Abstract
Black-Scholes equation of dual currency exchange option pricing is a typical multi-asset option pricing model. It is important to research numerical solution of this equation. In this paper, accelerated additive operator splitting (AOS) differential algorithm is used to transform the multi-dimensional Black-Scholes equation into equivalent one-dimensional equations. Then ’explicit-implicit’ and ’implicit-explicit’ schemes will be constructed. These schemes proved to be stable and convergent unconditionally and they have second-order accuracy. Finally, the numerical example shows the effectiveness of the accelerated AOS difference algorithm. It illustrates that accelerated AOS algorithm effectively avoids the computational complexity of the high-dimensional Black-scholes equation, and dramatically improves the computational speed. Therefore, it is applicable for multi-asset option pricing.
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References
Wilmott, P., Howison, S., Dewynne, J.: The mathematics of financial derivative. Cambridge University Press, England (1996)
Jiang, L.: Mathematical Modeling and Methods of Option Pricing. Higher Education Press, Beijing (2008) (in Chinese)
Jiang, L., Xu, C., Ren, X.: Mathematical model and case analysis of the pricing of financial derivatives. Higher Education Press, Beijing (2008) (in Chinese)
Li, Y., Huang, L.: The Study of dual currency and delay option. Hunan University Press (2011) (in Chinese)
Per, L., Persson, J., von Sydow, L., Tysk, J.: Space-time adaptive finite difference method for European multi-asset options. Computers Mathematics with Applications 5(8), 1159–1180 (2007)
Yang, X., Wu, L.: A new kind of effective difference schemes for solving the payment of dividend Black-Scholes equation. In: Third International Conference on Computer and Network Technology, vol. 5, pp. 304–309 (2011)
Weickert, J., ter Haar Romeny, B.M., Viergever, M.A.: An efficient and reriable scheme for nonlinear diffusion filtering. Transaction on image Processing 7(3), 398–410 (1998)
Zhang, Y., Yang, X.: On the acceleration of AOS schemes for nonlinear diffusion filtering. Journal of Multimedia 5(6), 605–612 (2010)
Zhao, S.: Finance derivative tools pricing. China Financial and Economic. Publishing House, Beijing (2008) (in Chinese)
Zhang, S.: Finite difference numerical calculation for parabolic equation with boundary condition. Science Press, Beijing (2010) (in Chinese)
Yang, X., Liu, Y.: A Study on a New Kind of Universal Difference Schemes for Solving Black-Scholes Equation. International Journal of Information and Science System 3(2), 251–260 (2007)
Persson, J., von Sydow, L.: Pricing European Multi-asset Options Using a Space-time Adaptive FD-method, Technical report 2003-059, ISSN 1404-3203
Smereka, P.: Semi-Implicit Level Set Methods for Curvature and Surface Diffusion Motion. Journal of Scientific Computing 19(1-3) (2003)
Weickert, J.: Applications of nonlinear diffusion in image processing and computer vision, Acta Math, Univ. Comenianae LXX, 30–35 (2001)
Company, R., Gonzalez, A.L.: Numerical Solution of Modified Black-Scholes Equation Stock Options with Discrete Dividend. Mathematical and Computer Modeling 44(12), 1058–1068 (2006)
Elliott, R.J., Kopp, P.E.: Mathematics of Financial Markets. Springer, New York (1999)
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Yang, X., Zhou, G., Wang, G. (2012). Accelerated Additive Operator Splitting Differential Algorithm for Qual Currency Exchange Option Pricing Model. In: Zhao, M., Sha, J. (eds) Communications and Information Processing. Communications in Computer and Information Science, vol 289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31968-6_34
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DOI: https://doi.org/10.1007/978-3-642-31968-6_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31967-9
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