A general control variate method for option pricing under Lvy processes
We present a general control variate method for simulating path dependent options under Lvy processes. It is based on fast numerical inversion of the cumulative distribution functions and exploits the strong correlation of the payoff of the original option and the payoff of a similar option under geometric Brownian motion. The method is applicable for all types of Lvy processes for which the probability density function of the increments is available in closed form. Numerical experiments confirm that our method achieves considerable variance reduction for different options and Lvy processes. We present the applications of our general approach for Asian, lookback and barrier options under variance gamma, normal inverse Gaussian, generalized hyperbolic and Meixner processes.
control variate option pricing lvy processes numerical inversion finance monte carlo simulation