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Pricing Early-Exercise and Discrete Barrier Options by Fourier-Cosine Series Expansions

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  • Fang, Fang
  • Oosterlee, Kees

Abstract

We present a pricing method based on Fourier-cosine expansions for early-exercise and discretely-monitored barrier options. The method works well for exponential Levy asset price models. The error convergence is exponential for processes characterized by very smooth transitional probability density functions. The computational complexity is $O((M-1) N \log{N})$ with $N$ a (small) number of terms from the series expansion, and $M$, the number of early-exercise/monitoring dates.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 9248.

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Date of creation: Jun 2008
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Handle: RePEc:pra:mprapa:9248

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  1. Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
  2. 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.
  3. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers, Massachusetts Institute of Technology (MIT), Sloan School of Management 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  4. Ariel Almendral & Cornelis W. Oosterlee, 2007. "On American Options Under the Variance Gamma Process," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 14(2), pages 131-152.
  5. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 75(2), pages 305-332, April.
  6. 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.
  7. Kenneth J. Singleton & Len Umantsev, 2002. "Pricing Coupon-Bond Options And Swaptions In Affine Term Structure Models," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 12(4), pages 427-446.
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Cited by:
  1. Jun Cheng & Jin Zhang, 2012. "Analytical pricing of American options," Review of Derivatives Research, Springer, Springer, vol. 15(2), pages 157-192, July.
  2. Helin Zhu & Fan Ye & Enlu Zhou, 2013. "Fast Estimation of True Bounds on Bermudan Option Prices under Jump-diffusion Processes," Papers 1305.4321, arXiv.org.
  3. Marjon Ruijter & Kees Oosterlee (CWI), 2012. "Two-dimensional Fourier cosine series expansion method for pricing financial options," CPB Discussion Paper, CPB Netherlands Bureau for Economic Policy Analysis 225, CPB Netherlands Bureau for Economic Policy Analysis.

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