Exotic Options Workbook and Ref Material

8/3/2019 Exotic Options Workbook and Ref Material

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Exotic Options andTrading Strategies

Workbook and Reference

Guide


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SECTION 1 OPTIONSBASICS


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Options

1.1. Definition and Features

An options contract gives the holder the right, but not the obligation, to buy or sell a givenunderlying product at a fixed price on a given date in exchange for a premium.

The following is key terminology for options contracts:Term Meaning

Strike price Price at which the option buyer has the right to buy or sell theunderlying.

Expiration Date and time on which the holder/buyer of the option loses theright to buy or sell.

Writer The option seller is also known as the option writer

Premium The amount paid by the option buyer to the option writer for theright.

Call option Buyer has the right to buy the underlying

Put option Buyer has the right to sell the underlying

Exercise Process of deciding and advising option seller/writer of intentionto exercise the right under the option

Life of option As exercise period - time until expiration

Exercise period As life of option - time until expiration

American Option Can be exercised at any time in a given period

European Option Exercise on expiration date only

Bermudan Option Exercise on a given range of dates.

In the money Given current market rates it is likely that the option will beexercised. A call option is in the money when the strike price isbelow the current market price. A put option is in the moneywhen the strike price is above the current market price

Out of the money Given current market rates it is unlikely that the option will beexercised.

At the money When the strike price is equal to the current market price

Breakeven Price The price of the underlying at which neither a profit nor a loss ismade. This occurs where underlying price - premium=strike price

Naked options Where the writer of a call option does not hold the underlyingstock or the right to buy the underlying stock if the buyer of theoption exercises his right then he is said to be exposed, uncoveredor naked

Covered options Where the writer of a call option holds the underlying stock orholds a hedge to buy the underlying stock if the buyer exercisesagainst him he is said to be covered.


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Term Meaning

Assignment Act by which the exchange designates an option writer forfulfilment of his obligation to sell or buy the underlying assetunder an exchange traded contract.

At the Money, Out of the Money, In the Money

The most profitable time to exercise an option is when it is In the Money. The following tableshows how an option contract moves in and out of the money as the price of the underlyingmoves:

-4

-3

-2

-1

0

1

2

3

4

Underlying Price

ProfitorLoss

Profit or Loss 3 2 1 0 -1 -2 -3

16 17 18 19 20 21 22

In the Money

Out Of the Money

At the

mone

Options may be standardised Exchange Traded Contracts (XTC) or customised Over the Counter(OTC) contracts. Exchange traded contracts may be exposed to daily margin calls where theexchange takes a proportion of the value of the loss as a deposit from the buyer.Exchange members and brokers charge commission to their clients to conduct the trades on theirbehalf.Exchanges include:

LIFFE (London International Financial Futures and Options Exchange

CBOT: Chicago Board of Trade

CME: Chicago Mercantile Exchange. A more detailed list is included as an Appendix.

Exchange traded options usually have expiry out to 2 years. Over the counter options can be

written for any period but typically not more than 10 years.OTC options include caps, collars and floors, which are covered in a separate section.The risk for option writers can be limitless especially where naked options are sold. These occurwhere the writer does not hold the underlying and is therefore exposed to movements in themarket price.Underlying includes

Currencies

Interest rates such as 3 month libor


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Securities

Swaps (see separate section on swaptions)

Futures

In the financial times on Weds 23rd October the following prices were quoted for three-month

Eurodollar options on CME. As per the contract specifications detailed below this gives thebuyer the right to buy one Eurodollar futures contract on CME.

Strike Price Calls Puts

Nov Dec Jan Nov Dec Jan

98.125 0.13 0.06 - 0.03 0.05 -

98.25 0.06 0.1 - 0.09 0.13 0.28

98.375 0.04 0.07 - 0.19 0.22 -

98.5 0.02 0.04 - 0.29 0.32 -

Note Eurodollars are time deposits denominated in U.S. dollars that are deposited in commercialbanks outside the U.S., and they have long served as a benchmark interest rate for corporatefunding. The Eurodollar futures contract on CME represents an interest rate on a three-monthdeposit of $1 million.

Option Premiums

Option premiums are calculated according to the value it has. The value is split into 2 parts:

Intrinsic ValueThe difference between the underlying and the strike prices

For a call option: Intrinsic Value = Underlying price - strike price

For a put option: Intrinsic Value = strike price - underlying price

Intrinsic value is always > zero

Time ValueThis is the amount of the premium which represents the risk to the writer that he option will movein the money before expiry

Time Value = Premium - Intrinsic ValueThe time value of the option is at its highest value on trade date and decreases/decays to zero onexpiry date.

