A Bayesian nonparametric approach to option pricing

Abstract

Accurately modeling the implied volatility surface is of great importance to option pricing, trading and hedging. In this paper, we investigate the use of a Bayesian nonparametric approach to fit and forecast the implied volatility surface with observed market data. More specifically, we explore Gaussian Processes with different kernel functions characterizing general covariance functions. We also obtain posterior distributions of the implied volatility and build confidence intervals for the predictions to assess potential model uncertainty. We apply our approach to market data on the S&P 500 index option market in 2018, analyzing 322,983 options. Our results suggest that the Bayesian approach is a powerful alternative to existing parametric pricing models.