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MODULE 5

DERIVATIVES

Rise of Derivatives

The global economic order that emerged after World War II was a system where many

less developed countries administered prices and centrally allocated resources. Even the

developed economies operated under the Bretton Woods system of fixed exchange rates.

The system of fixed prices came under stress from the 1970s onwards. High inflation and

unemployment rates made interest rates more volatile. The Bretton Woods system was

dismantled in 1971, freeing exchange rates to fluctuate. Less developed countries like

India began opening up their economies and allowing prices to vary with market

conditions.

Price fluctuations make it hard for businesses to estimate their future production costs

and revenues.2 Derivative securities provide them a valuable set of tools for managing

this risk. This article describes the evolution of Indian derivatives markets, the popular

derivatives instruments, and the main users of derivatives in India. I conclude by

assessing the outlook for Indian derivatives markets in the near and medium term.

Development of Derivative Markets in IndiaDerivatives markets have been in existence in India in some form or other for a long

time. In the area of commodities, the Bombay Cotton Trade Association started futures

trading in 1875 and, by the early 1900s India had one of the worlds largest futures

industry. In 1952 the government banned cash settlement and options trading and

derivatives trading shifted to informal forwards markets. In recent years, government

policy has changed, allowing for an increased role for market-based pricing and less

suspicion of derivatives trading. The ban on futures trading of many commodities was

lifted starting in the early 2000s, and national electronic commodity exchanges were

created.

In the equity markets, a system of trading called badla involving some elements of

forwards trading had been in existence for decades.6 However, the system led to a

number of undesirable practices and it was prohibited off and on till the Securities and

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Exchange Board of India (SEBI) banned it for good in 2001. A series of reforms of the

stock market between 1993 and 1996 paved the way for the development of

exchangetraded equity derivatives markets in India. In 1993, the government created the

NSE in collaboration with state-owned financial institutions. NSE improved the

efficiency and transparency of the stock markets by offering a fully automated screen-

based trading system and real-time price dissemination. In 1995, a prohibition on trading

options was lifted. In 1996, the NSE sent a proposal to SEBI for listing exchange-traded

derivatives. The report of the L. C. Gupta Committee, set up by SEBI, recommended

a phased introduction of derivative products, and bi-level regulation (i.e., self-

regulation by exchanges with SEBI providing a supervisory and advisory role).

Another report, by the J. R. Varma Committee in 1998, worked out various operational

details such as the margining systems. In 1999, the Securities Contracts (Regulation) Act

of 1956, or SC(R)A, was amended so that derivatives could be declared securities. This

allowed the regulatory framework for trading securities to be extended to derivatives. The

Act considers derivatives to be legal and valid, but only if they are traded on exchanges.

Finally, a 30-year ban on forward trading was also lifted in 1999.

The economic liberalization of the early nineties facilitated the introduction of derivatives

based on interest rates and foreign exchange. A system of market-determined exchange

rates was adopted by India in March 1993. In August 1994, the rupee was made fully

convertible on current account. These reforms allowed increased integration between

domestic and international markets, and created a need to manage currency risk. Figure 1

shows how the volatility of the exchange rate between the Indian Rupee and the U.S.

dollar has increased since 1991.7 The easing of various restrictions on the free movement

of interest rates resulted in the need to manage interest rate risk.

Meaning and definition

In finance, a derivative is a financial instrument derived from some other asset; rather

than trade or exchange the asset itself, market participants enter into an agreement to

exchange cash, assets or some other value at some future date based on the underlying

asset.

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The term derivatives indicates that it has no independent value ie., its value is entirely

derived from value of underlying asset. The underlying asset can be securities,

commodities, bullion, currency, indices, live stock etc. Derivative means a forward,

future, option or any other hybrid contract of pre determined fixed duration, linked for the

purpose of contract fulfilment to the value of a specified real or financial asset or to an

index of securities.

There are many types of financial instruments that are grouped under the term

derivatives, but options/futures and swaps are among the most common.

BASIC FEATURES OF DERIVATIVES

1. As derivatives are not physical assets , transactions are setteled by

offsetting/squaring transactions. The difference in value of derivative is cash

setteled.

2. There is no limit on number of units transacted in derivative market because there

is no physical asset to be transacted.

3. Derivative markets are usually the screen based /computarised.

4. Derivatives are secondary market securities and and cannot help raising funds to a

firm.

5. Derivative market is quiet liquid and transactions can be effected easily.

6. Derivative provides a hedging against different risks.

The participants in a derivatives market

Hedgers use futures or options markets to reduce or eliminate the risk associated

with price of an asset.

Speculators use futures and options contracts to get extra leverage in betting on

future movements in the price of an asset. They can increase both the potential

gains and potential losses by usage of derivatives in a speculative venture.

Arbitrageurs are in business to take advantage of a discrepancy between prices in

two different markets. If, for example, they see the futures price of an asset getting

out of line with the cash price, they will take offsetting positions in the two markets

to lock in a profit.

