Solutions to an integro-differential equations by Regime-Switching Le´vy process in Le´vy market

We study the numerical solutions for an integro-diferential parabolic problem modeling a process with jumps and stochastic volatility in Financial Mathematics. We present two general algorithms to calculate numerical solutions. The algorithms are implemented in PDE2D, as a general purpose and as partial differential equation solver. We use The regime-switching Levy model to combine jump-diffusion under the form of a Levy process, and Markov regime-switching where all parameters depend on the value of a continuous time Markov chain

Keywords:

integro-diferential equation , numerical methods , option valuation.