Note an at the money option or out of the money option premium is entirely time value as theintrinsic value is zero.

Settling Options

Once an option has been traded a premium is payable. Further amounts are then only payable ifthe option is exercised. The nature of the settlement can either by physical or cash:

Strike prices of

futures contracts as100 - eurodollar rate

Expiry Months - the actualdate is specified by the

exchange

The premium for the option. For example the premium for a

December option with a strike price of 98.375 is $0.22


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Physical: this means that the option is actually delivered. So if the option is on an equitythe seller/writer of the option must deliver to the buyer/holder of the option the definedequity in return for cash representing the strike x number of shares agreed in the option.

Cash: For some products the physical delivery of the underlying is not feasible, forexample and interest rate option. Therefore cash is settled for the difference between themarket rate and the option rate based on the agreed notional.

It should be noted that cash settlement can also be agreed even though physicalsettlement is possible. Taking the example of the equity option again. Assume thatthe option is to buy 100 BP shares for 12 on 31/1/03. On the exercise date themarket price is 15 therefore the holder of the option exercises his right to buy butrequest cash settlement. The option writer will therefore pay the option holder 100 x(15- 12) to settle the option.

Pricing Options

The value of an option is dependent on the following factors: Strike price

Underlying price

As the price of the underlying rises the premium of a call option will increase andthe premium for a put option will fall. As the price of the underlying falls thepremium of a put option will increase and the premium of a put option will fall.

Time to expiry

The premium for an option will be higher for options with a longer period to expiryas there is more opportunity for the option to move In the Money.

Rate of movement of the underlying price - volatility

This measures the rate at which the underlying price fluctuates. It is the mostimportant factor in option valuations. Volatility is considered in terms of historicalvolatility and implied volatility.Historical volatility considers historical prices over time and is used to estimate

future volatilityImplied volatility is the future volatility level as quoted by the market.

Interest rates

These generally play a relatively insignificant role in the value of options. Thiselement relates to the cost of carry of the option - i.e. the cost of funding the optionpurchase or the opportunity cost. There is an inverse relationship. If interest ratesare falling then the premium rates will rise because the buyer of the option must becompensated for the lost opportunity of investing the option premium at higher rates

Volatility

As noted above this measures the rate at which the underlying price fluctuates. It is the mostimportant factor in option valuations. Volatility is considered in terms of historical volatility andimplied volatility.Volatilities are quoted as percentages and represent the standard deviation of the underlying. Theconfidence level of the volatility forecast being correct for one standard deviation (1) either sideof the mean is 68%, 2= 95%, 3 = 99.7%.


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For example the Euro interest rates for one year are 3.5% and the one-year volatility is forecast at10%. Therefore the standard deviation is 0.35 and for two standard deviations 0.70. Thisgives the following interest rate ranges:

Confidence Range

1 68.27% 3.15%-3.85%

2 95.45% 2.8%-4.2%

3 99.73% 2.45%-4.55%

4 99.99% 2.1%-4.9%

5 99.9999% 1.75%-5.25%

6 99.9999998% 1.4%-5.6%

Over the counter options are quoted in terms of volatility whereas XTC options are quoted interms of premiums as seen above.

The higher the volatility the higher the premium as the underlying price is more likely to moveaway from the strike price.

Margin

Margins are charged as a form of security to the exchange or broker on XTC options. They arenormally set as a percentage of the full value of the options. There are two types:

Initial margin is the amount of money, which a customer must deposit in his accountwhenever he establishes an options position. These margins must be deposited for bothlong and short positions. Initial margins normally range from 5 to 20 percent of the fullvalue of the options contracts. After depositing initial margin requirements, if the market

3.53.15 3.85

68% confidence

4.22.8

95% confidence


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moves in the customer's favour, the amount in excess of the initial margin requirementsmay either be withdrawn or used for margining additional positions.

Maintenance or variation margin. If the market moves against the customer, they will berequired to deposit additional monies in their account. This is known as maintenance orvariation margin. A maintenance margin call is issued when the customer's account valuefalls below the maintenance margin requirement, usually about 75% of the initial marginrequirement. When this happens, the customer will have to deposit sufficient funds tobring the balance in his account back up to the level of initial margin requirements.Maintenance margin calls can be met by cash deposits, deposits of Treasury Bills,transfer of funds from a related account, liquidation of positions, market appreciation orany combination of the above. During periods of extreme volatility or for very largepositions, accounts can be called for margin at any time. This type of call must usuallybe met immediately by either a wire transfer or the liquidation of positions.