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Types of derivatives

OTC and exchange-traded

Broadly speaking there are two distinct groups of derivative contracts, which

are distinguished by the way that they are traded in market:

Over-the-counter (OTC) derivatives are contracts that are traded (and privately

negotiated) directly between two parties, without going through an exchange or

other intermediary. Products such as swaps, forward rate agreements, and

exotic options are almost always traded in this way. The OTC derivatives

market is huge. According to the Bank for International Settlements, the

total outstanding notional amount is USD 298 trillion (as of 2005)[1].

Exchange-traded derivatives are those derivatives products that are traded via

Derivatives exchanges. A derivatives exchange acts as an intermediary to all

transactions, and takes Initial margin from both sides of the trade to act as a

guarantee. The world's largest[2] derivatives exchanges (by number of

transactions) are theKorea Exchange(which lists KOSPI Index Futures &

Options), Eurex (which lists a wide range of European products such as interest

rate & index products), Chicago Mercantile Exchange and theChicago

Board of Trade. According to BIS, the combined turnover in the world's

derivatives exchanges totalled USD 344 trillion during Q4 2005.

Types of Derivatives

Forwards: A forward contract is a customized contract between two entities, where

settlement takes place on a specific date in the future at todays pre-agreed price.

http://en.wikipedia.org/wiki/Swap_(finance)http://en.wikipedia.org/wiki/Forward_rate_agreementhttp://en.wikipedia.org/wiki/Exotic_optionhttp://en.wikipedia.org/wiki/Bank_for_International_Settlementshttp://en.wikipedia.org/wiki/#_note-afghhttp://en.wikipedia.org/wiki/Derivatives_exchangehttp://en.wikipedia.org/wiki/Initial_marginhttp://en.wikipedia.org/wiki/#_note-foweekhttp://en.wikipedia.org/wiki/Korea_Exchangehttp://en.wikipedia.org/wiki/Korea_Exchangehttp://en.wikipedia.org/wiki/Korea_Exchangehttp://en.wikipedia.org/wiki/KOSPIhttp://en.wikipedia.org/wiki/Eurexhttp://en.wikipedia.org/wiki/Chicago_Mercantile_Exchangehttp://en.wikipedia.org/wiki/Chicago_Board_of_Tradehttp://en.wikipedia.org/wiki/Chicago_Board_of_Tradehttp://en.wikipedia.org/wiki/Chicago_Board_of_Tradehttp://en.wikipedia.org/wiki/Swap_(finance)http://en.wikipedia.org/wiki/Forward_rate_agreementhttp://en.wikipedia.org/wiki/Exotic_optionhttp://en.wikipedia.org/wiki/Bank_for_International_Settlementshttp://en.wikipedia.org/wiki/#_note-afghhttp://en.wikipedia.org/wiki/Derivatives_exchangehttp://en.wikipedia.org/wiki/Initial_marginhttp://en.wikipedia.org/wiki/#_note-foweekhttp://en.wikipedia.org/wiki/Korea_Exchangehttp://en.wikipedia.org/wiki/KOSPIhttp://en.wikipedia.org/wiki/Eurexhttp://en.wikipedia.org/wiki/Chicago_Mercantile_Exchangehttp://en.wikipedia.org/wiki/Chicago_Board_of_Tradehttp://en.wikipedia.org/wiki/Chicago_Board_of_Trade

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Futures: A futures contract is an agreement between two parties to buy or sell an asset at

a certain time in the future at a certain price. Futures contracts are special types of

forward contracts in the sense that the former are standardized exchange-traded contracts

Options: Options are of two types - calls and puts. Calls give the buyer the right but not

the obligation to buy a given quantity of the underlying asset, at a given price on or

before a given future date. Puts give the buyer the right, but not the obligation to sell a

given quantity of the underlying asset at a given price on or before a given date.

Warrants: Options generally have lives of upto one year, the majority of options traded

on options exchanges having a maximum maturity of nine months. Longer-dated options

are called warrants and are generally traded over-the-counter.

LEAPS: The acronym LEAPS means Long-Term Equity Anticipation Securities. These

are options having a maturity of upto three years.

Baskets: Basket options are options on portfolios of underlying assets. The underlying

asset is usually a moving average or a basket of assets. Equity index options are a form of

basket options.

Swaps: Swaps are private agreements between two parties to exchange cash flows in the

future according to a prearranged formula. They can be regarded as portfolios of forward

contracts. The two commonly used swaps are :

Interest rate swaps: These entail swapping only the interest related cash flows

between the parties in the same currency.

Currency swaps: These entail swapping both principal and interest between the

parties, with the cashflows in one direction being in a different currency than those

in the opposite direction.

Swaptions: Swaptions are options to buy or sell a swap that will become operative at the

expiry of the options. Thus a swaption is an option on a forward swap. Rather than have

calls and puts, the swaptions market has receiver swaptions and payer swaptions. A

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receiver swaption is an option to receive fixed and pay floating. A payer swaption is an

option to pay fixed and receive floating.

