Comparison of numerical schemes on multi-dimensional Black-Scholes equations
Bull. Korean Math. Soc. 2013 Vol. 50, No. 6, 2035-2051
Printed November 1, 2013
Joonglee Jo and Yongsik Kim
Ajou University, Ajou University
Abstract : 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.
Keywords : Black-Scholes equation, operator splitting method, equity-linked security, parallel computation, message passing interface
MSC numbers : Primary 65M06, 91G20, 91G60
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