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Improved radial basis function methods for multi-dimensional option pricing
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- Pettersson, Ulrika (author)
- Uppsala universitet,Avdelningen för teknisk databehandling,Numerisk analys,ndim
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- Larsson, Elisabeth (author)
- Uppsala universitet,Avdelningen för teknisk databehandling,Numerisk analys,ndim
- Marcusson, Gunnar (author)
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- (creator_code:org_t)
- 2006
- English.
- Series: Technical report / Department of Information Technology, Uppsala University, 1404-3203 ; 2006-028
- Reports (other academic/artistic)
Abstract
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Computer Sciences (hsv//eng)
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- rap (subject category)
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