Examples

Some common examples of these derivatives are:

UNDERLYING

CONTRACT TYPE

Exchange

traded

futures

Exchange

traded

options

OTC swap OTC forward OTC option

Equity Index

DJIA Index

future

NASDAQ

Index future

Option on

DJIA Index

future

Option on

NASDAQ

Index future

n/a Back-to-back n/a

Money

market

Eurodollar

future

Euribor

future

Option on

Eurodollar

future

Option on

Euribor

future

Interest

rate swap

Forward rate

agreement

Interest

rate cap

and floor

Swaption

Basis swap

Bonds Bond futureOption on

Bond futuren/a

Repurchase

agreement

Bond

option

Single Stocks

Single-

stock

future

Single-share

option

Equity

swap

Repurchase

agreement

Stock

option

Warrant

Turbo

warrant

http://en.wikipedia.org/wiki/Equity_Indexhttp://en.wikipedia.org/wiki/DJIAhttp://en.wikipedia.org/wiki/NASDAQhttp://en.wikipedia.org/wiki/DJIAhttp://en.wikipedia.org/wiki/NASDAQhttp://en.wikipedia.org/wiki/Money_markethttp://en.wikipedia.org/wiki/Money_markethttp://en.wikipedia.org/wiki/Interest_rate_swaphttp://en.wikipedia.org/wiki/Interest_rate_swaphttp://en.wikipedia.org/wiki/Forward_rate_agreementhttp://en.wikipedia.org/wiki/Forward_rate_agreementhttp://en.wikipedia.org/wiki/Interest_rate_cap_and_floorhttp://en.wikipedia.org/wiki/Interest_rate_cap_and_floorhttp://en.wikipedia.org/wiki/Interest_rate_cap_and_floorhttp://en.wikipedia.org/wiki/Swaptionhttp://en.wikipedia.org/wiki/Basis_swaphttp://en.wikipedia.org/wiki/Bond_(finance)http://en.wikipedia.org/wiki/Repurchase_agreementhttp://en.wikipedia.org/wiki/Repurchase_agreementhttp://en.wikipedia.org/wiki/Bond_optionhttp://en.wikipedia.org/wiki/Bond_optionhttp://en.wikipedia.org/wiki/Stockhttp://en.wikipedia.org/wiki/Single-stock_futureshttp://en.wikipedia.org/wiki/Single-stock_futureshttp://en.wikipedia.org/wiki/Single-stock_futureshttp://en.wikipedia.org/wiki/Equity_swaphttp://en.wikipedia.org/wiki/Equity_swaphttp://en.wikipedia.org/wiki/Stock_optionhttp://en.wikipedia.org/wiki/Stock_optionhttp://en.wikipedia.org/wiki/Warrant_(finance)http://en.wikipedia.org/wiki/Turbo_warranthttp://en.wikipedia.org/wiki/Turbo_warranthttp://en.wikipedia.org/wiki/Equity_Indexhttp://en.wikipedia.org/wiki/DJIAhttp://en.wikipedia.org/wiki/NASDAQhttp://en.wikipedia.org/wiki/DJIAhttp://en.wikipedia.org/wiki/NASDAQhttp://en.wikipedia.org/wiki/Money_markethttp://en.wikipedia.org/wiki/Money_markethttp://en.wikipedia.org/wiki/Interest_rate_swaphttp://en.wikipedia.org/wiki/Interest_rate_swaphttp://en.wikipedia.org/wiki/Forward_rate_agreementhttp://en.wikipedia.org/wiki/Forward_rate_agreementhttp://en.wikipedia.org/wiki/Interest_rate_cap_and_floorhttp://en.wikipedia.org/wiki/Interest_rate_cap_and_floorhttp://en.wikipedia.org/wiki/Interest_rate_cap_and_floorhttp://en.wikipedia.org/wiki/Swaptionhttp://en.wikipedia.org/wiki/Basis_swaphttp://en.wikipedia.org/wiki/Bond_(finance)http://en.wikipedia.org/wiki/Repurchase_agreementhttp://en.wikipedia.org/wiki/Repurchase_agreementhttp://en.wikipedia.org/wiki/Bond_optionhttp://en.wikipedia.org/wiki/Bond_optionhttp://en.wikipedia.org/wiki/Stockhttp://en.wikipedia.org/wiki/Single-stock_futureshttp://en.wikipedia.org/wiki/Single-stock_futureshttp://en.wikipedia.org/wiki/Single-stock_futureshttp://en.wikipedia.org/wiki/Equity_swaphttp://en.wikipedia.org/wiki/Equity_swaphttp://en.wikipedia.org/wiki/Stock_optionhttp://en.wikipedia.org/wiki/Stock_optionhttp://en.wikipedia.org/wiki/Warrant_(finance)http://en.wikipedia.org/wiki/Turbo_warranthttp://en.wikipedia.org/wiki/Turbo_warrant

