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Open AccessArticle

Iterative Speedup by Utilizing Symmetric Data in Pricing Options with Two Risky Assets

1
Department of Mathematics & Finance, Gachon University, 1342 Seongnamdaero, Sujeong-gu, Seongnam-si, Gyeonggi-do 13120, Korea
2
Department of Risk Management, Kiwoom Securities Co., Ltd., 18 Yeouinaru-ro 4(sa)-gil, Yeongdeungpo-gu, Seoul 07331, Korea
*
Author to whom correspondence should be addressed.
Academic Editors: Doo-Soon Park and Shu-Ching Chen
Symmetry 2017, 9(1), 12; https://doi.org/10.3390/sym9010012
Received: 29 September 2016 / Revised: 9 January 2017 / Accepted: 13 January 2017 / Published: 21 January 2017
(This article belongs to the Special Issue Scientific Programming in Practical Symmetric Big Data)
The Crank–Nicolson method can be used to solve the Black–Scholes partial differential equation in one-dimension when both accuracy and stability is of concern. In multi-dimensions, however, discretizing the computational grid with a Crank–Nicolson scheme requires significantly large storage compared to the widely adopted Operator Splitting Method (OSM). We found that symmetrizing the system of equations resulting from the Crank–Nicolson discretization help us to use the standard pre-conditioner for the iterative matrix solver and reduces the number of iterations to get an accurate option values. In addition, the number of iterations that is required to solve the preconditioned system, resulting from the proposed iterative Crank–Nicolson scheme, does not grow with the size of the system. Thus, we can effectively reduce the order of complexity in multidimensional option pricing. The numerical results are compared to the one with implicit Operator Splitting Method (OSM) to show the effectiveness. View Full-Text
Keywords: Black–Scholes equation; Operator Splitting Method (OSM); Crank–Nicolson; iterative solver Black–Scholes equation; Operator Splitting Method (OSM); Crank–Nicolson; iterative solver
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Pak, D.; Han, C.; Hong, W.-T. Iterative Speedup by Utilizing Symmetric Data in Pricing Options with Two Risky Assets. Symmetry 2017, 9, 12.

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