A FAST AND ROBUST NUMERICAL METHOD FOR OPTION PRICES AND GREEKS IN A JUMP-DIFFUSION MODEL

Abstract

We propose a fast and robust finite difference method for Merton`s jump diffusion model, which is a partial integro-differential equation. To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. Also, we use non-uniform grids to increase efficiency. We present numerical experiments such as evaluation of the option prices and Greeks to demonstrate a performance of the proposed numerical method. The computational results are in good agreements with the exact solutions of the jump-diffusion model.