How to price derivatives
'B y far the most significant event in finance during the past decade has been the extraordinary development and expansion of financial derivatives. These instruments enhance the ability to differentiate risk and allocate it to those investors most able and willing to take it - a process that has undoubtedly improved national productivity growth and standards of living.' -- Alan Greenspan. Chairman, Board of Governors of the US Federal Reserve System.
The primary objectives of any investor are to maximise returns and minimise risks. Derivatives are contracts that originated from the need to minimise risk.
The word 'derivative' originates from mathematics and refers to a variable, which has been derived from another variable. Derivatives are so called because they have no value of their own. They derive their value from the value of some other asset, which is known as the underlying.
For example, a derivative of the shares of Infosys (underlying), will derive its value from the share price (value) of Infosys. Similarly, a derivative contract on soybean depends on the price of soybean.
Derivatives are specialised contracts which signify an agreement or an option to buy or sell the underlying asset of the derivate up to a certain time in the future at a prearranged price, the exercise price.
The contract also has a fixed expiry period mostly in the range of 3 to 12 months from the date of commencement of the contract. The value of the contract depends on the expiry period and also on the price of the underlying asset.
For example, a farmer fears that the price of soybean (underlying), when his crop is ready for delivery will be lower than his cost of production.
Let's say the cost of production is Rs 8,000 per ton. In order to overcome this uncertainty in the selling price of his crop, he enters into a contract (derivative) with a merchant, who agrees to buy the crop at a certain price (exercise price), when the crop is ready in three months time (expiry period).
In this case, say the merchant agrees to buy the crop at Rs 9,000 per ton. Now, the value of this derivative contract will increase as the price of soybean decreases and vice-a-versa.
If the selling price of soybean goes down to Rs 7,000 per ton, the derivative contract will be more valuable for the farmer, and if the price of soybean goes down to Rs 6,000, the contract becomes even more valuable.
This is because the farmer can sell the soybean he has produced at Rs .9000 per tonne even though the market price is much less. Thus, the value of the derivative is dependent on the value of the underlying.
If the underlying asset of the derivative contract is coffee, wheat, pepper, cotton, gold, silver, precious stone or for that matter even weather, then the derivative is known as a commodity derivative.
If the underlying is a financial asset like debt instruments, currency, share price index, equity shares, etc, the derivative is known as a financial derivative.
Derivative contracts can be standardized and traded on the stock exchange. Such derivatives are called exchange-traded derivatives. Or they can be customised as per the needs of the user by negotiating with the other party involved.
Such derivatives are called over-the-counter (OTC) derivatives. Continuing with the example of the farmer above, if he thinks that the total production from his land will be around 150 quintals, he can either go to a food merchant and enter into a derivatives contract to sell 150 quintals of soybean in three months time at Rs 9,000 per ton. Or the farmer can go to a commodities exchange, like the National Commodity and Derivatives Exchange Limited, and buy a standard contract on soybean.
The standard contract on soybean has a size of 100 quintals. So the farmer will be left with 50 quintals of soybean uncovered for price fluctuations.
However, exchange traded derivatives have some advantages like low transaction costs and no risk of default by the other party, which may exceed the cost associated with leaving a part of the production uncovered.
Some of the most basic forms of Derivatives are Futures, Forwards and Options.
Futures and Forwards
As the name suggests, futures are derivative contracts that give the holder the opportunity to buy or sell the underlying at a pre-specified price some time in the future.
They come in standardized form with fixed expiry time, contract size and
price. Forwards are similar contracts but customisable in terms of contract size, expiry date and price, as per the needs of the user.
Option contracts give the holder the option to buy or sell the underlying at a pre-specified price some time in the future. An option to buy the underlying is known as a Call Option.
On the other hand, an option to sell the underlying at a specified price in the future is known as Put Option.
In the case of an option contract, the buyer of the contract is not obligated to exercise the option contract. Options can be traded on the stock exchange or on the OTC market.
History of derivatives
The history of derivatives is surprisingly longer than what most people think. Some texts even find the existence of the characteristics of derivative contracts in incidents of Mahabharata. Traces of derivative contracts can even be found in incidents that date back to the ages before Jesus Christ.
However, the advent of modern day derivative contracts is attributed to the need for farmers to protect themselves from any decline in the price of their crops due to delayed monsoon, or overproduction.
The first 'futures' contracts can be traced to the Yodoya rice market in Osaka, Japan around 1650. These were evidently standardised contracts, which made them much like today's futures.
The Chicago Board of Trade (CBOT), the largest derivative exchange in the world, was established in 1848 where forward contracts on various commodities were standardised around 1865. From then on, futures contracts have remained more or less in the same form, as we know them today.
Derivatives have had a long presence in India. The commodity derivative market has been functioning in India since the nineteenth century with organized trading in cotton through the establishment of Cotton Trade Association in 1875. Since then contracts on various other commodities have been introduced as well.
Exchange traded financial derivatives were introduced in India in June 2000 at the two major stock exchanges, NSE and BSE. There are various contracts currently traded on these exchanges.
National Commodity & Derivatives Exchange Limited (NCDEX) started its operations in December 2003, to provide a platform for commodities trading.
The derivatives market in India has grown exponentially, especially at NSE. Stock Futures are the most highly traded contracts on NSE accounting for around 55% of the total turnover of derivatives at NSE, as on April 13, 2005.
Risk Management Tools
Derivatives are powerful risk management tools. To illustrate, lets take the example of an investor who holds the stocks of Infosys, which are currently trading at Rs 2,096.
Infosys options are traded on the National Stock Exchange of India, which gives the owner the right to buy (call) shares of Infosys at Rs 2,220 each (exercise price), expiring on 30th June 2005. Now if the share price of Infosys remains less than or equal to Rs 2,200, the contract would be worthless for the owner and he would lose the money he paid to buy the option, known as premium.
However, the premium is the maximum amount that the owner of the contract can lose. Hence he has limited his loss. On the other hand, if the share price of Infosys goes above Rs 2,220, the owner of the call option can exercise the contract, buy the share at Rs 2,220 and make profits by selling the share at the market price of Infosys.
The upward gain can be unlimited. Say the share price of Infosys zooms to Rs .3,000 by June 2005, the owner of the call option can buy the shares at Rs 2,220, the exercise price of the option, and then sell it in the market for Rs 3,000.
Making a profit of Rs 780 less the premium that has been paid. If the premium paid to buy the call option is say Rs 10, the profit would be Rs 770.
Derivatives are an innovation that has redefined the financial services industry and it has assumed a very significant place in the capital markets.
However, trading in derivatives is complicated and risky. The derivatives have been blamed for the loss of fortunes at many times in history. We will look at derivatives as a vehicle of investment available to investors, risks and returns associated with them, in our next article.
Nupur Hetamsaria is Visiting Research Scholar, Syracuse University, NY; and Vivek Kaul is a freelance writer.
Nupur Hetamsaria and Vivek KaulSource: www.rediff.com