A hybrid computational approach for option pricing

Abstract

In this paper, we propose a novel numerical approach for option pricing with the combination of the MC (Monte Carlo) simulation and the PDE (partial differential equation) approach. Our motivation originates from the fact that within a finite life time of an option contract, the underlying price as well as the range of volatility are expected to vary within a relatively small region centered around the current value of the underlying and the volatility and hence there is no need to compute option prices for the underlying and the volatility values beyond this region. Thus, our hybrid approach takes the advantage of both the MC simulation and PDE approach to form an approach that takes the MC simulation as a special case with the region being extremely small and the PDE approach as another special case with the region being extremely large. Through numerical experiments, we demonstrate that such a hybrid approach enhances computational efficiency, while maintaining the same level of accuracy when either the MC simulation or the PDE approach is used alone for the option prices computed within a suitably chosen interested region.