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by R. Zvan, P. A. Forsyth, K. Vetzal
Journal of Computational Finance
ftp://cs-archive.uwaterloo.ca/cs-archive/CS-96-28/CS-96-28.ps.Z
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Abstract:
We explore the pricing of Asian options by numerically solving the the associated partial differential equations. We demonstrate that numerical PDE techniques commonly used in finance for standard options are inaccurate in the case of Asian options and illustrate modifications which alleviate this problem. In particular, the usual methods generally produce solutions containing spurious oscillations. We adapt flux limiting techniques originally developed in the field of computational fluid dynamics in order to rapidly obtain accurate solutions. We show that flux limiting methods are total variation diminishing (and hence free of spurious oscillations) for non-conservative PDEs such as those typically encountered in finance, for fully explicit, and fully and partially implicit schemes. We also modify the van Leer flux limiter so that the second-order total variation diminishing property is preserved for non-uniform grid spacing. 1
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