Numerical Solution of Jump-Diffusion SDEs

This paper formulates and analyzes a discretization scheme for a jump-diffusion process with general state-dependent drift, volatility, jump intensity, and jump size. The jump times of the process are constructed as time-changed Poisson arrival times, and the Euler method is used to generate the process between the jump epochs. Under conditions on the coefficient functions specifying the process, the scheme is proved to converge weakly with order one for functions with polynomial growth. The use of higher-order methods between the jumps does generally not improve the weak order of convergence. Numerical experiments illustrate the results