Mathematical Techniques in Finance

CHAPTER 4Forwards and Futures

Derivatives, or contingent claims, are contracts based on an underlying asset or transaction. The characteristics and design of these contracts can range from an agreement to buy or sell an asset in the future at a specific price to complex structured products with complicated payoffs.

4.1 FORWARDS

We shall start with the simplest contingent claim, a forward contract. On a given trading day (), in a spot transaction between two counterparties—say exchange of money for an asset (buy/sell)—the transaction will happen at . In a forward contract, the terms of the transaction are set and agreed to at , but the transaction is shifted to some later forward date, . For example, on trade date , in a spot transaction one can buy 100 shares of a stock for its current (spot) market price, . Alternatively, on same trade date , one can agree to buy the 100 shares in 3 ...