Simulating the Evolution of the Implied Distribution

Abstract

Motivated by the implied stochastic volatility literature (Britten-Jones and Neuberger (1998), Derman and Kani (1997), Ledoit and Santa-Clara (1998)) this paper proposes a new and general method for constructing smile-consistent stochastic volatility models. The method is developed by recognizing that option pricing and hedging can be accomplished via the simulation of the implied risk neutral distribution. We devise an algorithm for the simulation of the implied distribution, when the first two moments change over time. The algorithm can be implemented easily, and it is based on an economic interpretation of the concept of mixture of distributions. It can also be generalized to cases where more complicated forms for the mixture are assumed. Implied Distribution, Mixture of Distributions, Simulation

Keywords: Smile-consistent stochastic volatility models,

JEL Classification: G13