A fourier-based valuation method for bermudan and barrier options under heston's model

Fang Fang; Cornelis W. Oosterlee

doi:10.1137/100794158

A fourier-based valuation method for bermudan and barrier options under heston's model

Fang Fang^*, Cornelis W. Oosterlee

^*Corresponding author for this work

extern

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

Abstract

We develop an efficient Fourier-based numerical method for pricing Bermudan and discretely monitored barrier options under the Heston stochastic volatility model. The two-dimensional pricing problem is dealt with by a combination of a Fourier cosine series expansion, as in [F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826-848, F. Fang and C. W. Oosterlee, Numer. Math., 114 (2009), pp. 27-62], and high-order quadrature rules in the other dimension. Error analysis and experiments confirm a fast error convergence.

Original language	English
Pages (from-to)	439-463
Number of pages	25
Journal	SIAM Journal on Financial Mathematics
Volume	2
Issue number	1
DOIs	https://doi.org/10.1137/100794158
Publication status	Published - 2011
Externally published	Yes

Keywords

Bermudan options
Fourier cosine expansions
Heston model
Numerical quadrature

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10.1137/100794158

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abstract = "We develop an efficient Fourier-based numerical method for pricing Bermudan and discretely monitored barrier options under the Heston stochastic volatility model. The two-dimensional pricing problem is dealt with by a combination of a Fourier cosine series expansion, as in [F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826-848, F. Fang and C. W. Oosterlee, Numer. Math., 114 (2009), pp. 27-62], and high-order quadrature rules in the other dimension. Error analysis and experiments confirm a fast error convergence.",

keywords = "Bermudan options, Fourier cosine expansions, Heston model, Numerical quadrature",

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AU - Oosterlee, Cornelis W.

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AB - We develop an efficient Fourier-based numerical method for pricing Bermudan and discretely monitored barrier options under the Heston stochastic volatility model. The two-dimensional pricing problem is dealt with by a combination of a Fourier cosine series expansion, as in [F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826-848, F. Fang and C. W. Oosterlee, Numer. Math., 114 (2009), pp. 27-62], and high-order quadrature rules in the other dimension. Error analysis and experiments confirm a fast error convergence.

KW - Bermudan options

KW - Fourier cosine expansions

KW - Heston model

KW - Numerical quadrature

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JO - SIAM Journal on Financial Mathematics

JF - SIAM Journal on Financial Mathematics

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ER -

A fourier-based valuation method for bermudan and barrier options under heston's model

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Keywords

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