895,

850

1,98

4−

1,74

0,30

03,

475

Lon

gP

rem

ium

−68

7,05

01,

522

−52

7,32

01,

053

Shor

tP

rem

ium

327,

940

726

248,

070

495

Pro

fit/C

ost

ofO

ptio

nSt

rate

gy44

4,68

84,

236

1,29

0,32

04,

076

Shar

eof

Tot

al0.

44%

0.00

4%1.

29%

0.00

4%

Note

s:“E

nd-o

f-Per

iod

USD

Tra

nsac

ted”

repr

esen

tsth

ecu

mul

ativ

eva

lue

ofda

ilydy

nam

icde

lta

hedg

ing

and

inte

rest

cost

s.E

ach

cont

ract

size

isU

SD10

,000

and

ther

ear

e10

,000

cont

ract

sis

sued

.The

tabl

ede

pict

sth

eva

lues

for

seri

esw

hen

the

por

tfol

iopos

itio

nis

neut

ral(W

-put

/W-c

allsp

read

ratio

of1)

asw

ellas

for

abi

ased

por

tfol

io,w

ith

aW

-put

/W-c

allsp

read

grea

ter

than

1du

ring

aper

iod

ofap

prec

iation

.T

heca

lcul

atio

nsre

flect

thos

ede

scri

bed

inth

esu

mm

ary

tabl

e6.

The

nega

tive

valu

esre

flect

aco

stor

outlay

offu

nds

for

the

cent

ralba

nk,w

here

asth

epos

itiv

eva

lues

refle

ctfu

nds

acqu

ired

byth

ece

ntra

lba

nk.


Figure 11. Intervention Impact on COPUSD underTrending Depreciation

Notes: This figure presents a sample of the simulation results for the W-spreadstrategy. Here, we depict the impact of dynamic delta hedging on the value ofthe exchange rate under various depreciation scenarios. The top three graphsillustrate persistent depreciation without any shocks. The bottom three graphsillustrate depreciation with a “shock” to the exchange rate. Included are both theneutral strategy (W-put/W-call spread ratio equal to 1) and a biased strategy(W-put/W-call spread ratio equal to 0.25). Adopting the W-strategy allows thecentral bank to lower volatility while stabilizing the trend.

5.3 Simulation with Intervention Impact on ExchangeRate Movements

After establishing the operations of the W-strategy above, we nowpresent the impact of the W-strategy on exchange rate movements.We consider the following scenarios: persistent depreciation, depre-ciation with a shock, persistent appreciation, appreciation with ashock, and volatility with no trend. Specifically, we are simulatinghow dynamic delta hedging of the W-strategy affects the exchangerate. This represents the day-to-day purchases/sales in the spot mar-ket conducted by the central bank until the time to maturity of theoptions bundle.

Figure 11 illustrates the impact of the W-strategy on exchangerate movements under depreciation pressure when there is no inter-vention impact, when a neutral W-strategy is enacted, and when


Table 10. Volatility for Intervention Impact ofW-Strategy under Trending Depreciation

Series 1 Series 2 Series 3 Simulation

Volatility (No Intervention) 16.76 34.39 29.89 29.85Volatility (Neutral W-Strategy) 10.61 26.56 21.72 23.14Volatility Reduction 37% 23% 27% 22%Volatility (Biased W-Strategy) 8.05 23.15 18.53 20.32Volatility Reduction 52% 33% 38% 32%



Notes: This table presents the volatility measures of the COPUSD related to the inter-vntion impacts illustrated in figure 11. The “Simulation” column represents the averagevalues across 100 simulations in each scenario. The volatility reduction percentages repre-sent 1− VolIntervention

VolNoIntervention. In all cases, the W-strategy is effective in lowering volatility of

the COPUSD, which is calculated as the standard deviation of the exchange rate duringthe time to maturity of the option.

a biased W-strategy is enacted. As can be seen, the trend remainsconsistent even with the use of the W-strategy, but the volatility ofthe exchange rate is smoothed. Furthermore, the trend is stabilizedwhen dynamic delta hedging dictates the size of the daily interven-tion. The depreciation is not as severe when the central bank isbuying/selling USD in the spot market to uphold its delta-hedgingposition. As can be seen in table 10, exchange rate volatility duringthe time to maturity is lower when the strategy is enacted, and islowest when the strategy is biased with a stronger position in calls.This holds true even with the presence of a sizable shock in theexchange rate (steep and sudden depreciation).

