Bayesian inference approach to inverse problem in a fractional option pricing model

Abstract

As is well known to us, the Black-Scholes (B-S) model is an important and useful mathematical model for pricing a European options contract. However, because some strict assumptions in this model are not consistent with the real financial market, there are many limitations in practical applications. This paper investigates the inverse option problems (IOP) in a fractional option pricing model, which is derived from the finite moment log-stable (FMLS) model. We identify the model coefficients such as tail index α and the implied volatility σ from the measured data by using three statistical inversion schemes which are well known as Markov Chain Monte Carlo (MCMC) algorithm, slice sampling algorithm and Hamiltonian/hybrid Monte Carlo (HMC) algorithm. Our numerical tests indicate that these Bayesian inference approaches can recover the unknown coefficients well.