IDEAS home Printed from https://ideas.repec.org/a/wly/jfutmk/v40y2020i10p1548-1561.html
   My bibliography  Save this article

Dynamic programming for valuing American options under a variance‐gamma process

Author

Listed:
  • Hatem Ben‐Ameur
  • Rim Chérif
  • Bruno Rémillard

Abstract

Lévy processes provide a solution to overcome the shortcomings of the lognormal hypothesis. A growing literature proposes the use of pure‐jump Lévy processes, such as the variance‐gamma (VG) model. In this setting, explicit solutions for derivative prices are unavailable, for instance, for the valuation of American options. We propose a dynamic programming approach coupled with finite elements for valuing American‐style options under an extended VG model. Our numerical experiments confirm the convergence and show the efficiency of the proposed methodology. We also conduct a numerical investigation that focuses on American options on S&P 500 futures contracts.

Suggested Citation

  • Hatem Ben‐Ameur & Rim Chérif & Bruno Rémillard, 2020. "Dynamic programming for valuing American options under a variance‐gamma process," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(10), pages 1548-1561, October.
    • Handle: RePEc:wly:jfutmk:v:40:y:2020:i:10:p:1548-1561
    DOI: 10.1002/fut.22148
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/fut.22148
    Download Restriction: no
    File URL: https://libkey.io/10.1002/fut.22148?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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. Vladimir K. Kaishev & Dimitrina S. Dimitrova, 2009. "Dirichlet Bridge Sampling for the Variance Gamma Process: Pricing Path-Dependent Options," Management Science, INFORMS, vol. 55(3), pages 483-496, March.
    3. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components1," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 39-55, October.
    4. Athanassios N. Avramidis & Pierre L'Ecuyer, 2006. "Efficient Monte Carlo and Quasi-Monte Carlo Option Pricing Under the Variance Gamma Model," Management Science, INFORMS, vol. 52(12), pages 1930-1944, December.
    5. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Working Paper 1159, Economics Department, Queen's University.
    6. Nisha Rambeerich & Desire Yannick Tangman & Muddun Bhuruth, 2011. "Numerical pricing of American options under infinite activity Lévy processes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(9), pages 809-829, September.
    7. 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.
    8. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
    9. Filippo Fiorani & Elisa Luciano & Patrizia Semeraro, 2010. "Single and joint default in a structural model with purely discontinuous asset prices," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 249-263.
    10. Dingeç, Kemal Dinçer & Hörmann, Wolfgang, 2012. "A general control variate method for option pricing under Lévy processes," European Journal of Operational Research, Elsevier, vol. 221(2), pages 368-377.
    11. Gareth G. Haslip & Vladimir K. Kaishev, 2014. "Lookback option pricing using the Fourier transform B-spline method," Quantitative Finance, Taylor & Francis Journals, vol. 14(5), pages 789-803, May.
    12. Ross A. Maller & David H. Solomon & Alex Szimayer, 2006. "A Multinomial Approximation For American Option Prices In Lévy Process Models," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 613-633, October.
    13. Elton A. Daal & Dilip B. Madan, 2005. "An Empirical Examination of the Variance-Gamma Model for Foreign Currency Options," The Journal of Business, University of Chicago Press, vol. 78(6), pages 2121-2152, November.
    14. Ariel Almendral & Cornelis W. Oosterlee, 2007. "On American Options Under the Variance Gamma Process," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(2), pages 131-152.
    15. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    16. Evis Këllezi & Nick Webber, 2004. "Valuing Bermudan options when asset returns are Levy processes," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 87-100.
    17. repec:dau:papers:123456789/1392 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Winston Buckley & Sandun Perera, 2019. "Optimal demand in a mispriced asymmetric Carr–Geman–Madan–Yor (CGMY) economy," Annals of Finance, Springer, vol. 15(3), pages 337-368, September.
    2. Ivanov Roman V., 2018. "On risk measuring in the variance-gamma model," Statistics & Risk Modeling, De Gruyter, vol. 35(1-2), pages 23-33, January.
    3. Gian P. Cervellera & Marco P. Tucci, 2017. "A note on the Estimation of a Gamma-Variance Process: Learning from a Failure," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 363-385, March.
    4. Claudia Yeap & Simon S Kwok & S T Boris Choy, 2018. "A Flexible Generalized Hyperbolic Option Pricing Model and Its Special Cases," Journal of Financial Econometrics, Oxford University Press, vol. 16(3), pages 425-460.
    5. Kao, Lie-Jane & Wu, Po-Cheng & Lee, Cheng-Few, 2012. "Time-changed GARCH versus the GARJI model for prediction of extreme news events: An empirical study," International Review of Economics & Finance, Elsevier, vol. 21(1), pages 115-129.
    6. Vladimir K. Kaishev & Dimitrina S. Dimitrova, 2009. "Dirichlet Bridge Sampling for the Variance Gamma Process: Pricing Path-Dependent Options," Management Science, INFORMS, vol. 55(3), pages 483-496, March.
    7. Nicola Cantarutti & Jo~ao Guerra, 2016. "Multinomial method for option pricing under Variance Gamma," Papers 1701.00112, arXiv.org, revised Feb 2018.
    8. Roman V. Ivanov & Katsunori Ano, 2016. "On exact pricing of FX options in multivariate time-changed Lévy models," Review of Derivatives Research, Springer, vol. 19(3), pages 201-216, October.
    9. Roman V. Ivanov, 2018. "Option Pricing In The Variance-Gamma Model Under The Drift Jump," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-19, June.
    10. Erdinc Akyildirim & Alper A. Hekimoglu & Ahmet Sensoy & Frank J. Fabozzi, 2023. "Extending the Merton model with applications to credit value adjustment," Annals of Operations Research, Springer, vol. 326(1), pages 27-65, July.
    11. Fiorani, Filo, 2004. "Option Pricing Under the Variance Gamma Process," MPRA Paper 15395, University Library of Munich, Germany.
    12. Salem, Marwa Belhaj & Fouladirad, Mitra & Deloux, Estelle, 2022. "Variance Gamma process as degradation model for prognosis and imperfect maintenance of centrifugal pumps," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    13. Xu Guo & Yutian Li, 2016. "Valuation of American options under the CGMY model," Quantitative Finance, Taylor & Francis Journals, vol. 16(10), pages 1529-1539, October.
    14. Liuren Wu, 2006. "Dampened Power Law: Reconciling the Tail Behavior of Financial Security Returns," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1445-1474, May.
    15. Akira Yamazaki, 2016. "Generalized Barndorff-Nielsen And Shephard Model And Discretely Monitored Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-34, June.
    16. Laura Ballotta, 2009. "Pricing and capital requirements for with profit contracts: modelling considerations," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 803-817.
    17. repec:dau:papers:123456789/1392 is not listed on IDEAS
    18. Yuanda Chen & Zailei Cheng & Haixu Wang, 2023. "Option Pricing for the Variance Gamma Model: A New Perspective," Papers 2306.10659, arXiv.org.
    19. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    20. Chan, Tat Lung (Ron), 2019. "Efficient computation of european option prices and their sensitivities with the complex fourier series method," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    21. Jacques Pézier & Johanna Scheller, 2011. "A Comprehensive Evaluation of Portfolio Insurance Strategies," ICMA Centre Discussion Papers in Finance icma-dp2011-15, Henley Business School, University of Reading.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jfutmk:v:40:y:2020:i:10:p:1548-1561. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/0270-7314/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.