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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.

Suggested Citation

  • Fang, Fang & Oosterlee, Kees, 2008. "Pricing Early-Exercise and Discrete Barrier Options by Fourier-Cosine Series Expansions," MPRA Paper 9248, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:9248
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    References listed on IDEAS

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    Cited by:

    1. Kathrin Glau & Mirco Mahlstedt & Christian Potz, 2018. "A new approach for American option pricing: The Dynamic Chebyshev method," Papers 1806.05579, arXiv.org.
    2. Laura Ballotta & Ioannis Kyriakou, 2015. "Convertible bond valuation in a jump diffusion setting with stochastic interest rates," Quantitative Finance, Taylor & Francis Journals, vol. 15(1), pages 115-129, January.
    3. A. Golbabai & L. Ballestra & D. Ahmadian, 2014. "A Highly Accurate Finite Element Method to Price Discrete Double Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 44(2), pages 153-173, August.
    4. Tat Lung Chan, 2017. "Singular Fourier-Pad\'e Series Expansion of European Option Prices," Papers 1706.06709, arXiv.org, revised Nov 2017.
    5. Jun Cheng & Jin Zhang, 2012. "Analytical pricing of American options," Review of Derivatives Research, Springer, vol. 15(2), pages 157-192, July.
    6. Ki Wai Chau & Cornelis W. Oosterlee, 2016. "On the wavelets-based SWIFT method for backward stochastic differential equations," Papers 1611.06098, arXiv.org.
    7. Carolyn E. Phelan & Daniele Marazzina & Gianluca Fusai & Guido Germano, 2019. "Hilbert transform, spectral filters and option pricing," Annals of Operations Research, Springer, vol. 282(1), pages 273-298, November.
    8. Carl Chiarella & Boda Kang & Gunter H. Meyer, 2010. "The Evaluation Of Barrier Option Prices Under Stochastic Volatility," Research Paper Series 266, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. Lech A. Grzelak & Cornelis W. Oosterlee & Sacha Van Weeren, 2012. "Extension of stochastic volatility equity models with the Hull--White interest rate process," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 89-105, July.
    10. Amirhossein Sobhani & Mariyan Milev, 2017. "A Numerical Method for Pricing Discrete Double Barrier Option by Legendre Multiwavelet," Papers 1703.09129, arXiv.org, revised Mar 2017.
    11. Adrien Genin & Peter Tankov, 2016. "Optimal importance sampling for L\'evy Processes," Papers 1608.04621, arXiv.org.
    12. Laura Ballota & Griselda Deelstra & Grégory Rayée, 2015. "Quanto Implied Correlation in a Multi-Lévy Framework," Working Papers ECARES ECARES 2015-36, ULB -- Universite Libre de Bruxelles.
    13. Helin Zhu & Fan Ye & Enlu Zhou, 2015. "Fast estimation of true bounds on Bermudan option prices under jump-diffusion processes," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1885-1900, November.
    14. Marjon Ruijter & Kees Oosterlee, 2012. "Two-dimensional Fourier cosine series expansion method for pricing financial options," CPB Discussion Paper 225, CPB Netherlands Bureau for Economic Policy Analysis.
    15. Alev{s} v{C}ern'y, 2016. "Discrete-Time Quadratic Hedging of Barrier Options in Exponential L\'{e}vy Model," Papers 1603.03747, arXiv.org.
    16. 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.
    17. Fei Cong & Cornelis W. Oosterlee, 2017. "Accurate and Robust Numerical Methods for the Dynamic Portfolio Management Problem," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 433-458, March.
    18. Jain, Shashi & Oosterlee, Cornelis W., 2015. "The Stochastic Grid Bundling Method: Efficient pricing of Bermudan options and their Greeks," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 412-431.
    19. Rob Aalbers & Marjon Ruijter & Kees Oosterlee, 2014. "The social discount rate under a stochastic A2 scenario," CPB Discussion Paper 296, CPB Netherlands Bureau for Economic Policy Analysis.
    20. Chunfa Wang, 2017. "Pricing European Options by Stable Fourier-Cosine Series Expansions," Papers 1701.00886, arXiv.org, revised Jan 2017.

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    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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