Figure 12 similarly illustrates the impact of the W-strategy onexchange rate movements under appreciation pressure. The dailyposition requires the central bank to sell USD under persistentappreciation, as presented in previous graphs. When the impact onthe exchange rate is accounted for, the W-strategy once again doesnot alter the trend of the exchange rate but lowers the volatility and


Figure 12. Intervention Impact on COPUSD underTrending Appreciation

Notes: This figure presents a sample of the simulation results for the W-spreadstrategy. Here, we depict the impact of dynamic delta hedging on the value ofthe exchange rate under various appreciation scenarios. The top three graphsillustrate persistent appreciation without any shocks. The bottom three graphsillustrate appreciation with a “shock” to the exchange rate. Included are boththe neutral strategy (W-put/W-call spread ratio equal to 1) and a biased strat-egy (W-put/W-call spread ratio equal to 4). Adopting the W-strategy allows thecentral bank to lower volatility while stabilizing the trend.

size of the change. In table 11, exchange rate volatility during timeto maturity is lowered when the central bank intervenes daily basedon the delta-hedging position dictated by the W-strategy. Volatilityis lowest when a biased, put-heavy strategy is enacted. Furthermore,as can be seen from figure 12, the trend is stabilized with the dailyinterventions via dynamic delta hedging.21

In figure 13, the exchange rate is moving with no specific trend.Even under this scenario, enacting the W-strategy lowers volatilityof the exchange rate. When there is no specific trend and no shockpresent, the neutral W-strategy provides an intervention position via

21It is important to note once again that if changes in the trend are driven bychanges in fundamentals, this cannot be changed by W-strategies or any interven-tion method, but central banks can observe the final composition of the W-spreadto obtain important insights from the market participants.


Table 11. Volatility for Intervention Impact ofW-Strategy under Trending Appreciation





Notes: This table presents the volatility measures of the COPUSD related to the inter-vntion impacts illustrated in figure 12. The “Simulation” column represents the averagevalues across 100 simulations in each scenario. The volatility reduction percentages repre-sent 1− VolIntervention



the dynamic delta hedge that lowers volatility more than a biasedstrategy. This can be seen in the figure as well as in table 12. Whena shock occurs during the time to maturity, the biased W-strategygives the central bank a stronger position in the spot market viadynamic delta hedging and therefore is more effective in lower-ing volatility. Both the neutral and biased strategies lead to lowervolatility in the exchange rate.

Once more, it is important to note that intervention followingthe delta-hedging position does not permanently alter the foreignexchange reserve balance. As discussed previously, at maturity, thecentral bank will have accumulated a foreign currency balance tosatisfy its obligations as the options are executed. The net effecton reserve balances will therefore be very close to zero. Therefore,dynamic delta hedging of this strategy allows the central bank toeffectively intervene in the spot market daily where the interven-tion position is based on market forces without depleting or over-accumulating foreign exchange reserves.


Figure 13. Intervention Impact on COPUSDunder No Trend

Notes: This figure presents a sample of the simulation results for the W-spreadstrategy. Here, we depict the impact of dynamic delta hedging on the value ofthe exchange rate under scenarios where the exchange rate does not follow aspecific trend. The top three graphs illustrate the COPUSD without any shocks.The bottom three graphs illustrate the exchange rate reaction with a “shock.”Included are both the neutral strategy (W-put/W-call spread ratio equal to 1)and a biased strategy (W-put/W-call spread ratio equal to 4 or 0.25, dependingon the shock). Adopting the W-strategy allows the central bank to lower volatilitywhile stabilizing the trend.

