Two-dimensional Fourier cosine series expansion method for pricing financial options

M. J. Ruijter; C. W. Oosterlee

doi:10.1137/120862053

Two-dimensional Fourier cosine series expansion method for pricing financial options

M. J. Ruijter^*, C. W. Oosterlee

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

The COS method for pricing European and Bermudan options with one underlying asset was developed in [F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31(2008), pp. 826-848] and [F. Fang and C. W. Oosterlee, Numer. Math., 114(2009), pp. 27-62]. In this paper, we extend the method to higher dimensions, with a multidimensional asset price process. The algorithm can be applied to, for example, pricing two-color rainbow options but also to pricing under the popular Heston stochastic volatility model. For smooth density functions, the resulting method converges exponentially in the number of terms in the Fourier cosine series summations; otherwise we achieve algebraic convergence. The use of an FFT algorithm, for asset prices modeled by Lévy processes, makes the algorithm highly efficient. We perform extensive numerical experiments.

Original language	English
Pages (from-to)	B642-B671
Journal	SIAM Journal on Scientific Computing
Volume	34
Issue number	5
DOIs	https://doi.org/10.1137/120862053
Publication status	Published - 2012
Externally published	Yes

Keywords

Basket options
European and Bermudan options
Fourier cosine expansion method
Heston dynamics
Lévy process
Two-color rainbow options

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10.1137/120862053

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abstract = "The COS method for pricing European and Bermudan options with one underlying asset was developed in [F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31(2008), pp. 826-848] and [F. Fang and C. W. Oosterlee, Numer. Math., 114(2009), pp. 27-62]. In this paper, we extend the method to higher dimensions, with a multidimensional asset price process. The algorithm can be applied to, for example, pricing two-color rainbow options but also to pricing under the popular Heston stochastic volatility model. For smooth density functions, the resulting method converges exponentially in the number of terms in the Fourier cosine series summations; otherwise we achieve algebraic convergence. The use of an FFT algorithm, for asset prices modeled by L{\'e}vy processes, makes the algorithm highly efficient. We perform extensive numerical experiments.",

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Two-dimensional Fourier cosine series expansion method for pricing financial options

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