Stochastic Finance, 4th Edition

1.3Derivative securities

In real financial markets, not only the primary assets are traded. There is also a large variety of securities whose payoff depends in a nonlinear way on the primary assets S0, S1, . . . , Sd, and sometimes also on other factors. Such financial instruments are usually called options, contingent claims, derivative securities, or just derivatives.

Example 1.20. Under a forward contract, one agent agrees to sell to another agent an asset at time 1 for a price K which is specified at time 0. Thus, the owner of a forward contract on the ith asset gains the difference between the actual market price Si and the delivery price K if Si is larger than K at time 1. If Si < K, the owner loses the amount K − Si to the issuer of the ...