Option Pricing with Infinitely Divisible Distributions

Abstract

This paper presents new option pricing formulas that generalize the Black-Scholes [1973] model by incorporating an extra skewness parameter. These formulas are derived in pricing models where one cannot price options by replicating their payoffs with stock and bond portfolios. Instead there is a unique set of homogeneous path-independent arbitrage-free contingent claim prices. Examples include negative-binomial and inverse-binomial generalizations of Cox, Ross, and Rubinstein's [1979] binomial formula. This paper extends these option formulas to infinitely divisible continuous time processes by taking limits of the discrete models. The continuous time processes include the Black-Scholes [1973] diffusion case in addition to finite variance jump processes and infinite variance stable processes. The valuation theory extends to American options and other path-dependent claims.

JEL Classification: G13