Comparison of numerical schemes on multi-dimensional Black-Scholes equations

摘要

In this paper, we study numerical schemes for solving multi-dimensional option pricing problem. We compare the direct solving meth-od and the emph{Operator Splitting Method}(OSM) by using finite difference approximations. By varying parameters of the emph{Black-Scholes equations} for the maximum on the call option problem, we observed that there is no significant difference between the two methods on the convergence criterion except a huge difference in computation cost. Therefore, the two methods are compatible in practice and one can improve the time efficiency by combining the OSM with parallel computation technique. We show numerical examples including the emph{Equity-Linked Security}(ELS) pricing based on either two assets or three assets by using the OSM with the emph{Monte-Carlo Simulation} as the benchmark.