Methods for Extracting the Implied Distributions in Option Prices

This paper examines a variety of methods for extracting implied probability distributions from option prices. I critically analyze and extend approaches suggested by Derman and Kani (1994), Rubinstein (1994) and Shimko (1993). I develop a new simulated method of moments estimation procedure. I parameterize the underlying asset return process as a mixture of log-normal densities, price the options using Monte Carlo methods, and compare these simulated price ``moments'' to the market data. The mixture density is quite promising in explaining the volatility smile. I compare these estimators in two data exercises. One is a standard Black-Scholes model, and the other a model that display a volatility smile. I find that the simulated moments method proves to be the most robust.