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Foreign

exchangeFX future

Option on

FX future

Currency

swapFX forward FX option

Credit n/a n/a

Credit

defaultswap

n/a

Credit

defaultoption

Other examples of underlyings are:

Economic derivatives that pay off according to economic reports ([1]) as

measured and reported by national statistical agencies

Energy derivatives that pay off according to a wide variety of indexed energy

prices. Usually classified as either physical or financial, where physical means the

contract includes actual delivery of the underlying energy commodity (oil, gas,

power, etc)

Commodities

Freight derivatives

Inflation derivatives

Insurance derivatives

Weather derivatives

Credit derivatives

FORWARDS

Forward contract is an agreement entered today between two parties namely buyer and

seller wherein buyer agrees to buy a particular asset at a particular price on a particular

date. In a forward contract, two parties irrevocably agree tosettle a trade at a future date,

for a stated price and quantity. No money changes hands at the time the trade is agreed

upon.

Suppose a buyer L and a seller S agree to do a trade in 100 grams of gold on 31 Dec 2001

at Rs.5,000/tola. Here, Rs.5,000/tola is the forward price of 31 Dec 2001 Gold.

http://en.wikipedia.org/wiki/Foreign_exchangehttp://en.wikipedia.org/wiki/Foreign_exchangehttp://en.wikipedia.org/wiki/Currency_swaphttp://en.wikipedia.org/wiki/Currency_swaphttp://en.wikipedia.org/wiki/Credit_default_swaphttp://en.wikipedia.org/wiki/Credit_default_swaphttp://en.wikipedia.org/wiki/Credit_default_swaphttp://en.wikipedia.org/wiki/Credit_default_optionhttp://en.wikipedia.org/wiki/Credit_default_optionhttp://en.wikipedia.org/wiki/Credit_default_optionhttp://en.wikipedia.org/w/index.php?title=Economic_derivative&action=edithttp://en.wikipedia.org/w/index.php?title=Economic_report&action=edithttp://biz.yahoo.com/c/e.htmlhttp://en.wikipedia.org/wiki/Energy_derivativehttp://en.wikipedia.org/wiki/Commoditieshttp://en.wikipedia.org/wiki/Freight_derivativeshttp://en.wikipedia.org/wiki/Inflation_derivativeshttp://en.wikipedia.org/w/index.php?title=Insurance_derivatives&action=edithttp://en.wikipedia.org/wiki/Weather_derivativeshttp://en.wikipedia.org/wiki/Credit_derivativeshttp://en.wikipedia.org/wiki/Foreign_exchangehttp://en.wikipedia.org/wiki/Foreign_exchangehttp://en.wikipedia.org/wiki/Currency_swaphttp://en.wikipedia.org/wiki/Currency_swaphttp://en.wikipedia.org/wiki/Credit_default_swaphttp://en.wikipedia.org/wiki/Credit_default_swaphttp://en.wikipedia.org/wiki/Credit_default_swaphttp://en.wikipedia.org/wiki/Credit_default_optionhttp://en.wikipedia.org/wiki/Credit_default_optionhttp://en.wikipedia.org/wiki/Credit_default_optionhttp://en.wikipedia.org/w/index.php?title=Economic_derivative&action=edithttp://en.wikipedia.org/w/index.php?title=Economic_report&action=edithttp://biz.yahoo.com/c/e.htmlhttp://en.wikipedia.org/wiki/Energy_derivativehttp://en.wikipedia.org/wiki/Commoditieshttp://en.wikipedia.org/wiki/Freight_derivativeshttp://en.wikipedia.org/wiki/Inflation_derivativeshttp://en.wikipedia.org/w/index.php?title=Insurance_derivatives&action=edithttp://en.wikipedia.org/wiki/Weather_derivativeshttp://en.wikipedia.org/wiki/Credit_derivatives

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The buyerL is said to be long and the sellerS is said to be short.

Once the contract has been entered into, L is obligated to pay S Rs. 500,000 on 31

Dec 2001, and take delivery of 100 tolas of gold. Similarly, S is obligated to be ready to

accept Rs.500,000 on 31 Dec 2001, and give 100 tolas of gold in exchange.

Features

Its a unique contract between two parties buyer and

seller

Forward is unique in terms of size, time and types of asset.

Price fixation may not be transparent and is publicly not

disclosed.

Forwards are traded off the exchanges and exposed to default

risk.

Forward markets tend to be afflicted by poor liquidity and from unreliability deriving

from counterparty risk (also called credit risk).

FUTURES

A futures contract is an agreement between two parties to buy or sell an asset at a certain

time in the future at a certain price. Futures contracts are special types of forward

contracts in the sense that the former are standardized exchange-traded contracts

Features Futures are organized or standardized contract in terms

of quantity, quality, delivery time and place of settlement

Three parties are involved buyer, seller and clearing

house.