6. Conclusion

Foreign exchange intervention as a means to smooth volatility andprotect the economy from external shocks is an underlying con-cern for many emerging market policymakers. Many now strugglewith finding strategies that would limit volatility while allowingthem to maintain flexible exchange rates. Currently, spot marketpurchase/sale of USD to limit volatility is an imperfect solutionto this issue because the intervention may overshoot/undershootits intended goal and set off speculative activity. This paper hasargued that the use of currency options may be a stronger and moremarket-driven approach to foreign exchange interventions.

In past literature, currency options have been considered as apotential tool for central bank currency market intervention, butthose strategies have fallen short because they considered only one


Table 12. Volatility for Intervention Impact ofW-Strategy under No Trend





Notes: This table presents the volatility measures of the COPUSD related to the inter-vntion impacts illustrated in figure 12. The “Simulation” column represents the averagevalues across 100 simulations in each scenario. The volatility reduction percentages repre-sent 1 – VolIntervention



side of the market (call or put) or only one position (short or long).With the W-spread strategy, the central bank is operating in bothsides of market with more than one position. The intervention stilloccurs in the spot market, but it is now driven by market forcesthat dictate the size of the purchase/sale of USD on a daily basisthrough dynamic delta hedging, as well as at contract maturity. Theportfolio mix of calls and puts can be altered by the central bankor change based on market expectations, making the central bank’sposition more responsive to the market. A major secondary benefitto this strategy, and the use of options by central banks in general,is the establishment or deepening of risk markets. In many emerg-ing market economies, local import/export businesses would benefitfrom access to options in the local currency, yet these tools makeup only a small share of the total foreign exchange tools currentlyavailable (BIS 2016).

The goal of the analysis presented in this paper has been to laythe foundation for a serious discussion on the implementation of cur-rency options as a central bank policy tool. We find that with an


alternative option trading strategy, such as the W-spread strategy,the central bank can reach its goal of limiting exchange rate volatil-ity and smoothing the exchange rate trend with a market-drivenintervention approach.

Appendix. Offsetting Position of Market Participants

For every transaction in the options market the central bank engagesin, there is an offsetting position by a market participant that mustpurchase or sell the option. It is important to understand what hap-pens, in terms of delta hedging, on the other side of the market whenthe central bank is engaging in the W-spread proposed in this paper.Traders can choose to hedge part or all of their net portfolio position.Since hedging can be costly and not all market participants have thesame motives to use the options markets,22 not all traders will hedgetheir entire portfolio position, which has important implications forour analysis.

The hedging of the short position is what may exacerbate theadverse movements in the exchange rates. If we start by assumingthat when the central bank is holding a net long position through theW-spread, there is only one trader that is holding all of the offset-ting options, which implies that this trader would be in a net shortportfolio position, making it feasible that this trader may engage indelta hedging. His delta hedging increases volatility and can poten-tially modify the exchange rate trend, which is problematic for thecentral bank. However, the likelihood of one trader holding all of thecentral bank’s offsetting position is very small, and it is not advis-able for the central bank to allow such a situation to materialize. Onthe other hand, for individual hedgers and speculators, it is costlyto hedge their entire position in the options market. Moreover, somemay be using the option itself as the risk-management tool of choice.Therefore, the hedging activity of traders may not match one for onethe hedging activity of the central bank.

Tables 13 to 15 present the total USD that is purchased and soldby central banks and market participants when the central bank is

22For example, exporters and importers in general are not interested in deltahedging their positions. They use options to eliminate exchange rate uncertaintyat maturity.