Both Initial and variation margins are calculated based on the value of the portfolio, which willestablish a series of possible market movements to the option portfolio and take the worst-caseoutcome.The variation margin is calculated as follows:

These tick values are specified in the contract specifications, which are drawn up by the relevantexchanges.

Margin Calculation Methods

The most widely used is SPAN (Standard Portfolio Analysis of Risk), which applies to allLIFFE contracts, to all US futures exchanges (e.g. CME, CBOT, NYBOT) and to manyoverseas futures exchanges (e.g. MATIF, SIMEX).

Basic Trading Strategies

Each option strategy has a different profit profile. The four basic strategies are: Buy a call

Buy a put

Write/Sell a call

Write/Sell a put

These are explained below:

Buy a call

Variation Margin = number of contracts xnumber of ticks moved since last margin call x

tick value


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An investor believes that an American equity will increase in price. He does not currently havethe cash to buy the stock. Therefore he buys a European call on the stock with a strike price of

$12 three months hence. A premium of $1 is charged. The profit/value profile is: If the price of the underlying is $12 or less the option holder will do nothing. If the

holder were to exercise the option he would be buying the stock for more than he couldbuy it in the cash market. He does not exercise and he loses only the price of the option -the premium

At an underlying price of $13 the option holder exercises the option as he can now buy at

$12 and sell at $13 at a profit of $1. This offsets the premium giving a net profit of nil -known as the breakeven point.

At an underlying price of $14 the option holder makes a gain of $1 being the price atwhich underlying could be sold ($14) less the strike price at which he will buy theunderlying ($12) less the premium ($1).

The profit rises by $1 for every $1 rise in the underlying price.

Buy a put

A UK company sells products to the US. It receives payment in USD. On 1 May 2006 itreceives an order for goods worth $100,000, which will be paid for on 1 December 2006. Thecurrent exchange rate is $1.40 dollars per pound or 0.7143 pounds per dollar for which it wouldget 71,429. It buys a put option to sell dollars on 1 December for 0.7143 pounds per dollar. Thepremium is 3,000

-2

-1

0

1

2

3

4

5

6

9 10 11 12 13 14 15 16 17 18

Price of underlying

Profit/Loss

Premium.

Strike price

Out of the money In the money

Break even price $13


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If the /$ exchange rate (the underlying) is 0.7143 or more the option holder does notexercise the option as it can sell them dollars for more in the market. It loses only theprice of the option - the premium.

The breakeven point is at 0.6843 pounds to the dollar as at this point if the option holderexercises the option it will receive 71,429 giving him a net profit of 68,429 which is

the same price as if it did not have the option and sold his dollars at the current spot priceof 0.6843.

As the price of sterling to the dollar falls its gain increases.

On the other side of these buy options is the seller. Their profiles are as follows:

Sell a call

A trader sells a call to an investor who believes that an American equity will increase in price.The details are that he sells a European call on the stock with a strike price of $12 three monthshence. A premium of $1 is charged. The profit/value profile is:

Premium.

Strike price 0.7143

Out of the moneyIn the money

Break even price 0.6843

-5000

0

5000

10000

15000

20000

/$ 0.5263 0.5556 0.5882 0.6250 0.6667 0.7143 0.7692 0.8333 0.9091 1.0000

profit/loss 15,797 12,873 9,605 5,929 1,762 -3,000 -3,000 -3,000 -3,000 -3,000

1 2 3 4 5 6 7 8 9 10


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Until the investor exercises the option the trader is in profit as he keeps the premium.

Once the investor exercises the option (any price after $12) the traders profit is erodeduntil a price of $13 or more.

At a price of $15 the trader makes loss of $2, as he must sell to the option buyer for $12but has to buy in the market for $15, a loss on covering the trade of $3 against which hesets his premium of $1.

In fact the loss potential for the trader, if he does not already hold the underlying asset, is

unlimited. The writing/selling of uncovered or naked options as these are known is anextremely risky business for this reason.

Unsurprisingly the traders position is the mirror of the investors.

Sell a put

A trader sells to a UK company a put option to sell dollars on 1 December for 0.7143 pounds perdollar. The premium is 3,000

-6

-5

-4

-3

-2

-1

0

1

2

9 10 11 12 13 14 15 16 17 18

market price

profitorloss

Premium.

Strike price

Out of the money In the money

Break even price $13


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Until the company exercises the option the trader is in profit as he keeps the premium.

