Unbiased Simulation Estimators for Jump-Diffusions

Guanting Chen, Alexander D. Shkolnik, Kay Giesecke

Abstract: We develop and analyze an unbiased Monte Carlo estimator for a functional of a one-dimensional jump-diffusion process with a state-dependent drift, volatility, jump intensity and jump size. The approach combines a change of measure to sample the jumps with the parametrix method to simulate the diffusions. Under regularity conditions on the coefficient functions as well as the functional, we prove the unbiasedness and the finite variance property of the estimator. Numerical experiments illustrate the performance of the scheme.