Option pricing from a Bayesian perspective using the Dirichlet process.

Abstract

There exist a wide variety of models for the pricing of derivative securities such as call and put options. This thesis introduces an alternative option pricing methodology based on a Monte Carlo simulation of the Dirichlet process. The model is constructed in a Bayesian framework, using the properties initially described by Ferguson [10, 11]. Given historical stock prices up to the present, we simulate various sample paths for future stock prices. This procedure is conducted under the hypothesis that the prior distribution of the stock returns has a Dirichlet process structure. The predicted option prices are then computed by averaging the option prices obtained for each simulated sample path. A considerable advantage of this model is that random draws are sampled from a mixed distribution which consists of a prior guess and the empirical process based on the initial random sample of stock returns. The methodology is applied to various examples throughout this thesis. The results are compared with some existing models, including exponential Brownian motion and the Black-Scholes option pricing formula.