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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.
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참고문헌 (10)
참고문헌 신청
D. J. Duffy / 2006 / Finite Di erence Methods in Financial Engineering / Wiley
E. G. Haug / 2006 / The Complete Guide To Option Pricing Formulas / McGraw-Hill
J. B. Perot / 1993 / An analysis of the fractional step method / J. Comput. Phys 108 (1) : 51 ~ 58
J. W. Thomas / 1995 / Numerical Partial Differential Equations: Finite Difference Methods / Springer
N. N. Yanenko / 1971 / The Method of Fractional Steps / Springer
E. G. Haug / 2006 / The Complete Guide To Option Pricing Formulas / McGraw-Hill
J. B. Perot / 1993 / An analysis of the fractional step method / J. Comput. Phys 108 (1) : 51 ~ 58
J. W. Thomas / 1995 / Numerical Partial Differential Equations: Finite Difference Methods / Springer
N. N. Yanenko / 1971 / The Method of Fractional Steps / Springer
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