Option pricing under a jump-telegraph diffusion model with jumps of random size

摘要

We present a finite difference method to solve a system of two Partial-Integro Differential Equations which arise from pricing an option under a Jump-Telegraph Diffusion Model for the underlying asset, considering the risk-neutral valuation formula under an equivalent martingale measure. This system is fully discretized using an Implicit-Explicit two-time level scheme and quadrature formulas. The resulting two tridiagonal algebraic linear systems are solved recursively using the Thomas Algorithm. Some numerical results are presented and the numerical order of convergence for the method is estimated. Finally, the robustness of the method is validated against an exact solution obtained for a perturbed problem.