Fast fourier transform option pricing: efficient approximation methods under multi-factor stochastic volatility and jumps

J. P. F. Charpin; M. Cummins

doi:10.1007/978-1-4614-3433-7_7

Fast fourier transform option pricing: efficient approximation methods under multi-factor stochastic volatility and jumps

J. P. F. Charpin, M. Cummins

Accounting And Finance

Research output: Chapter in Book/Report/Conference proceeding › Chapter

1 Citation (Scopus)

Abstract

Fourier option-pricing methods are popular due to the dual benefits of wide applicability and computational efficiency. The literature tends to focus on a limited subset of models with analytic conditional characteristic functions (CCFs). Models that require numerical solutions of the CCF undermine the efficiency of Fourier methods. To tackle this problem, an ad hoc approximate numerical method was developed that provide CCF values accurately much faster than traditional methods. This approximation, based on averaging, Taylor expansions and asymptotic behaviour of the CCFs, is presented and tested for a range of affine models, with multi-factor stochastic volatility and jumps. The approximation leads to average run-time accelerations up to 50 times those of other numerical implementations, with very low absolute and relative errors reported.

Original language	English
Title of host publication	Topics in Numerical Methods for Finance
Editors	Mark Cummins, Finbarr Murphy, John J.H. Miller
Place of Publication	New York
Publisher	Springer
Pages	115-137
Number of pages	23
ISBN (Print)	9781461434320, 9781461434320
DOIs	https://doi.org/10.1007/978-1-4614-3433-7_7
Publication status	Published - 1 Jan 2012

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	19
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Funding

Jean Charpin acknowledges the support of the Mathematics Applications Consortium for Science and Industry ( www.macsi.ul.ie ) funded by the Science Foundation Ireland Mathematics Initiative grant 06/MI/005.

Keywords

fast Fourier transform
option price
stochastic volatility
strike price
saddlepoint approximation

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10.1007/978-1-4614-3433-7_7

Cite this

Charpin, J. P. F., & Cummins, M. (2012). Fast fourier transform option pricing: efficient approximation methods under multi-factor stochastic volatility and jumps. In M. Cummins, F. Murphy, & J. J. H. Miller (Eds.), Topics in Numerical Methods for Finance (pp. 115-137). (Springer Proceedings in Mathematics and Statistics; Vol. 19). Springer. https://doi.org/10.1007/978-1-4614-3433-7_7

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abstract = "Fourier option-pricing methods are popular due to the dual benefits of wide applicability and computational efficiency. The literature tends to focus on a limited subset of models with analytic conditional characteristic functions (CCFs). Models that require numerical solutions of the CCF undermine the efficiency of Fourier methods. To tackle this problem, an ad hoc approximate numerical method was developed that provide CCF values accurately much faster than traditional methods. This approximation, based on averaging, Taylor expansions and asymptotic behaviour of the CCFs, is presented and tested for a range of affine models, with multi-factor stochastic volatility and jumps. The approximation leads to average run-time accelerations up to 50 times those of other numerical implementations, with very low absolute and relative errors reported.",

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Charpin, JPF & Cummins, M 2012, Fast fourier transform option pricing: efficient approximation methods under multi-factor stochastic volatility and jumps. in M Cummins, F Murphy & JJH Miller (eds), Topics in Numerical Methods for Finance. Springer Proceedings in Mathematics and Statistics, vol. 19, Springer, New York, pp. 115-137. https://doi.org/10.1007/978-1-4614-3433-7_7

Fast fourier transform option pricing: efficient approximation methods under multi-factor stochastic volatility and jumps. / Charpin, J. P. F.; Cummins, M.
Topics in Numerical Methods for Finance. ed. / Mark Cummins; Finbarr Murphy; John J.H. Miller. New York: Springer, 2012. p. 115-137 (Springer Proceedings in Mathematics and Statistics; Vol. 19).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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T1 - Fast fourier transform option pricing

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AU - Cummins, M.

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N2 - Fourier option-pricing methods are popular due to the dual benefits of wide applicability and computational efficiency. The literature tends to focus on a limited subset of models with analytic conditional characteristic functions (CCFs). Models that require numerical solutions of the CCF undermine the efficiency of Fourier methods. To tackle this problem, an ad hoc approximate numerical method was developed that provide CCF values accurately much faster than traditional methods. This approximation, based on averaging, Taylor expansions and asymptotic behaviour of the CCFs, is presented and tested for a range of affine models, with multi-factor stochastic volatility and jumps. The approximation leads to average run-time accelerations up to 50 times those of other numerical implementations, with very low absolute and relative errors reported.

AB - Fourier option-pricing methods are popular due to the dual benefits of wide applicability and computational efficiency. The literature tends to focus on a limited subset of models with analytic conditional characteristic functions (CCFs). Models that require numerical solutions of the CCF undermine the efficiency of Fourier methods. To tackle this problem, an ad hoc approximate numerical method was developed that provide CCF values accurately much faster than traditional methods. This approximation, based on averaging, Taylor expansions and asymptotic behaviour of the CCFs, is presented and tested for a range of affine models, with multi-factor stochastic volatility and jumps. The approximation leads to average run-time accelerations up to 50 times those of other numerical implementations, with very low absolute and relative errors reported.

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KW - stochastic volatility

KW - strike price

KW - saddlepoint approximation

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T3 - Springer Proceedings in Mathematics and Statistics

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PB - Springer

CY - New York

ER -

Fast fourier transform option pricing: efficient approximation methods under multi-factor stochastic volatility and jumps

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