Once the company exercises the option (any price below 0.7143) the traders profit iseroded until a price of 0.6843 or less.

At a price of 0.5 the trader makes loss of 18,429, as he must buy $100,000 from the

option buyer for 0.7143 pounds to the dollar, which costs 71,429. The best he can sellhis dollars for is 0.5 for which he receives 50,000.

In fact the loss potential for the trader if he does not already hold the underlying asset issignificant. However in this case he is limited to the cost of the sterling of 71,429 as theprice cannot go below zero.

Again the option seller/writers position is the mirror of the buyers.

The Greeks

Each of the factors influencing the value of options is named a Greek letter as follows:

Greek Symbol Influence Calculation

Delta or Change in price ofthe underlying Change in premiumChange in Underlying Price

Gamma Change in delta Change in Delta

Change in Underlying Price

-20000

-15000

-10000

-5000

0

5000

Market rate

Profitorloss

/$ 0.5263 0.5556 0.5882 0.6250 0.6667 0.7143 0.7692 0.8333 0.9091 1.0000

Profit/Loss -15,797 -12,873 -9,605 -5,929 -1,762 3,000 3,000 3,000 3,000 3,000

1 2 3 4 5 6 7 8 9 10

Premium.

Strike price 0.7143

Out of the moneyIn the money

Break even price 0.6843


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Greek Symbol Influence Calculation

Vega (not actuallya Greek letter soalso Epsilon,Lappa)

Change in thevolatility of theunderlyinginstrument price

Change in Premium

Change in Volatility

Theta Change in time toexpiry

Change in Premium

Change in time to expiry

Rho Change in interestrate to fund theunderlyinginstrument

Change in Premium

Change in cost of funding

Creation of Contracts

Like futures exchange traded option contracts are defined by the exchange on which they are to

be traded. The following is the contract specification for the against $ Option on LIFFE. Thespecifications for any contracts can be found from the website of the exchange concerned

Unit of trading 25000

Delivery/expiry months March, June, September, December

Delivery/Exercise/expiry day Exercise on any business day. Delivery on thethird business day after the exercise day. Expiryat 17.00 on the last trading day

Last Trading Day 16.02 3 business days before third Wednesdayof expiry month

Quotations US $ per pound

Minimum price movement (tick sizeand value)

0.01cents per

($2.5)

Trading Hours 08.34-16.02

Exchange traded options are traded in a pit by brokers on an open outcry system as forfutures. Open outcry simply means that the bid and offer price and volumes are shouted out intothe pit for anyone to hear.OTC options are agreed individually between two parties, typically a bank and their client. Alldetails are agreed in writing via a confirmation.

Uses

As shown in the examples:HedgingTo provide protection against adverse price movements in the interest rate, currency andsecurities markets.

Speculation/Trading


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Making gains by buying and selling options. Profit and loss is made because of movement in theprice of the underlying.

Income and Valuation

IncomeProfit and loss is made according to value of the options, which in turn will vary according to theprice of the underlying. For an option buyer the only cost may be the premium if the option is notexercised. The option seller receives premium income. The potential costs are limitless if nakedoptions are written.

ValueExchange Trade Options: In the case of XTC options the value is the current price of the optionas quoted by the exchange, which will be, derived using the same methodologies as described forOTC options.Over The Counter Options: The valuation of options is complicated and further detailed trainingmust be obtained by anyone involved in the checking of the valuation of options. The value ofoptions depends on the following factors:

Current market price of the underlying asset - the higher the current price the more likelyit is that a call option will be exercised as the strike price is more likely to be below thecurrent price.

Strike price - the lower the strike price the more likely it is that a call option will beexercised.

Time to maturity - the longer the period to the maturity the more likely the option will beexercised as there is more time for the option to move in the money

Volatility of the underlying - this measure the extent to which the price moves. The morevolatile the underlyings price the more likely it is that the strike price will fall below themarket price in the case of a call option.

Whether the option is American or European Style - with an American style option thebuyer has more opportunity for the option to be in the money


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SECTION 2- TRADING

STRATEGIES


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Complex Trading Strategies

Complex trading strategies are combinations of two or more simple strategies.

