Derivatives Of Financial Derivatives

The purpose of this report is to conduct an analysis on the various methods of pricing certain financial derivatives, as well as hedging European options.

A derivative is a security whose payoff is dependent on the fluctuating value of one or more underlying assets. Over the past decade or so derivatives have become very important financial instruments for the transfers of financial risk. Derivatives are generally used to hedge risk exposure or to speculate by taking on additional risk in the hope of exploiting this risk for profit. Derivatives can be traded directly on financial exchanges or over the counter with investment banks. It is also common for many financial products to have derivatives embedded in their design, for example many investment contracts offered by insurance companies offer some sort of guarantee where the initial investment (and possibly future contributions) are guaranteed. This can be seen as a put option on the investment performance of the fund. Determining the price/value of these options/guarantees is essential to the success of these products. For example, the demise of Equitable Life (the oldest life insurer in the UK) can be put down to poor valuation of guaranteed rates they had offered on certain annuity products – they subsequently closed to new business in 2000. In this report, we will be analysing derivatives such as forward and future contracts, as well as various options.

A forward contract on a stock or commodity is a contract to buy/sell a specific amount of that stock or commodity for a specific price (known as the delivery price K) on a specified future date (maturity T). Forward contracts are generally used to lock in the price of a commodity and eliminate the uncertainty surroundin...

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...ecified price. An American option can be exercised at any time prior to expiry while a European option can only be exercised at expiry.

A European call option gives the buyer the right but not the obligation to buy the underlying at a prescribed price K (the strike price) at maturity time T. A European put option gives the buyer the right but not the obligation to sell the underlying at a prescribed price K at maturity time T. The payoff from an option is always non-negative and for European options is determined by the difference between the strike price and stock price at maturity T. American options have similar payoffs except we must take into account that American options can be exercised at any time up to expiry. In the following sections we will discuss the methods used for pricing options. We will also analyse various ways of hedging European options.