Tab

le13

.C

entr

alB

ank

and

Tra

der

s’H

edgi

ng

Pos

itio

ns

with

100

Per

cent

Hed

ge

Net

USD

Net

USD

Purc

hase

dby

Cen

tralB

ank

Net

USD

Purc

hase

dby

Tra

der

sTra

nsa

cted

Calls

Puts

Calls

Puts

by

Both

Long

Long

Short

Long

Long

Short

Short

Short

Long

Short

Short

Long

Ex.R

ate

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

Net

USD

CO

PU

SD

USD

USD

USD

USD

USD

USD

100%

100%

100%

100%

100%

100%

2044

.00

−5,

856

−5,

042

5,45

14,

144

4,95

8−

4,54

95,

856

5,04

2−

5,45

1−

4,14

4−

4,95

84,

549

020

50.0

0−

494

−49

849

9−

494

−49

849

949

449

8−

499

494

498

−49

90

2053

.00

−23

1−

230

232

−23

1−

230

232

231

230

−23

223

123

0−

232

020

54.0

0−

66−

5561

−66

−55

6166

55−

6166

55−

610

2054

.00

−45

−32

39−

45−

3239

4532

−39

4532

−39

020

60.0

0−

489

−51

850

7−

489

−51

850

748

951

8−

507

489

518

−50

70

2066

.00

−44

4−

484

466

−44

4−

484

466

444

484

−46

644

448

4−

466

020

76.0

0−

627

−72

367

8−

627

−72

367

862

772

3−

678

627

723

−67

80

2076

.00

−77

−78

79−

77−

7879

7778

−79

7778

−79

020

85.0

0−

524

−64

658

6−

524

−64

658

652

464

6−

586

524

646

−58

60

2093

.00

−35

9−

467

413

−35

9−

467

413

359

467

−41

335

946

7−

413

020

99.0

0−

214

−29

225

2−

214

−29

225

221

429

2−

252

214

292

−25

20

2106

.00

−21

7−

316

264

−21

7−

316

264

217

316

−26

421

731

6−

264

021

11.0

0−

122

−18

715

2−

122

−18

715

212

218

7−

152

122

187

−15

20

2114

.00

−61

−97

78−

61−

9778

6197

−78

6197

−78

021

19.0

0−

69−

118

91−

69−

118

9169

118

−91

6911

8−

910

2126

.00

−56

−10

678

−56

−10

678

5610

6−

7856

106

−78

021

35.0

0−

32−

6847

−32

−68

4732

68−

4732

68−

470

2141

.00

−10

−25

16−

10−

2516

1025

−16

1025

−16

0

(con

tinu

ed)


Tab

le13

.(C

ontinued

)

Net

USD

Net

USD

Purc

hase

dby

Cen

tralB

ank

Net

USD

Purc

hase

dby

Tra

der

sTra

nsa

cted

Calls

Puts

Calls

Puts

by

Both

Long

Long

Short

Long

Long

Short

Short

Short

Long

Short

Short

Long

Ex.R

ate

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

Net

USD

CO

PU

SD

USD

USD

USD

USD

USD

USD

100%

100%

100%

100%

100%

100%

2144

.00

−3

−9

6−

4−

96

39

−6

49

−6

021

49.0

0−

2−

63

−2

−6

32

6−

32

6−

30

2156

.00

−1

−2

1−

1−

21

12

−1

12

−1

021

62.0

00

00

00

00

00

00

00

2166

.00

00

00

00

00

00

00

021

75.0

00

00

00

00

00

00

00

2182

.00

00

00

00

00

00

00

021

88.0

00

00

00

00

00

00

00

2189

.00

00

00

00

00

00

00

021

95.0

00

00

00

00

00

00

00

2196

.00

00

00

00

00

00

00

021

96.0

00

00

00

00

00

00

00

Tot

al−

9,99

9−

9,99

99,

999

01

−1

9,99

99,

999

−9,

999

0−

11

0

Note

s:T

his

table

illu

stra

tes

the

spot

mar

ket

pos

itio

nof

the

cent

ral

ban

kan

dtr

ader

sduri

ng

dai

lydyn

amic

del

tahed

ging

ofa

W-s

pre

adw

hen

ther

eis

per

sist

ent

dep

reci

atio

n.It

repre

sent

sth

enet

hed

ging

stra

tegy

wher

eea

chco

ntra

ctin

the

stra

tegy

isfo

rU

SD

10,0

00.H

ere,

the

trad

ers

are

hed

ging

100

per

cent

ofth

eir

pos

itio

n.