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Contract expires on a pre-specified date which is called

the expiry date of the contract.

On expiry futures can be settled by delivery of the underlying

asset or cash.

Cash settlement enables the settlement of obligations arising out

of the futures/option contract in cash.

Futures are traded in organized exchanges only.

Exchange provides counter party guarantee through its clearing

house.

Participating parties have to deposit an initial cash margin as

well as the difference in traded price and actual price on dailybasis.

Determinants of future prices

Supply and demand on the secondary market determines the futures price. Price of future

refers to the rate at which the futures contract will be entered into. The basic determinants

of future prices are spot rate and other carrying costs which in turn based on rate of

interest and time involved.

On dates prior to 31 Dec 2000, the Nifty futures expiring on 31 Dec 2000 trade at

a price that purely reflect supply and demand. There is a separate order book for each

futures product which generates its own price.

Economic arguments give us a clear idea about what the price of a futuresshouldbe.

If the secondary market prices deviate from these values, it would imply the presence of

arbitrage opportunities, which (we might expect) would be swiftly exploited. But there is

nothing innate in the market which forces the theoretical prices to come about.

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OPTIONS

The right but not the obligation to buy (sell) some underlying cash instrument at a pre-

determined rate on a pre-determined expiration date in a pre-set notional amount.

An option is the right, but not the obligation, to buy or sell something at a stated date

at a stated price. A call option gives one the right to buy, a put option gives one the

right to sell.

The buyer /holder of the option purchases the right from seller / writer for a

consideration which is called a premium. The seller / writer of an option is obligated to

settle the option as per the terms of contract when the buyer /holder exercises his right.

The underlying asset could be an index, security etc.

Features

Options are organized or standardized contract

Three parties are involved buyer, seller and clearing

house.

Contract expires on a pre-specified date which is called

the expiry date of the contract.

Futures are traded in organized exchanges only.

Exchange provides counter party guarantee through its clearing

house.

Call option ( an option to buy )

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A call option is a financial contract giving the owner the right but not the obligation to

buy a pre-set amount of the underlying financial instrument at a pre-set price with a pre-

set maturity date.

Put Option ( an option to sell)

A put option is a financial contract giving the owner the right but not the obligation to sell

a pre-set amount of the underlying financial instrument at a pre-set price with a pre-set

maturity date.

European Style Option

It is an option that has to be exercisable only on expiry date An option that can be

exercised only at expiry as opposed to an American Style option that can be exercised at

any time from inception of the contract. European Style option contracts can be closed

out early, mimicking the early exercise property of American style options in most cases.

American Style Option

It is an option that can be exercisable on or before expiry date. An option that can be

exercised at any time from inception as opposed to a European Style option which can

only be exercised at expiry. Early exercise of American options may be warranted by

arbitrage. European Style option contracts can be closed out early, mimicking the early

exercise property of American style options in most cases.

Premium charged in case of American option is more compared to that of European

option. This is because, in case of American option can be exercised at any time before

expiry date.

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Naked option or covered option

A call option is covered if it is covered or written against asset owned by the option

writer. In case of excise of the call option by the option holder , the option writer can

deliver the asset or price differential. On the other hand, if the option is not covered by

physical asset, it is known as Naked option.

Differences between forward, future and option

Features Forward Future Option

Standardization No Yes Yes

Liquidity NO Yes Yes

Margin No Yes Yes

Guarantor No CH CH

Obligation to perform B&S B&S SellerDefault risk Yes No No

Parties 2 3 3

Contract closure By delivery By paying price

differentials

By paying price

differentials

Strike Price

The price at which the holder of a derivative contract exercises his right if it is economic

to do so at the appropriate point in time as delineated in the financial product's contract.

Valuation of options

Valuation depends upon number of factors viz,

1. Current price of the underlying asset

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V = VolatilityT-t = Time to maturity

We can then apply these input variables into the following set of equations to derive theprice for a European call option on a non-dividend stock:

And for a European put option on a non-dividend stock:

Where N(d1) and N(d2) are the cumulative normal distribution functions for d1 and d2,which are defined as:

d2 can be further simplified as:

By means of substitution.

In order to compute the cumulative normal distribution function, we can consider thepartial derivative of N(x).

We then apply the terms and to the equation and we obtain the solutions to theterms (as defined above). We will shortly discuss the Partial differential equationsresulting in the Black-Scholes equation and its greeks.

The Model (Dividend Paying) - Merton (1973)

For a dividend paying stock, we can alter the standard Black-Scholes model toincorporate an annual dividend yield (extended by Merton in 1973) and include the term"d" (no-subscript) as being the dividend yield per year.

