Option Pricing In Two-factor Markov-modulated Jump-diffusion Stochastic Volatility Models

This article investigates the valuation of options when the dynam-ic of the risky assets are governed by a two-factor Markov-modulated stochastic volatility model and a two-factor Markov-modulated jump-diffusion stochastic volatility model.The first stochastic volatility fol-lows an CIR process.The market parameters,for instance,the market interest rate,the appreciation rate and the second stochastic volatil-ity of the underlying risk asset depend on states of the economy which are modelled by a continuous-time finite-state Markov chain.For the rare events,we use a compound Poisson process with log nor-mal jump amplitude to describe the jumps.The market described by the two-factor Markov-modulated stochastic volatility model and the two-factor Markov-modulated jump-diffusion stochastic volatil-ity model are incomplete in general,the martingale is not unique.We employ the regime switching Esscher transform to determine a martingale pricing measure for valuing options.We consider the val-uation of the European and American options.A system of coupled partial differential integral equations satisfied by the European op-tion prices in derived.We also derive a decomposition result for an American put option into its European counterpart and early exercise premium.Finally,numerical illustrations are given.