Fourier Transform Methods for Regime-Switching Jump-Diffusions and the Pricing of Forward Starting Options

TL;DR

This paper develops Fourier transform techniques for pricing options under a regime-switching jump-diffusion model driven by a Markov chain, and provides a closed-form solution for forward starting options, with numerical illustrations.

Contribution

It introduces Fourier methods for regime-switching jump-diffusions and derives a closed-form solution for forward starting options, extending to stochastic volatility models.

Findings

Efficient Fourier-based pricing for regime-switching jump-diffusions.

Closed-form solution for forward starting options.

Numerical results demonstrating model applicability.

Abstract

In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strike to efficiently calculate the value of various types of options and as a concrete example of application, we present some numerical results within a two-state regime switching version of the Merton jump-diffusion model. Then we develop a closed-form solution to the problem of pricing a Forward Starting Option and use this result to approximate the value of such a derivative in a general stochastic volatility framework.