The value of a call option can be calculated as:

Where d1 and d2 equals:

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And similarly, the non-dividend version of the model, we can simplify d2 as being:

The value of a put can be calculated using the put-call parity (for non dividend payingoptions):

or for dividend paying options:

Or with the full formula:

The work done by Black & Scholes in the 70's made way for further pricing ofderivatives and in particular, exotic options. The Black-Scholes partial differentialequation also enabled derivation of the 'greeks' of option pricing.

The Black-Scholes model today is used in everyday pricing of options and futures andalmost all formulas for pricing of exotic options such as barriers, compounds and asianoptions take their foundation from the Black-Scholes model.

Advantages & Limitations

Advantage: The main advantage of the Black-Scholes model is speed -- it lets youcalculate a very large number of option prices in a very short time.

Limitation: The Black-Scholes model has one major limitation: it cannot be used toaccurately price options with an American-style exercise as it only calculates the optionprice at one point in time -- at expiration. It does not consider the steps along the waywhere there could be the possibility of early exercise of an American option.

As all exchange traded equity options have American-style exercise (ie they can be

exercised at any time as opposed to European options which can only be exercised atexpiration) this is a significant limitation.

The exception to this is an American call on a non-dividend paying asset. In this case thecall is always worth the same as its European equivalent as there is never any advantagein exercising early.

Various adjustments are sometimes made to the Black-Scholes price to enable it to

approximate American option prices (eg the Fischer Black Pseudo-American

http://www.hoadley.net/options/FAQs.htm#Early%20Exercisehttp://www.hoadley.net/options/FAQs.htm#Early%20Exercise

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Advantages & Limitations

Advantage: The big advantage the binomial model has over the Black-Scholes model isthat it can be used to accurately price American options. This is because with thebinomial model it's possible to check at every point in an option's life (ie at every step ofthe binomial tree) for the possibility ofearly exercise (eg where, due to eg a dividend, or

a put being deeply in the money the option price at that point is less than its intrinsicvalue).

Where an early exercise point is found it is assumed that the option holder would elect toexercise, and the option price can be adjusted to equal the intrinsic value at that point.This then flows into the calculations higher up the tree and so on.

The on-line binomial tree graphical option calculatorhighlights those points in the treestructure where early exercise would have have caused an American price to differ from aEuropean price.

The binomial model basically solves the same equation, using a computational procedurethat the Black-Scholes model solves using an analytic approach and in doing so provides

opportunities along the way to check for early exercise for American options.Limitation: The main limitation of the binomial model is its relatively slow speed. It'sgreat for half a dozen calculations at a time but even with today's fastest PCs it's not apractical solution for the calculation of thousands of prices in a few seconds.

Relationship to the Black-Scholes model

The same underlying assumptions regarding stock prices underpin both the binomial andBlack-Scholes models: that stock prices follow a stochastic process described bygeometric brownian motion. As a result, for European options, the binomial modelconverges on the Black-Scholes formula as the number of binomial calculation steps

increases. In fact the Black-Scholes model for European options is really a special case ofthe binomial model where the number of binomial steps is infinite. In other words, thebinomial model provides discrete approximations to the continuous process underlyingthe Black-Scholes model.

Whilst the Cox, Ross & Rubinstein binomial model and the Black-Scholes model

ultimately converge as the number of time steps gets infinitely large and the length of

each step gets infinitesimally small this convergence, except for at-the-money

options, is anything but smooth or uniform. To examine the way in which the two

models converge see the on-line Black-Scholes/Binomial convergence analysis

calculator. This lets you examine graphically how convergence changes as the

number of steps in the binomial calculation increases as well as the impact on

convergence of changes to the strike price, stock price, time to expiration, volatility

and risk free interest rate.

http://www.hoadley.net/options/FAQs.htm#Early%20Exercisehttp://www.hoadley.net/options/binomialtree.aspxhttp://www.hoadley.net/options/binomialvsbs.aspxhttp://www.hoadley.net/options/binomialvsbs.aspxhttp://www.hoadley.net/options/FAQs.htm#Early%20Exercisehttp://www.hoadley.net/options/binomialtree.aspxhttp://www.hoadley.net/options/binomialvsbs.aspxhttp://www.hoadley.net/options/binomialvsbs.aspx

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For example, an investor realizing returnsfrom an equity investment can swap those

returns into less risky fixed income cash flowswithout having to liquidate the equities.

A corporation with floating ratedebt can swap that debt into a fixed rate obligation

without having to retire and reissue debt.

This is illustrated in Exhibit 1. Suppose you are receiving Cash Flow Stream A from a

counterpart. You would like to change the nature of that cash flow streamperhaps

making it less risky. Rather than attempt to renegotiate the obligation with the

counterpart, you enter into a swap agreement with another party. Under that agreement,

you swap Cash Flow Stream A for a Cash Flow Stream B, which better suits your needs.

With a Swap, You Can Change the

Character of an Asset Without Having to

Liquidate the Asset.

By entering into a swap with a third party, you can convert

a Cash Flow Stream A into a different Cash Flow Stream B.

