Bayesian Implied Random Trees

Abstract

The price of an Option is equal to the discounted expected payoff function under a suitable ‘risk-neutral’ measure. The importance of understanding this risk neutral measure for asset pricing has led to many competing methods for inference. We propose a Bayesian implied random tree approach to avoid model miss-specifications that can come from standard approaches. The model builds a generalized binomial tree along the lines of Rubinstein (1994), based on a Quadrature model with a finite number of support points for the risk neutral distribution at maturity. Our approach is straightforward, flexible, and can accommodate complicated path-dependent options, such as a collection of American options with multiple time to maturities. We demonstrate our approach via a simulation study. For numerical purposes, we provide efficient Gibbs sampling with slice sampling in the case that only European options with one time to maturity are used. In an empirical analysis using S&P 500 index options, our method requires only a small number of support points to perform as well as the most competing methods in terms of model fit. This is a joint work with Professor John Liechty at Pennsylvania State University.