Option Pricing with Infinitely Divisible Distributions
Steve Heston, Washington University

The project paper analyzes option pricing for “unhedgeable” processes. Such processes include processes in which discrete jumps can take place. The paper shows that there is a unique set of homogenous-path independent arbitrage-free contingent claim prices. Option pricing formulas for infinitely divisible continuous time processes are derived by taking limits of discrete models. The results include the Black-Scholes model, and a two parameter generalization of the model that depends on both volatility and skewness. (Accepted Winter 1996.)