Tab

le14

.C

entr

alB

ank

and

Tra

der

s’H

edgi

ng

Pos

itio

ns

with

50Per

cent

Hed

ge Net

USD

Net

USD

Purc

hase

dby

Cen

tralB

ank

Net

USD

Purc

hase

dby

Tra

der

sTra

nsa

cted

Calls

Puts

Calls

Puts

by

Both

Long

Long

Short

Long

Long

Short

Short

Short

Long

Short

Short

Long

Ex.R

ate

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

Net

USD

CO

PU

SD

USD

USD

USD

USD

USD

USD

50%

50%

50%

50%

50%

50%

2044

.00

−5,

856

−5,

042

5,45

14,

144

4,95

8−

4,54

92,

928

2,52

1−

2,72

6−

2,07

2−

2,47

92,

275

−44

720

50.0

0−

494

−49

849

9−

494

−49

849

924

724

9−

250

247

249

−25

0−

493

2053

.00

−23

1−

230

232

−23

1−

230

232

116

115

−11

611

611

5−

116

−22

920

54.0

0−

66−

5561

−66

−55

6133

28−

3133

28−

31−

6020

54.0

0−

45−

3239

−45

−32

3923

16−

2023

16−

20−

3820

60.0

0−

489

−51

850

7−

489

−51

850

724

525

9−

254

245

259

−25

4−

500

2066

.00

−44

4−

484

466

−44

4−

484

466

222

242

−23

322

224

2−

233

−46

220

76.0

0−

627

−72

367

8−

627

−72

367

831

436

2−

339

314

362

−33

9−

672

2076

.00

−77

−78

79−

77−

7879

3939

−40

3939

−40

−76

2085

.00

−52

4−

646

586

−52

4−

646

586

262

323

−29

326

232

3−

293

−58

420

93.0

0−

359

−46

741

3−

359

−46

741

318

023

4−

207

180

234

−20

7−

413

2099

.00

−21

4−

292

252

−21

4−

292

252

107

146

−12

610

714

6−

126

−25

421

06.0

0−

217

−31

626

4−

217

−31

626

410

915

8−

132

109

158

−13

2−

269

2111

.00

−12

2−

187

152

−12

2−

187

152

6194

−76

6194

−76

−15

721

14.0

0−

61−

9778

−61

−97

7831

49−

3931

49−

39−

8021

19.0

0−

69−

118

91−

69−

118

9135

59−

4635

59−

46−

9621

26.0

0−

56−

106

78−

56−

106

7828

53−

3928

53−

39−

8421

35.0

0−

32−

6847

−32

−68

4716

34−

2416

34−

24−

5321

41.0

0−

10−

2516

−10

−25

165

13−

85

13−

8−

19

(con

tinu

ed)


Tab

le14

.(C

ontinued

)