StraddleSimultaneously buying or selling of options of different types for the same strike price

Long Straddle:- Buying a call and a put at the same time for the same strike

Long Straddle payoff

A long straddle will make losses if at the time of exercise/Expiry the strike price is nearthe market price. This is because the investor has bought exposure to both the options. Along straddle will make a profit if there is a large movement in either direction

Buy a callBuy a Put

Price of underlying

Break even - CallBreak even -put

Losses

Profits

Losses

Profits

Zero


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Short Straddle:-Selling a call and a put at the same time for the same strike

Short Straddle Payoff

The short straddle will be profitable if the underlying price is close to the strike price atthe time of expiry. If there is a large movement in the underlying price in either direction

the straddle will result into a loss

Straddle Example/Excercise

let's assume that IBM is currently trading at $100 per share. Due to a significant eventthat will occur this month (an expected news event, earnings release, etc.), an investormight believe that the stock will move at least 10% in either direction. In this example,let's assume that both the IBM 100 put options and IBM 100 call options are trading at $3each. To take advantage of this the investor would enter into a straddle trade bypurchasing both the IBM 100 put for $3 and the IBM 100 call for $3 (for a total of $6 out

of pocket).

Draw the payoff diagram of the straddle

Calculate the profit or loss if

The market price had risen 10%

Losses

Profits

Sell a put

Sell a Call

Strike Price

Profits

Losses

Underlying priceZero


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The market price had fallen by 15%

If the market price moved by 2 %

Reasons for trading the straddle

Investor is trading on volatility. A long straddle useful when the investor is expecting a large movement in

underlying price in either side but is not sure which direction the same will be in. A short straddle will be useful when the investor is expecting a small movement

in the underlying price in either of the directions

StrangleDefinition: - Buying or selling of option of different types with different strikes

Long Strangle: - Buy a call with high strike price and put with low strike price

Profit Profile

Call break even

Put StrikeCall Strike

Put break even

Underlying price

Losses

Profits

zero

Buy a put

Buy a call


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A long strangle will make a profit if there is a large movement in the price of theunderlying in the either direction. If the underlying price is in between the two prices orclose to the same the strangle will lead to a loss

Short Strangle

Sell a call with high strike and a put with low strike

Short Strangle Payoff

A short strangle will be profitable if the underlying price is close to or in between the twostrike prices. However if there is a large movement in the underlying price in either of thedirection a short strangle position will be at a loss

Reasons for trading in Strangles

Investor is trading on volatility. A long straddle useful when the investor is expecting a large movement in

underlying price in either side but is not sure which direction the same will be in. A short straddle will be useful when the investor is expecting a small movement

in the underlying price in either of the directions The underlying price movement has to be greater than in case of a strangle, hence

the premium paid by the buyer of the strangle will be lower

Put Break even Put Strike Call strikeCall break even

Losses

Profits

zero Underlying price

Sell a call

Sell a put


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Strangle Example/Excercise

Reliance is currently trading at 325. The investor expects a big jump in prices due to de

- merger of the company but is not sure how the same will affect the price He buys a callat 360 and a put at 300. He pays a premium of Rs.10/share on call and 5/share on put.The contract size is 200 shares.

Answer the following

1. When will the investor start making profit?

2. When will he make a loss?

3. What is his breakeven point?

4. If at the time of expiry reliance was trading at the following prices calculate netprofit or a loss

a. 380b. 370c. 350d. 335e. 310

Spreads

Definition- Buying or selling of options of the same type with different strike price

Long Call Spreads:- Buy a call with low strike price and sell a call with high strike price.Also known as bull call spreads. The expiry and the underlying should be same

Bull spreads have limited profit potential. The risks are also limited to the premium paid

Bull call spread Payoff

A bull call spread will be profitable if the underlying price is greater than the breakevenpoint. The breakeven point for the bull call spread will be the lower strike + premium.This can be better explained by way of an example

Assume XYZ Stock is trading at 102.50. You buy 1 XYZ Apr 100 call at a premium ofRs.9 and sell XYZ Apr 110 call at Rs.5.

The net cost of the spread is Rs.4.


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The maximum risk is Rs.4.The maximum gain will be the spread (110-100) premium = Rs.6.

Breakeven point will be at 104 ( Lower strike + premium).

If the price remains at 102.50 the investor will exercise the call hence will gain 2.5. Thebuyer of the high strike will not exercise the call. This will result in a total loss of 1.5

If the market price is 108 again the investor will exercise the long call and gain Rs.8 Theshort call will not be exercised. Resulting in a net profit of 8-4 = Rs.4

If the price is 99 neither options will be exercised resulting in a net loss of 4

If the price is more than 110 both the long and the short calls will be exercised. Theinvestor will pay and receive on both hence the maximum gain the investor can have is 6.

