A Bayesian take on option pricing with Gaussian processes

TL;DR

This paper introduces a Bayesian approach using Gaussian processes for local volatility modeling in option pricing, providing a probabilistic framework for calibration and uncertainty quantification based on market data.

Contribution

It presents a novel Bayesian inference method with Gaussian process priors for local volatility, enhancing calibration and uncertainty estimation in option pricing models.

Findings

Effective calibration to S&P 500 data

Rich probabilistic representation of local volatility

Quantified uncertainty in option pricing

Abstract

Local volatility is a versatile option pricing model due to its state dependent diffusion coefficient. Calibration is, however, non-trivial as it involves both proposing a hypothesis model of the latent function and a method for fitting it to data. In this paper we present novel Bayesian inference with Gaussian process priors. We obtain a rich representation of the local volatility function with a probabilistic notion of uncertainty attached to the calibrate. We propose an inference algorithm and apply our approach to S&P 500 market data.