Market Risk Analysis Volume III: Pricing, Hedging and Trading Financial Instruments

III.3

Options

III.3.1 INTRODUCTION

An option is a contract that gives the purchaser the right to enter into another contract during a particular period of time. We call it a derivative because it is a contract on another contract. The underlying contract is a security such as a stock or a bond, a financial asset such as a currency, or a commodity, or an interest rate.¹ The option contract that gives the right to buy the underlying is termed a call option, and the right to sell the underlying is termed a put option. Interest rate options give the purchaser the right to pay or receive an interest rate, and in the case of swaptions the underlying contract is a swap.

Options began trading in the seventeenth century, when the ability to purchase share options contributed to the South Sea bubble and options on tulip bulbs were traded in Amsterdam. The first exchange listed options were on the Marché à Prime in France. About 10% of trading on shares was carried out on this market, where shares were sold accompanied with a 3-month at-the-money put option.² The existence of this market prompted Louis Bachelier, in 1900, to derive a formula for the evaluation of options based on arithmetic Brownian motion.³ The first independently traded exchange listed options were on commodities: e.g. gold options in Germany during the 1930s. But these options were not popular because of the difficulty of valuing them, plus the absence of margining requirements by the exchange.

Then in 1973 two important ...