Reasons for trading in Bull spreads

Investor expects that the price will rise up to a certain level Wants to minimize the premium cost.

Buy a Call

Losses

0

Profits

Sell a Call


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Log Put Spread:- Buy one put with high strike price and sell another put with a lowstrike price. The expiry and the strike for both should options being the same. Long putspreads are also called bear spreads.

Bear spreads have limited profit potential. The risks are also limited to the premium paid

Bear Spread payoff

The payoff from the long put spread can be better understood by way of an example.

QRS stock is currently trading at 63.75 an investor is expecting a fall in the prices from63.75 to 60.00 hence he buys a bear spread. He buys a put at 65 premium of 5.5 and sellsa put at 60 for a premium of 3.25.

The net cost of the put to the investor is 2.25

The Maximum gain will be spread minus the premium = 2.75

Breakeven will be higher strike premium

If on the expiration date the stock is trading at 63.75 the long put will beexercised. The gain from the same will be 1.25. The net loss will be 1.00. The

0

Profits

Buy a Put

Sell a put

Losses


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short put will not be exercised as the strike price is less than the market price,hence option is not in the money.

At 62.75 There will be no profit no loss

AT 60.00 The long put will be exercised. The gain from exercise being 5. Netprofit being 2.75

At 59 both the puts will be exercises and the investor will pay on one put andreceive on another

o On long call he received 6o On short call he pays 1o Net receipt 5o Less the net premium paid of 2.25o Net gain of 2.75

Thus his profits are limited to 2.75.

Reason .for trading in Bear Spreads

Investor expects that the price will rise up to a certain level Wants to minimize the premium cost.

Spreads Exercise

1. How is a bull call spread created?

1. Buy a short-term call and sell a long-term call2. Buy a call with a higher strike price and sell a call with a lower strike price3. Buy a call with a lower strike price and sell a call with a higher strike price

2. Which of the following is an example of a bear put spread?

1. Buy 1 CDE Aug 120 put @ 7.50Sell 1 CDE Aug 110 put @ 4

2. Buy 1 LMN 85 put @ 2Sell 1 LMN 90 pt @ 3.75

3. Buy 2 JQQ 35 puts @ 2.25Sell 1 JQQ 40 put @ 5

3. Assume you purchase the following bull call spread:Buy 1 STS 40 call 3.75Sell 1 STS 45 call 1.75


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4. If the price of STS stock is $39 at expiration, what is the profit or loss fromthis bull call spread?

1. Profit of 32. Profit of 23. Loss of 2

4. Loss of 3.75

5. Assume you purchase the following bear put spread:Buy 1 EFG May 95 put @ 6.50Sell 1 EFG May 85 put @ 2.25If the price of EFG stock is $84 at expiration, what is the profit or loss fromthis bear put spread

1. Profit 6.502. Profit 5.753. Loss 4.25

4. Loss 2.25

6. Assume you purchase the following bull call spreadBuy 1 ABC Nov 60 call 5.75Sell 1 ABC Nov 65 call 3.50If the price of ABC stock is $64 at expiration, what is the profit or loss fromthis bull call spread?

1. Profit 2.752. Profit 1.753. Loss 2.254. Loss 2.75


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SECTION 2- Exotic Options


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Average/Asian options

Definition:- An option whose payoff depends on the average of the underlying over thelife of the option

Can beAverage Price:- The payoff is difference between the strike and average of theunderlying price.

Average Strike:- An option where the strike rate equals the average of the underlyingindex over the life of the option. The Strike is not set on onset. It is derived as the averageof the underlying price. On expiration the current underlying price is compared with theaverage calculated and the payoff is determined

Example:-

A multinational GBP based company has a large flow of foreign currency receipts overthe year. While each individual receipt is difficult to forecast and only small, over theyear the total USD income equals in excess of USD 25 million. The current spot rate is1GBP = 1.50USD. Given the random timing of the cashflows and the small individualsize, traditional FX options have proved to be impractical. The company can considerusing an Average Rate Strike Option. The company is comfortable that the total incomein one year will exceed USD 25 million. The company could purchase a 1 yr USD 25mmWeekly Average Strike Rate Put option at say 1.75%. Each week the USD/GBP spot ratewould be noted from an agreed source at an agreed time. The strike rate for the option isthen set at the end of the year at the calculated average rate and used to calculate the

value of the option:

USD 25,000,000 * (Spot at Maturity - Average Strike) * days/365

Assuming the average strike equals 1.43 and the USD/GBP spot rate at maturity is 1.60,the option payout would equal:

USD 25,000,000 * (1.60 - 1.43) * 365/365 = USD 4,250,000 or GBP 2,656,250

The company achieves a general hedge against a falling USD at a reasonable cost.