This does now require the liquidation or renegotiation of

Cash Flow Stream A. Indeed, the counterpart paying you

Cash Flow Stream A doesn't even need to know about the

offsetting swap.

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A vanilla swap is any swap with fairly standardized provisions. The term is usually

applied to vanilla interest rate swaps orvanilla currency swaps. Vanilla swaps are

appealing because pricing tends to be transparent and transaction costs are small.

Vanilla swaps can be used to speculate or to quickly hedge the market risk of a position

without necessarily offsetting the specific cash flows of that position.

Swaps can also be customized to offset the specific cash flows of a position. Dealers

often structure such non-vanilla swaps for clients. They may charge a fee for doing so,

and pricing may reflect a large bid-ask spread (caveat emptor). An asset swap is a non-

vanilla swap customized to change the character of a specific asset. A liability swap is

such a swap customized to change the character of a specific liability.

Swaps are also categorized according to the nature of the cash flow streams being

exchanged.

interest rate swaps

currency swaps

Swaps have traded since the 1980s. The first known transaction was a currency swap

between the World Bank and IBM in August 1981

Interest rate swaps

It is the exchange of one set of cash flows for another. A pre-set index,

notional amount and set of dates of exchange determine each set of cash

flows. The most common type of interest rate swap is the exchange offixed

rate flows for floating rate flows under which cash flows of a fixed rate loan

are exchanged for those of a floating rate loan. Among these, the most

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common use a 3-month or 6-month Libor rate (or Euribor, if the currency is

the Euro) as their floating rate. These are called vanilla interest rate

swaps. There is also a liquid market for floating-floating interest rate swaps

what are known as basis swaps.

Consider an example. Two banks enter into a vanilla interest rate swap. The term is four

years. They agree to swap fixed rateUSD payments at 4.6% in exchange for 6-month

USD Libor payments. At the outset, the fixed rate payments are known. The first floating

rate payment is also known, but the rate will depend on future values of Libor.

Interest rate swaps are used for many purposes. If acorporation has borrowed money at

a floating rate of interest but would prefer to lock in a fixed rate, it can swap its floating

rate payments into fixed rate payments. This is illustrated here

Swapping Floating Debt into Fixed

By entering into a swap with a third party, a corporation can

convert floating rate payments into fixed rate payments.

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offer more favorable terms on a USD loan. The corporation could take the USD loan and

then find a third party willing to swap it into an equivalent AUD loan. In this manner, the

firm would obtain its AUD loan but at more favorable terms than it would have obtained

with a direct AUD loan. That advantage must, of course, be balanced against the

transaction costs,pre-settlement risk and settlement risk associated with the

swap. This is illustrated in Exhibit

Swapping a USD Loan Into an AUD Loan

By entering into a swap with a third party, a corporation can

convert an USD loan into an AUD loan.

WARRANTS

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A warrant, like an option, gives the holder the right but not the obligation to buy an

underlying security at a certain price, quantity and future time. However, unlike an

option, an instrument of the stock exchange, a warrant is issued by a company. The

security represented in the warrant (usually share equity) is delivered by the issuing

company instead of an investor holding the shares.

Companies will often include warrants as part of a new-issue offering to entice investors

into buying the new security. A warrant can also increase a shareholder's confidence in a

stock, if the underlying value of the security actually does increase overtime.

There are two different types of warrants: a call warrant and aput warrant. A call warrant

represents a specific number of shares that can be purchased from the issuer at a specific

price, on or before a certain date. A put warrant represents a certain amount of equity that

can be sold back to the issuer at a specified price, on or before a stated date.

Characteristics of a Warrant

Warrant certificates have stated particulars regarding the investment tool they represent.

All warrants have a specified expiry date, the last day the rights of a warrant can be

executed. Warrants are classified by their exercise style: an American warrant, for

instance, can be exercised anytime before or on the stated expiry date, and a European

warrant, on the other hand, can be carried out only on the day of expiration.

The underlying instrument the warrant represents is also stated on warrant certificates. A

warrant typically corresponds to a specific number of shares, but it can also represent a

commodity, index or a currency.

The exercise orstrike price is the amount that must be paid in order to either buy the call

warrant or sell the put warrant. Thepayment of the strike price results in a transfer of the

specified amount of the underlying instrument.

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The conversion ratio is the number of warrants needed in order to buy (or sell) one

investment tool. Therefore, if the conversion ratio to buy stock XYZ is 3:1, this means

that the holder needs three warrants in order to purchase one share. Usually, if the

conversion ratio is high, the price of the share will be low, and vice versa. (In the case of

an index warrant, an index multiplier would be stated instead. This figure would be used

to determine the amount payable to the holder upon the exercise date.)

Investing In Warrants

Warrants are transferable, quoted certificates, and they tend to be more attractive for

medium-term to long-term investment schemes. Tending to be high risk, high return

investment tools that remain largely unexploited in investment strategies, warrants are

also an attractive option forspeculators and hedgers. Transparency is high and warrants

offer a viable option for private investors as well. This is because the cost of a warrant is

commonly low, and the initial investment needed to command a large amount of equity is

actually quite small.

