Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(6): 2035-2051

Printed November 1, 2013

https://doi.org/10.4134/BKMS.2013.50.6.2035

Copyright © The Korean Mathematical Society.

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

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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