Advantages

Lower premium Customised General protection of small regular cash flows Accurate reflection of the underlying price over a period.


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Useful ways of protecting a series of cash flows against rate moves when thedates of receipts cannot be accurately predicted.

Disadvantages

General protection rather than specific

Barrier Option

Definition:-Barrier options are a family of options that either come alive or die whenpredetermined trigger points (barriers) are reached. Most available options can be adaptedto be barrier options

There are two major types

Knock Ins and Knock Outs.

Knock In options come alive when the barrier is reached. They can be

Down and in: - Will come alive when the underlying price falls to a barrier level

Up and in: - Will come alive when the underlying price rises to the barrier level

Knock out options die when the barrier is reached.

Down and out: - Will die when the underlying price falls to a barrier level

Up and out: - Will die when the underlying price rises to the barrier level

The barrier can be any tradable variable and may or may not be directly related to theunderlying of the original option.

These can be call or a put

These can be either European or American options

The Barrier can be either

Inside Barrier: - Where the barrier relates to the price of the underlying asset

Outside side barrier: - Where the barrier relates to price of another asset

Pricing


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The price of a barrier option depends upon the probability of the barrier being reached,and the value of the underlying option if it is reached. They are therefore very sensitive tovolatility.

Advantages

Cheaper than standard options Flexibility in setting the barrier level and thus the cost of the option Can be linked to any underlying Customised to clients exposures

Disadvantages

The rate protection is contingent upon an "independent" event

Binary options

Payout in case is fixed amount if the option is in the money at the time of expiration.Binary is zero or one, there are only two possibilities. Similarly in binary options if theoption is in the money at the time of expiry then a fixed sum is paid. The level ofunderlying is irrelevant. They are also known as digital option

Digital Options are relatively common. As volatility increases the digital options becomecheaper compared to the conventional options as the there is only a fixed payout

Digital options can be

Cash or nothing - Where the cash is paid if the option is in the money

Asset or nothing: - Payoff is an asset if the option is in the money

One Touch Digital: - If the barrier is reached anytime during the life of the option thenbuyer receives the payout 2 days after the expiry

Instant one touch: - Buyer received a payout 2 days after the barrier is reached

Digital Knock in: - Combination of digital and knock in. A fixed payoff if the option is inthe money at the time of expiry and the barrier has been reached

Digital Knock out: - Combination of digital and knock out. A fixed payoff if the option isin the money at the time of expiry and the barrier has not been reached


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Ladder Options

Definition :- With a Ladder option, the strike is periodically reset when the underlyingtrades through specified trigger levels, at the same time locking in the profit between theold and the new strike.

The trigger strikes appear as rungs on a ladder. Ladder options can be structured to resetthe strike in either one or both directions. The Ladder option is also known as a Ratchetoption and Lock-In option.

Example

An investment fund that is bullish on the USD wants to buy USD calls. If the fund buys aEuropean call it can only exercise the option at the maturity date. If it buys an Americancall though, it will face the problem of when to exercise the option. The fund decides tobuy a Ladder Option with a strike of 1.65 and a ladder with rungs starting at 1.65, going

upwards in steps of 5 pf to a maximum of 1.80. Now every time USD/DEM reaches anew rung, the strike will be reset to that rung and a 5 pf profit locked in. So if during thelifetime of the deal USD/DEM reaches its high at 1.7620, the highest rung reached willbe 1.75 and the strike will thus be set accordingly, while the profit of 10 pf (1.75-1.65)will be locked in. At expiry the fund will receive the greater of (a)closing spot lessoriginal strike, and (b) highest rung reached less original strike. If in our example, thehighest level was 1.7620 but the rate closes at 1.53, the fund will receive 10 pf only. Ifhowever the spot closes at 1.762, the fund will receive 11.2 pf.

Pricing

A Ladder Option can be viewed as a series of Knock-In and Knock-Out call and putoptions each struck at a different ladder level. Our above example is made up bycombining a 165 call and a series of bought and sold Knock-In Puts (see "FX Knock-InOptions").

Advantages

Less risky than traditional options as profits locked in as underlying performs No need to constantly watch the underlying market levels Ladder options are applicable for risk averse option buyers as profits are

progressively locked in without losing the option position.

Disadvantages

More expensive than a normal option


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Cliquet Options

Defination :- A Cliquet Option settles periodically and resets the strike at the then spot

level.

