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A Fast Fourier Transform Technique for Pricing American Options Under Stochastic Volatility

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  • Zhylyevskyy, Oleksandr

Abstract

This paper develops a non-finite-difference-based method of American option pricing under stochastic volatility by extending the Geske-Johnson compound option scheme. The characteristic function of the underlying state vector is inverted to obtain the vector's density using a kernel-smoothed fast Fourier transform technique. The method produces option values that are closely in line with the values obtained by finite-difference schemes. It also performs well in an empirical application with traded S&P 100 index options. The method is especially well suited to price a set of options with different strikes on the same underlying asset, which is a task often encountered by practitioners.

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  • Zhylyevskyy, Oleksandr, 2009. "A Fast Fourier Transform Technique for Pricing American Options Under Stochastic Volatility," Staff General Research Papers Archive 13112, Iowa State University, Department of Economics.
    • Handle: RePEc:isu:genres:13112
    DOI: 10.1007/s11147-009-9041-6
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    1. Yuanfeng Hu & Yixiang Tian & Luping Zhang, 2023. "Green Bond Pricing and Optimization Based on Carbon Emission Trading and Subsidies: From the Perspective of Externalities," Sustainability, MDPI, vol. 15(10), pages 1-20, May.
    2. Hu, Yuanfeng & Tian, Yixiang, 2024. "The role of green reputation, carbon trading and government intervention in determining the green bond pricing: An externality perspective," International Review of Economics & Finance, Elsevier, vol. 89(PB), pages 46-62.
    3. Kirkby, J. Lars & Nguyen, Duy & Cui, Zhenyu, 2017. "A unified approach to Bermudan and barrier options under stochastic volatility models with jumps," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 75-100.
    4. Zhylyevskyy, Oleksandr, 2012. "Efficient Pricing of European-Style Options Under Heston's Stochastic Volatility Model," Staff General Research Papers Archive 34827, Iowa State University, Department of Economics.
    5. Chen, Ding & Härkönen, Hannu J. & Newton, David P., 2014. "Advancing the universality of quadrature methods to any underlying process for option pricing," Journal of Financial Economics, Elsevier, vol. 114(3), pages 600-612.
    6. Andersson, Kristoffer & Oosterlee, Cornelis W., 2021. "A deep learning approach for computations of exposure profiles for high-dimensional Bermudan options," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    7. Andersson, Kristoffer & Oosterlee, Cornelis W., 2021. "Deep learning for CVA computations of large portfolios of financial derivatives," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    8. Zhylyevskyy, Oleksandr, 2012. "Joint Characteristic Function of Stock Log-Price and Squared Volatility in the Bates Model and Its Asset Pricing Applications," Staff General Research Papers Archive 35559, Iowa State University, Department of Economics.
    9. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, vol. 13(2), pages 177-217, July.
    10. Zafar Ahmad & Reilly Browne & Rezaul Chowdhury & Rathish Das & Yushen Huang & Yimin Zhu, 2023. "Fast American Option Pricing using Nonlinear Stencils," Papers 2303.02317, arXiv.org, revised Oct 2023.
    11. Chinonso I. Nwankwo & Weizhong Dai & Ruihua Liu, 2023. "Compact Finite Difference Scheme with Hermite Interpolation for Pricing American Put Options Based on Regime Switching Model," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 817-854, October.
    12. Chinonso Nwankwo & Weizhong Dai & Ruihua Liu, 2019. "Compact Finite Difference Scheme with Hermite Interpolation for Pricing American Put Options Based on Regime Switching Model," Papers 1908.04900, arXiv.org, revised Jun 2020.
    13. Susanne Griebsch, 2013. "The evaluation of European compound option prices under stochastic volatility using Fourier transform techniques," Review of Derivatives Research, Springer, vol. 16(2), pages 135-165, July.
    14. Maximilian Ga{ss} & Kathrin Glau & Maximilian Mair, 2015. "Magic points in finance: Empirical integration for parametric option pricing," Papers 1511.00884, arXiv.org, revised Nov 2016.
    15. Feng, Chengxiao & Tan, Jie & Jiang, Zhenyu & Chen, Shuang, 2020. "A generalized European option pricing model with risk management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

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    More about this item

    Keywords

    stochastic volatility; heston model; Geske-Johnson scheme; fast fourier transform; characteristic function inversion;
    All these keywords.

    JEL classification:

    • G00 - Financial Economics - - General - - - General

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