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A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions

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  • Fang, Fang
  • Oosterlee, Kees

Abstract

Here we develop an option pricing method for European options based on the Fourier-cosine series, and call it the COS method. The key insight is in the close relation of the characteristic function with the series coefficients of the Fourier-cosine expansion of the density function. In most cases, the convergence rate of the COS method is exponential and the computational complexity is linear. Its range of application covers different underlying dynamics, including L\'evy processes and Heston stochastic volatility model, and various types of option contracts. We will present the method and its applications in two separate parts. The first one is this paper, where we deal with European options in particular. In a follow-up paper we will present its application to options with early-exercise features.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 9319.

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Date of creation: 10 Mar 2008
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Handle: RePEc:pra:mprapa:9319

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Keywords: option pricing; European options; Fourier-cosine expansion;

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References

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  1. Andricopoulos, Ari D. & Widdicks, Martin & Duck, Peter W. & Newton, David P., 2003. "Universal option valuation using quadrature methods," Journal of Financial Economics, Elsevier, Elsevier, vol. 67(3), pages 447-471, March.
  2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
  3. Mark Broadie & Yusaku Yamamoto, 2003. "Application of the Fast Gauss Transform to Option Pricing," Management Science, INFORMS, INFORMS, vol. 49(8), pages 1071-1088, August.
  4. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, Econometric Society, vol. 68(6), pages 1343-1376, November.
  5. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
  6. Lord, Roger & Fang, Fang & Bervoets, Frank & Oosterlee, Kees, 2007. "A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes," MPRA Paper 1952, University Library of Munich, Germany.
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Cited by:
  1. Stefano, Pagliarani & Pascucci, Andrea & Candia, Riga, 2011. "Expansion formulae for local Lévy models," MPRA Paper 34571, University Library of Munich, Germany.
  2. Jun Cheng & Jin Zhang, 2012. "Analytical pricing of American options," Review of Derivatives Research, Springer, vol. 15(2), pages 157-192, July.
  3. Corsi, Fulvio & Fusari, Nicola & La Vecchia, Davide, 2013. "Realizing smiles: Options pricing with realized volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 107(2), pages 284-304.
  4. repec:qut:auncer:2013_02 is not listed on IDEAS
  5. Carl Chiarella & Susanne Griebsch & Boda Kang, 2013. "Investigating Time-Efficient Methods to Price Compound Options in the Heston Model," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 328, Quantitative Finance Research Centre, University of Technology, Sydney.
  6. Jan Baldeaux & Alexander Badran, 2012. "Consistent Modeling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 306, Quantitative Finance Research Centre, University of Technology, Sydney.
  7. Grzelak, Lech & Oosterlee, Kees, 2010. "On cross-currency models with stochastic volatility and correlated interest rates," MPRA Paper 23020, University Library of Munich, Germany.
  8. Martijn Pistorius & Johannes Stolte, 2012. "Fast computation of vanilla prices in time-changed models and implied volatilities using rational approximations," Papers 1203.6899, arXiv.org.
  9. Samuel Drapeau & Michael Kupper & Antonis Papapantoleon, 2012. "A Fourier Approach to the Computation of CV@R and Optimized Certainty Equivalents," Papers 1212.6732, arXiv.org, revised Dec 2013.
  10. Pablo Olivares, 2014. "Pricing of Basket Options Using Polynomial Approximations," Papers 1404.3160, arXiv.org.
  11. Marjon Ruijter & Kees Oosterlee (CWI), 2012. "Two-dimensional Fourier cosine series expansion method for pricing financial options," CPB Discussion Paper 225, CPB Netherlands Bureau for Economic Policy Analysis.
  12. Adam Aleksander Majewski & Giacomo Bormetti & Fulvio Corsi, 2014. "Smile from the Past: A general option pricing framework with multiple volatility and leverage components," Papers 1404.3555, arXiv.org.
  13. Andrey Itkin, 2014. "Splitting and Matrix Exponential approach for jump-diffusion models with Inverse Normal Gaussian, Hyperbolic and Meixner jumps," Papers 1405.6111, arXiv.org, revised May 2014.
  14. Grzelak, Lech & Oosterlee, Kees, 2010. "An Equity-Interest Rate Hybrid Model With Stochastic Volatility and the Interest Rate Smile," MPRA Paper 20574, University Library of Munich, Germany.
  15. Grzelak, Lech & Oosterlee, Kees, 2009. "On The Heston Model with Stochastic Interest Rates," MPRA Paper 20620, University Library of Munich, Germany, revised 18 Jan 2010.
  16. A S Hurn & Kenenth A Lindsay & Andrew McClelland, 2013. "On the Efficacy of Fourier Series Approximations for Pricing European and Digital Options," NCER Working Paper Series, National Centre for Econometric Research 90, National Centre for Econometric Research.
  17. Singor, Stefan N. & Grzelak, Lech A. & van Bragt, David D.B. & Oosterlee, Cornelis W., 2013. "Pricing inflation products with stochastic volatility and stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 286-299.

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