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Fast Fourier Transform Option Pricing: Efficient Approximation Methods Under Multi-Factor Stochastic Volatility and Jumps

  • J. P. F. CharpinEmail author
  • M. Cummins
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 19)

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.

Keywords

Fast Fourier Transform Option Price Stochastic Volatility Strike Price Saddlepoint Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

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.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, Mathematics Application Consortium for Science and Industry (MACSI), College of Science and EngineeringUniversity of LimerickLimerickIreland
  2. 2.DCU Business SchoolDublin City UniversityDublin 9Ireland

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