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Sinh-Acceleration For B-Spline Projection With Option Pricing Applications

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  • SVETLANA BOYARCHENKO

    (Department of Economics, The University of Texas at Austin, 2225 Speedway Stop C3100, Austin, TX 78712–0301, USA)

  • SERGEI LEVENDORSKIĬ

    (Calico Science Consulting, Austin, TX 78748, USA)

  • J. LARS KYRKBY

    (ISYE, Georgia Institute of Technology, 755 Ferst Dr., Atlanta, GA 30313, USA)

  • ZHENYU CUI

    (School of Business, Stevens Institute of Technology, Babbio Dr., Hoboken, NJ 07030, USA)

Abstract

We clarify the relations among different Fourier-based approaches to option pricing, and improve the B-spline probability density projection method using the sinh-acceleration technique. This allows us to efficiently separate the control of different sources of errors better than the FFT-based realization allows; in many cases, the CPU time decreases as well. We demonstrate the improvement of the B-spline projection method through several numerical experiments in option pricing, including European and barrier options, where the SINH acceleration technique proves to be robust and accurate.

Suggested Citation

  • Svetlana Boyarchenko & Sergei Levendorskiä¬ & J. Lars Kyrkby & Zhenyu Cui, 2021. "Sinh-Acceleration For B-Spline Projection With Option Pricing Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(08), pages 1-50, December.
    • Handle: RePEc:wsi:ijtafx:v:24:y:2021:i:08:n:s0219024921500400
    DOI: 10.1142/S0219024921500400
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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Kirkby, J. Lars & Mitra, Sovan & Nguyen, Duy, 2020. "An analysis of dollar cost averaging and market timing investment strategies," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1168-1186.
    3. Svetlana I. Boyarchenko & Sergei Z. Levendorskiǐ, 2000. "Option Pricing For Truncated Lévy Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 549-552.
    4. Svetlana Boyarchenko & Sergei Levendorskiĭ, 2017. "Efficient Pricing Of Barrier Options And Credit Default Swaps In Lévy Models With Stochastic Interest Rate," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 1089-1123, October.
    5. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    6. 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.
    7. J. Lars Kirkby, 2017. "Robust barrier option pricing by frame projection under exponential Lévy dynamics," Applied Mathematical Finance, Taylor & Francis Journals, vol. 24(4), pages 337-386, July.
    8. Svetlana Boyarchenko & Sergei Levendorskiĭ, 2020. "Static and semistatic hedging as contrarian or conformist bets," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 921-960, July.
    9. Justin Lars Kirkby & Shijie Deng, 2019. "Static hedging and pricing of exotic options with payoff frames," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 612-658, April.
    10. S. Z. Levendorskiǐ, 2004. "Pricing Of The American Put Under Lévy Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 303-335.
    11. Fusai, Gianluca & Germano, Guido & Marazzina, Daniele, 2016. "Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options," European Journal of Operational Research, Elsevier, vol. 251(1), pages 124-134.
    12. Sergei Levendorskiĭ, 2012. "Efficient Pricing And Reliable Calibration In The Heston Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(07), pages 1-44.
    13. Svetlana Boyarchenko & Sergei Levendorskiĭ, 2019. "Sinh-Acceleration: Efficient Evaluation Of Probability Distributions, Option Pricing, And Monte Carlo Simulations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-49, May.
    14. Sergei Levendorskiĭ, 2016. "Pitfalls of the Fourier Transform Method in Affine Models, and Remedies," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(2), pages 81-134, March.
    15. Gianluca Fusai & I. Abrahams & Carlo Sgarra, 2006. "An exact analytical solution for discrete barrier options," Finance and Stochastics, Springer, vol. 10(1), pages 1-26, January.
    16. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    17. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    18. Svetlana I Boyarchenko & Sergei Z Levendorskii, 2002. "Non-Gaussian Merton-Black-Scholes Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4955, September.
    19. Svetlana Boyarchenko & Sergei Levendorskiĭ, 2013. "Efficient Laplace Inversion, Wiener-Hopf Factorization And Pricing Lookbacks," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(03), pages 1-40.
    20. Andricopoulos, Ari D. & Widdicks, Martin & Duck, Peter W. & Newton, David P., 2003. "Universal option valuation using quadrature methods," Journal of Financial Economics, Elsevier, vol. 67(3), pages 447-471, March.
    21. Liming Feng & Vadim Linetsky, 2008. "Pricing Discretely Monitored Barrier Options And Defaultable Bonds In Lévy Process Models: A Fast Hilbert Transform Approach," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 337-384, July.
    22. Mitya Boyarchenko & Sergei Levendorskiĭ, 2015. "Ghost calibration and the pricing of barrier options and CDS in spectrally one-sided L�vy models: the parabolic Laplace inversion method," Quantitative Finance, Taylor & Francis Journals, vol. 15(3), pages 421-441, March.
    23. Mitya Boyarchenko & Marco De Innocentis & Sergei Levendorskiĭ, 2011. "Prices Of Barrier And First-Touch Digital Options In Lévy-Driven Models, Near Barrier," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(07), pages 1045-1090.
    24. 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.
    25. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2017. "Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 46-62.
    26. Sergei Levendorskiĭ, 2014. "METHOD OF PAIRED CONTOURS AND PRICING BARRIER OPTIONS AND CDSs OF LONG MATURITIES," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(05), pages 1-58.
    27. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "A data-driven framework for consistent financial valuation and risk measurement," European Journal of Operational Research, Elsevier, vol. 289(1), pages 381-398.
    28. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    29. Mitya Boyarchenko & Sergei Levendorskiĭ, 2009. "Prices And Sensitivities Of Barrier And First-Touch Digital Options In Lévy-Driven Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(08), pages 1125-1170.
    30. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2017. "A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps," European Journal of Operational Research, Elsevier, vol. 262(1), pages 381-400.
    31. Kirkby, J. Lars & Nguyen, Duy, 2021. "Equity-linked Guaranteed Minimum Death Benefits with dollar cost averaging," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 408-428.
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    Cited by:

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