Advantages

Let us look at an example that illustrates one of the potential benefits of warrants. Say

that XYZ shares are currently priced on the market for $1.50 per share. In order to

purchase 1,000 shares, an investor would need $1,500. However, if the investor opted to

buy a warrant (representing one share) that was going for $0.50 per warrant, with the

same $1,500, he or she would be in possession of 3,000 shares instead!

Because the prices of warrants are low, the leverage and gearing they offer is high. This

means that there is a potential for larger capital gains and losses. While it is common for

both a share price and a warrant price to move in parallel (in absolute terms) the

percentage gain (or loss), will be significantly varied because of the initial difference in

price. Warrants generally exaggerate share price movements in terms of percentage

change.

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Let us look at another example to illustrate these points. Say that share XYZ gains $0.30

per share from $1.50, to close at $1.80. The percentage gain would be 20%. However,

with a $0.30 gain in the warrant, from $0.50 to $0.80, the percentage gain would be 60%.

In this example, the gearing factor is calculated by dividing the original share price by the

original warrant price: $1.50 / $0.50 = 3. The '3' is the gearing factor, and the higher the

number, the larger the potential for capital gains (or losses).

Warrants can offer significant gains to an investor during abull market. They can also

offer some protection to an investor during abear market. This is because as the price of

an underlying share begins to drop, the warrant may not realize as much loss because the

price, in relation to the actual share, is already low.

Disadvantages

Like any other type of investment, warrants also have their drawbacks and risks. As

mentioned above, the leverage and gearing warrants offer can be high. But these can also

work to the disadvantage of the investor. If we reverse the outcome of the example from

above and realize a drop in absolute price by $0.30, the percentage loss for the share price

would be 20%, while the loss on the warrant would be 60%!

Another disadvantage and risk to the warrant investor is that the value of the certificate

can drop to zero. If that were to happen before it is exercised, the warrant would lose any

redemption value.

Finally, a holder of a warrant does not have any voting, shareholding or dividend rights.

The investor can therefore have no say in the functioning of the company, even though he

or she is affected by any decisions made.

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Derivatives Instruments Traded in India

In the exchange-traded market, the biggest success story has been

derivatives on equityproducts. Index futures were introduced in June 2000, followed by

index options in June

2001, and options and futures on individual securities in July 2001 and

November 2001,

respectively. As of 2005, the NSE trades futures and options on 118

individual stocks and

3 stock indices. All these derivative contracts are settled by cash

payment and do not

involve physical delivery of the underlying product (which may be

costly).8

Derivatives on stock indexes and individual stocks have grown rapidly

since inception. In

particular, single stock futures have become hugely popular,

accounting for about half ofNSEs traded value in October 2005. In fact, NSE has the highest

volume (i.e. number of

contracts traded) in the single stock futures globally, enabling it to

rank 16 among world

exchanges in the first half of 2005. Single stock options are less

popular than futures.

Index futures are increasingly popular, and accounted for close to 40%

of traded value in

October 2005.

NSE launched interest rate futures in June 2003 but, in contrast to

equity derivatives,

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there has been little trading in them. One problem with these

instruments was faulty

contract specifications, resulting in the underlying interest rate

deviating erratically from

the reference rate used by market participants. Institutional investors

have preferred to

trade in the OTC markets, where instruments such as interest rate

swaps and forward rate

agreements are thriving. As interest rates in India have fallen,

companies have swapped

their fixed rate borrowings into floating rates to reduce funding costs.

Activity in OTC

markets dwarfs that of the entire exchange-traded markets, with daily

value of trading

estimated to be Rs. 30 billion in 2004 (FitchRatings, 2004).

Foreign exchange derivatives are less active than interest rate

derivatives in India, even

though they have been around for longer. OTC instruments in currency

forwards and

swaps are the most popular. Importers, exporters and banks use the

rupee forward market

to hedge their foreign currency exposure. Turnover and liquidity in this

market has been

increasing, although trading is mainly in shorter maturity contracts of

one year or less

(Gambhir and Goel, 2003). In a currency swap, banks and corporations

may swap its

rupee denominated debt into another currency (typically the US dollar

or Japanese yen),

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or vice versa. Trading in OTC currency options is still muted. There are

no exchangetraded currency derivatives in India.

Exchange-traded commodity derivatives have been trading only since

2000, and the

growth in this market has been uneven. The number of commodities

eligible for futures

trading has increased from 8 in 2000 to 80 in 2004, while the value of

trading has

increased almost four times in the same period . However, many

contracts

barely trade and, of those that are active, trading is fragmented over

multiple market

venues, including central and regional exchanges, brokerages, and

unregulated forwards

markets. Total volume of commodity derivatives is still small, less than

half the size of

equity derivatives.