In the paper, we propose a new efficient method for pricing barrier options in stochastic volatility models that can admit jumps. We use "local consistency" arguments to approximate the variance process with a finite, but sufficiently dense Markov chain. It results in a regime-switching Levy model with the dimension of the problem reduced by 1. In the regime-switching settings, we need to solve a system of partial integrodifferential equations subject to appropriate boundary conditions. To efficiently compute option prices conditioned on the variance states, we use an efficient numerical Wiener-Hopf factorization method. The method can be applied for the case of the Heston and the Bates models and other stochastic volatility Levy processes. Numerical experiments show that the approach suggested is in a good agreement with hybrid finite difference schemes and Monte Carlo simulations.
Keywords: mathematical modeling, options, numerical methods, Markov chains, stochastic volatility, Heston model