A Bayesian take on option pricing with Gaussian processes
This addresses the calibration problem in finance for option pricing, offering a probabilistic method that is incremental over existing approaches.
The paper tackles the non-trivial calibration of local volatility models for option pricing by introducing a novel Bayesian inference approach with Gaussian process priors, resulting in a rich representation of the volatility function with probabilistic uncertainty and application to S&P 500 market data.
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.