In the previous chapters we have seen that the dynamics of stock prices is a complex subject, and that a definitive model has yet to be constructed. The complexity of the entire financial system is even greater. Not only is the trading of financial securities complex, but additional sources of complexity come from the issuing of financial contracts on those fluctuating financial securities.

An important class of financial contracts is derivatives, a financial product whose price depends upon the price of another (often more basic) financial product [22, 45, 73, 74, 122, 127]. Examples of derivatives include forward contracts, futures, options, and swaps. Derivatives are traded either in over-the-counter markets or, in a more formalized way, in specialized exchanges. In this chapter, we examine the most basic financial contracts and procedures for their rational pricing. We consider idealized markets and we discuss the underlying hypothesis used in obtaining a rational price for such a contract.

Forward contracts

The simplest derivative is a forward contract. When a forward contract is stipulated, one of the parties agrees to buy a given amount of an asset at a specified price (called the forward price or the delivery price K) on a specified future date (the delivery date T). The other party agrees to sell the specified amount of the asset at the delivery price on the delivery date. The party agreeing to buy is said to have a long position, and the party agreeing to sell is said to have a short position.