Net

USD

Net

USD

Purc

hase

dby

Cen

tralB

ank

Net

USD

Purc

hase

dby

Tra

der

sTra

nsa

cted

Calls

Puts

Calls

Puts

by

Both

Long

Long

Short

Long

Long

Short

Short

Short

Long

Short

Short

Long

Ex.R

ate

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

Net

USD

CO

PU

SD

USD

USD

USD

USD

USD

USD

50%

50%

50%

50%

50%

50%

2144

.00

−3

−9

6−

4−

96

25

−3

25

−3

−7

2149

.00

−2

−6

3−

2−

63

13

−2

13

−2

−5

2156

.00

−1

−2

1−

1−

21

11

−1

11

−1

−2

2162

.00

00

00

00

00

00

00

021

66.0

00

00

00

00

00

00

00

2175

.00

00

00

00

00

00

00

021

82.0

00

00

00

00

00

00

00

2188

.00

00

00

00

00

00

00

021

89.0

00

00

00

00

00

00

00

2195

.00

00

00

00

00

00

00

021

96.0

00

00

00

00

00

00

00

2196

.00

00

00

00

00

00

00

0

Tot

al−

9,99

9−

9,99

99,

999

01

−1

5,00

05,

000

−5,

000

0−

11

−5,

000

Note

s:T

his

table

illu

stra

tes

the

spot

mar

ket

pos

itio

nof

the

cent

ral

ban

kan

dtr

ader

sduri

ng

dai

lydyn

amic

del

tahed

ging

ofa

W-s

pre

adw

hen

ther

eis

per

sist

ent

dep

reci

atio

n.It

repre

sent

sth

enet

hed

ging

stra

tegy

wher

eea

chco

ntra

ctin

the

stra

tegy

isfo

rU

SD

10,0

00.H

ere,

the

trad

ers

are

hed

ging

50per

cent

ofth

eir

pos

itio

n.


Tab

le15

.C

entr

alB

ank

and

Tra

der

s’H

edgi

ng

Pos

itio

ns

with

10Per

cent

Hed

ge Net

USD

Net

USD

Purc

hase

dby

Cen

tralB

ank

Net

USD

Purc

hase

dby

Tra

der

sTra

nsa

cted

Calls

Puts

Calls

Puts

by

Both

Long

Long

Short

Long

Long

Short

Short

Short

Long

Short

Short

Long

Ex.R

ate

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

Net

USD

CO

PU

SD

USD

USD

USD

USD

USD

USD

10%

10%

10%

10%

10%

10%

2044

.00

−5,

856

−5,

042

5,45

14,

144

4,95

8−

4,54

958

650

4−

545

−41

4−

496

455

−80

520

50.0

0−

494

−49

849

9−

494

−49

849

949

50−

5049

50−

50−

887

2053

.00

−23

1−

230

232

−23

1−

230

232

2323

−23

2323

−23

−41

220

54.0

0−

66−

5561

−66

−55

617

6−

67

6−

6−

108

2054

.00

−45

−32

39−

45−

3239

53

−4

53

−4

−68

2060

.00

−48

9−

518

507

−48

9−

518

507

4952

−51

4952

−51

−90

020

66.0

0−

444

−48

446

6−

444

−48

446

644

48−

4744

48−

47−

832

2076

.00

−62

7−

723

678

−62

7−

723

678

6372

−68

6372

−68

−1,

210

2076

.00

−77

−78

79−

77−

7879

88

−8

88

−8

−13

720

85.0

0−

524

−64

658

6−

524

−64

658

652

65−

5952

65−

59−

1,05

120

93.0

0−

359

−46

741

3−

359

−46

741

336

47−

4136

47−

41−

743

2099

.00

−21

4−

292

252

−21

4−

292

252

2129

−25

2129

−25

−45

721

06.0

0−

217

−31

626

4−

217

−31

626

422

32−

2622

32−

26−

484

2111

.00

−12

2−

187

152

−12

2−

187

152

1219

−15

1219

−15

−28

321

14.0

0−

61−

9778

−61

−97

786

10−

86

10−

8−

144

2119

.00

−69

−11

891

−69

−11

891

712

−9

712

−9

−17

321

26.0

0−

56−

106

78−

56−

106

786

11−

86

11−

8−

151

2135

.00

−32

−68

47−

32−

6847

37

−5

37

−5

−95

2141

.00

−10

−25

16−

10−

2516

13

−2

13

−2

−34

(con

tinu

ed)


Tab

le15

.(C

ontinued

)

Net

USD

Net

USD

Purc

hase

dby

Cen

tralB

ank

Net

USD

Purc

hase

dby

Tra

der

sTra

nsa

cted

Calls

Puts

Calls

Puts

by

Both

Long

Long

Short

Long

Long

Short

Short

Short

Long

Short

Short

Long

Ex.R

ate

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

(K1)