It is therefore a series of at-the-money options, but where the total premium is determinedin advance. A Cliquet can be thought of as a series of "pre-purchased" at-the-moneyoptions. The payout on each option can either be paid at the final maturity, or at the endof each reset period.

Example

A three year Cliquet Call on the FTSE with annual resets is a series of three annual at-the-money spot calls. The initial strike is set at say 3000. If at the end of year one, the

FTSE closes at 3300, the first call matures 10% in-the-money and this amount is paid tothe buyer. The call strike for year 2 is then reset at 3300. If at the end of year 2, the FTSEcloses at 2900, the call will expire worthless. The call strike for year 3 is then reset at2900. The alternative strategy would be to buy a one year at-the-money call and at theend of year one, buy another at-the-money one year call, and so on. The difference is thatthe cost of the Cliquet is known in advance, whereas the future cost of at-the-money callsis unknown. If volatility is LOWER than expected, the Cliquet will be more expensivethan buying the calls annually, if volatility is HIGHER than expected, the Cliquet will becheaper. A Cliquet option is therefore more attractive when volatility is expected toRISE.

The major advantage of the Cliquet, is that the probability of some payout is high. Overthe 3 year period, the chance that the market will close lower for three consecutive years,is much lower than the probability that the market will close lower at the END of threeyears i.e. there is a high probability that even if the market closes lower after three years,that it will have closed higher in at least one of the three years.

Pricing

A Cliquet is a series of at-the-money options. We can calculate the expected value ofthese options by generating the implied forward volatility curve (some methodology asgenerating implied forward interest rates. See "Implied Forwards"). The Cliquet premium

is the present value of the premiums for the option series. A Cliquet call is always moreexpensive than a straight at-the-money call with the same final maturity.

The number of reset periods is determined by the buyer in advance. More resets make theoption more expensive. A Coupe is a cheaper alternative to the Cliquet (see "CoupeOptions").


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The Cliquet is suitable for investors with a medium term investment horizon. It is lessrisky than ordinary medium term options, as there is less specific risk i.e. the reset facilitygives the buyer a "second" and "third" chance. This increases the chance of payout, butmust be balanced with the higher premium cost. As a series of "pre-purchased" options,the Cliquet is attractive to passive investors as it requires no intermediate management.

They have traditionally been attractive to retail and private investors when embedded indeposits and bonds (see "Structured Assets ") as they provide a low risk (capitalguaranteed) exposure to equity and Bond markets. Sophisticated investors use Cliquets totake advantage of future assumptions about volatility.

Advantages

There is a "second chance" as the strike is periodically reset Ideal medium term, passive investment Locks in the future cost of volatility

Disadvantages

More expensive than straight options with same final maturity

Lookback Options

Definition: - At maturity the buyer can "lookback" and set the most favorable strike tomaximize profit between strike and maturity. Lookback Options are also known asHindsight Options.

There are two types of Lookback option:

Set a strike at the start: - At maturity, the buyer can "lookback" over the life of the optionand choose the most favorable exercise point to maximize profit between strike andexercise.

Set a strike at maturity: - At maturity the buyer can "lookback" and set the mostfavorable strike to maximize profit between strike and maturity. Lookback Options arealso known as Hindsight Options.

Example

An investor expects a sharp rise in the CAC 40 over the next year. A straight 1 year callwith an at-the-money spot strike of 1900 would cost 236 points. A Lookback call strike1900 would cost 343 points but would give the investor the opportunity to lookback atmaturity and select the highest point reached by the CAC 40 as the exercise point thusmaximizing profit. If the CAC 40 is higher than 1900 at any time over the year, theinvestor is assured of some payout. The lookback feature is thus very attractive to


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investors as it gives the buyer the best possible payout. However, Lookback options aregenerally very expensive.

Pricing

Since the option will always choose the highest profit available, the major determinant ofthe option price will be the volatility of the underlying. The more volatile the underlying,the higher the probability that the underlying will move dramatically enough to allow theinvestor a significant profit, therefore the higher the volatility the more expensive theLookback.

Lookback Options are applicable for risk averse investors unsure about timing of themove in the underlying. They are lower risk as there is a high probability of return.However, they do involve a larger upfront premium.

Advantages

The buyer will always be able to lock in the most favorable profit that appearedduring the life of the option

Disadvantages

The Lookback Option will require higher premiums than conventional options

Exotic Options Workbook and Ref Material

Documents

Transcript of Exotic Options Workbook and Ref Material