Markov Chain Approximation method for Pricing Barrier Options with Stochastic Volatility and Jump

The purpose of this paper is to provide an efficient pricing method for barrier option with stochastic volatility and jump risk. First, by constructing a nonuniform variance grid and using local consistency arguments, this paper approximates the stochastic volatility jump-diffusion model with a finite and dense Markov chain; Then, the paper computes the rate matrix of the Markov chain by solving a system induced by local consistency conditions; And then the paper provides the character function of the Markov chain. At last, using Markov chain approximation method and Fourier transform technique, the paper obtains numerical solutions for barrier options pricing. Numerical results show that comparing with the Monte Carlo simulation, the proposed pricing technique is accurate, fast and easy to implement.