(K3)

(K2)

Net

USD

CO

PU

SD

USD

USD

USD

USD

USD

USD

10%

10%

10%

10%

10%

10%

2144

.00

−3

−9

6−

4−

96

01

−1

01

−1

−12

2149

.00

−2

−6

3−

2−

63

01

00

10

−9

2156

.00

−1

−2

1−

1−

21

00

00

00

−4

2162

.00

00

00

00

00

00

00

021

66.0

00

00

00

00

00

00

00

2175

.00

00

00

00

00

00

00

021

82.0

00

00

00

00

00

00

00

2188

.00

00

00

00

00

00

00

021

89.0

00

00

00

00

00

00

00

2195

.00

00

00

00

00

00

00

021

96.0

00

00

00

00

00

00

00

2196

.00

00

00

00

00

00

00

0

Tot

al−

9,99

9−

9,99

99,

999

01

−1

1,00

01,

000

−1,

000

00

0−

8,99

9

Note

s:T

his

table

illu

stra

tes

the

spot

mar

ket

pos

itio

nof

the

cent

ral

ban

kan

dtr

ader

sduri

ng

dai

lydyn

amic

del

tahed

ging

ofa

W-s

pre

adw

hen

ther

eis

per

sist

ent

dep

reci

atio

n.It

repre

sent

sth

enet

hed

ging

stra

tegy

wher

eea

chco

ntra

ctin

the

stra

tegy

isfo

rU

SD

10,0

00.H

ere,

the

trad

ers

are

hed

ging

10per

cent

ofth

eir

pos

itio

n.


hedging 100 percent of its net portfolio position in the W-spread,and the traders are hedging 100, 50, and 10 percent, respectivelyof their offsetting W-spread positions. In the examples presentedbelow, we assume that the COPUSD is depreciating, and that thehedging position (or spot market intervention driven by the hedgingposition) does not directly affect the movement of the exchange ratein this simulation. This assumption is used simply to convey thepositions the delta hedge would create in the spot market. Underthe depreciationary pressure, all calls are exercised, while the putsexpire without exercise. The delta hedging therefore nets to 10,000for each of the call positions and 0 for each of the put positions.

As can be seen in table 13, if both parties engage in 100 percentdelta hedging of their portfolios, then the hedging activity in thespot market between the central bank and traders cancel each otherout. If traders hedge anything less than 100 percent of their port-folio, the central bank’s hedging activity creates stabilizing transac-tions on the spot market to complement their intended interventiongoals. If traders hedge only 50 percent of their portfolio, as seen intable 14, then there is a net sale of USD on the spot market betweenthe traders and the central bank. Finally, if traders hedge only 10percent of their portfolio, the net position in the spot market is asale of USD 8,999, as seen in table 15. Therefore, if the net offset-ting position by market participants is hedged by anything less than100 percent, the delta-hedging activity of the central bank providesa spot market intervention strategy that complements the goals ofcurbing drastic movements of the exchange rate.

It is possible to assume that in fact the offsetting position wouldnot be hedged 100 percent, since the only agents interested indynamic delta hedging would be market markets and large currencytraders. Local import/export business and multinationals use theoption itself as a hedge. As a proxy, we can turn to the growthin forward contracts. According to the Triennial Foreign ExchangeMarket Survey conducted by the Bank for International Settlements,the share of options to total foreign exchange transactions in emerg-ing market economies has remained steady at 2.5 percent since 1998,which may be partially due to the shallowness of this market in theseeconomies. On the other hand, the use of forwards has increased from7 percent to 10 percent of total foreign exchange transactions, rep-resenting growth of 48 percent. By design, forward contracts are not


hedged and are used by non-market makers as a hedge in and ofthemselves, as the option would be in our proposed strategy. There-fore, if the central bank makes options more readily available to theseplayers by operating in and building up this market, it is possible toassume that the share of options that would be dynamically deltahedged would be less than 100 percent.

