Improved radial basis function methods for multi-dimensional option pricing

Pettersson, UlrikaUppsala universitet,Avdelningen för teknisk databehandling,Numerisk analys,ndim (author)

Technical report / Department of Information Technology, Uppsala University,1404-3203 ;2006-028

In this paper, we have derived a radial basis function (RBF) based method for the pricing of financial contracts by solving the Black-Scholes partial differential equation. As an example of a financial contract that can be priced with this method we have chosen the multi-dimensional European basket call option. We have shown numerically that our scheme is second order accurate in time and spectrally accurate in space for constant shape parameter. For other, non-optimal choices of shape parameter values, the resulting convergence rate is algebraic. We propose an adaptive node point placement that improves the accuracy compared with a uniform distribution. Compared with an adaptive finite difference method, the RBF method is 20-40 times faster in one and two space dimensions and has approximately the same memory requirements.

Larsson, ElisabethUppsala universitet,Avdelningen för teknisk databehandling,Numerisk analys,ndim(Swepub:uu)ela24874 (author)
Marcusson, Gunnar (author)
Persson, JonasUppsala universitet,Avdelningen för teknisk databehandling,Numerisk analys,ndim(Swepub:uu)joper677 (author)
Uppsala universitetAvdelningen för teknisk databehandling (creator_code:org_t)

By the author/editor: Pettersson, Ulri ...; Larsson, Elisabe ...; Marcusson, Gunna ...; Persson, Jonas

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Computational Ma ...

NATURAL SCIENCES: NATURAL SCIENCES; and Computer and Inf ...; and Computer Science ...

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