Option pricing in Markov-modulated exponential Lévy models with stochastic interest rates

Abstract

In this paper, we consider the problem of pricing European options, namely vanilla options, binary options and exchange options, whose underlying assets prices dynamics follow Markovian regime switching exponential Lévy models with stochastic interest rates, where the stochastic interest rates are driven by Markovian regime switching Hull–White process. We obtain the integral representations of the option prices by Fourier transform (FT) technique and some numerical results of 3-state case for Merton jump-diffusion model by the fast Fourier transform (FFT) approach. The numerical results show that the pricing formulas are considerably accurate and easy to be implemented.