References

Adler, G., and C. Tovar. 2011. “Foreign Exchange Intervention: AShield Against Appreciation Winds?” IMF Working Paper No.11/165.

Akinci, O., O. Culha, U. Ozlale, and G. Sahinbeyoglu. 2006. “TheEffectiveness of Foreign Exchange Intervention Under a Float-ing Exchange Rate Regime for the Turkish Economy: Post-CrisisPeriod Analysis.” Applied Economics 38 (12): 1371–88.

Archer, D. 2005. “Foreign Exchange Market Intervention: Methodsand Tactics.” BIS Papers 24: 40–55.

Bank for International Settlements. 2016. “Triennial Central BankSurvey of Foreign Exchange and OTC Derivatives Markets in2016.” Bank for International Settlements Triennial Survey.

Breuer, P. 1999. “Central Bank Participation in Currency OptionsMarkets.” IMF Working Paper No. 99/140.

Caballero, R. 2003. “On the International Financial Architecture:Insuring Emerging Markets.” NBER Working Paper No. 9570.

Chen, Z., ed. 1998. Currency Options and Exchange Rate Econom-ics. World Scientific Publishing Co.

Daude, C., E. Levy Yeyati, and A. Nagengast. 2014. “On the Effec-tiveness of Exchange Rate Interventions in Emerging Markets.”Working Paper No. 324, OECD Development Centre.

DeRosa, D. F. 2011. Options on Foreign Exchange. 3rd Edition.Wiley.

Domanski, D., E. Kohlscheen, and R. Moreno. 2016. “ForeignExchange Market Intervention in EMEs: What Has Changed?”BIS Quarterly Review (September): 65–79.

Egbert, B. 2007. “Central Bank Interventions, Communication andInterest Rate Policy in Emerging European Economies.” Journalof Comparative Economics 35 (2): 387–413.


Fratzscher, M., O. Gloede, L. Menkho, L. Sarno, and T. Stoher.2015. “When is Foreign Exchange Intervention Effective? Evi-dence from 33 Countries.” Discussion Paper No. 1518, DIWBerlin.

Garber, P. 1994. “Foreign Exchange Hedging with Synthetic Optionsand the Interest Rate Defense of a Fixed Exchange RateRegime.” IMF Working Paper No. 94/151.

Guinigundo, D. 2013. “A Note on the Effectiveness of Interventionin the Foreign Exchange Market: The Case of the Philippines.”’BIS Papers 73: 263–77.

Hull, J. C. 2012. Risk Management and Financial Institutions. 3rdEdition. John Wiley and Sons, Inc.

Keefe, H. G., and E. Rengifo. 2015. “Options and Central Bank Cur-rency Market Intervention: The Case of Colombia.” EmergingMarkets Review 23 (June): 1–25.

Leon, H., and O. H. Williams. 2012. “Effectiveness of Intervention ina Small Emerging Market: An Event Study Approach.” AppliedFinancial Economics 22 (21): 1811–20.

Malz, A. 1995. “Currency Option Markets and Exchange Rates: ACase Study of the US dollar in March 1995.” Current Issues inEconomics and Finance (Federal Reserve Bank of New York) 1(July).

Mihaljek, D., and F. Packer. 2010. “Derivatives in Emerging Mar-kets.” BIS Quarterly Review (December): 43–58.

Nedeljkovic, M., and C. Saborowski. 2017. “The Relative Effective-ness of Spot and Derivatives Based Intervention: The Case ofBrazil.” IMF Working Paper No. 17/11.

Wiseman, J. D. 1999. “Using Options to Stabilise FX: A NewExchange Rate Mechanism.” Paper based on Sections 2 and 3of Special Paper No. 84, Financial Markets Group of the LondonSchool of Economics.

Zapatero, F., and L. F. Reverter. 2003. “Exchange Rate Interventionwith Options.” Journal of International Money and Finance 22(2): 289–306.

Currency Option Trading Strategies as an Alternative Tool ... · Vol. 15 No. 2 Currency Option...

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