A General Control Variate Method for Lévy Models in Finance
This study proposes a new control variate method for Lévy models in finance. Our method generates a process of the control variate whose initial and terminal values coincide with those of the target Lévy model process, with both processes being driven by the same Brownian motion in the simulation. These features efficiently reduce the variance of the Monte Carlo simulation. As a typical application of this method, we provide the calculation scheme for pricing path-dependent exotic options.
We use numerical experiments to examine the validity of our method for both continuously and discretely monitored path-dependent options under variance gamma and normal inverse Gaussian models.