IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1903.07519.html
   My bibliography  Save this paper

A fast method for pricing American options under the variance gamma model

Author

Listed:
  • Weilong Fu
  • Ali Hirsa

Abstract

We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process which is constructed by replacing the calendar time by the gamma time in a Brownian motion with drift, which makes it a time-changed Brownian motion. In general, the finite difference method and the simulation method can be used for pricing under this model, but their speed is not satisfactory. So there is a need for fast but accurate approximation methods. In the case of Black-Merton-Scholes model, there are fast approximation methods, but they cannot be utilized for the variance gamma model. We develop a new fast method inspired by the quadratic approximation method, while reducing the error by making use of a machine learning technique on pre-calculated quantities. We compare the performance of our proposed method with those of the existing methods and show that this method is efficient and accurate for practical use.

Suggested Citation

  • Weilong Fu & Ali Hirsa, 2019. "A fast method for pricing American options under the variance gamma model," Papers 1903.07519, arXiv.org.
    • Handle: RePEc:arx:papers:1903.07519
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1903.07519
    File Function: Latest version
    Download Restriction: no
    ---><---

    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. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    3. Cartea, Álvaro & del-Castillo-Negrete, Diego, 2007. "Fractional diffusion models of option prices in markets with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 749-763.
    4. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. "Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    5. 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.
    6. repec:dau:papers:123456789/1380 is not listed on IDEAS
    7. Nick Webber & Claudia Ribeiro, 2003. "Valuing Path Dependent Options in the Variance-Gamma Model by Monte Carlo with a Gamma Bridge," Computing in Economics and Finance 2003 4, Society for Computational Economics.
    8. 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.
    9. Nick Webber & Claudia Ribeiro, 2003. "A Monte Carlo Method for the Normal Inverse Gaussian Option Valuation Model using an Inverse Gaussian Bridge," Computing in Economics and Finance 2003 5, Society for Computational Economics.
    10. Rama Cont & Ekaterina Voltchkova, 2005. "A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models," Post-Print halshs-00445645, HAL.
    11. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2007. "Self‐Decomposability And Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 31-57, January.
    12. 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.
    13. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    14. 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.
    15. Ali Hirsa & Tugce Karatas & Amir Oskoui, 2019. "Supervised Deep Neural Networks (DNNs) for Pricing/Calibration of Vanilla/Exotic Options Under Various Different Processes," Papers 1902.05810, arXiv.org.
    16. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ali Hirsa & Tugce Karatas & Amir Oskoui, 2019. "Supervised Deep Neural Networks (DNNs) for Pricing/Calibration of Vanilla/Exotic Options Under Various Different Processes," Papers 1902.05810, arXiv.org.
    2. Ali Hirsa & Weilong Fu, 2020. "An unsupervised deep learning approach in solving partial integro-differential equations," Papers 2006.15012, arXiv.org, revised Dec 2020.

    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. 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.
    2. Nicola Cantarutti & Jo~ao Guerra, 2016. "Multinomial method for option pricing under Variance Gamma," Papers 1701.00112, arXiv.org, revised Feb 2018.
    3. 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).
    4. Philipp N. Baecker, 2007. "Real Options and Intellectual Property," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-48264-2, July.
    5. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    6. Chan, Tat Lung (Ron), 2020. "Hedging and pricing early-exercise options with complex fourier series expansion," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    7. Ali Hirsa & Weilong Fu, 2020. "An unsupervised deep learning approach in solving partial integro-differential equations," Papers 2006.15012, arXiv.org, revised Dec 2020.
    8. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    9. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    10. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2012. "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    11. 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.
    12. Dilip B. Madan & King Wang, 2022. "Two sided efficient frontiers at multiple time horizons," Annals of Finance, Springer, vol. 18(3), pages 327-353, September.
    13. Ron Chan & Simon Hubbert, 2014. "Options pricing under the one-dimensional jump-diffusion model using the radial basis function interpolation scheme," Review of Derivatives Research, Springer, vol. 17(2), pages 161-189, July.
    14. Yuanda Chen & Zailei Cheng & Haixu Wang, 2023. "Option Pricing for the Variance Gamma Model: A New Perspective," Papers 2306.10659, arXiv.org.
    15. Ascione, Giacomo & Mehrdoust, Farshid & Orlando, Giuseppe & Samimi, Oldouz, 2023. "Foreign Exchange Options on Heston-CIR Model Under Lévy Process Framework," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    16. 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.
    17. Adrien Genin & Peter Tankov, 2016. "Optimal importance sampling for L\'evy Processes," Papers 1608.04621, arXiv.org.
    18. Piergiacomo Sabino, 2021. "Pricing Energy Derivatives in Markets Driven by Tempered Stable and CGMY Processes of Ornstein-Uhlenbeck Type," Papers 2103.13252, arXiv.org.
    19. Tim Leung & Marco Santoli, 2014. "Accounting for earnings announcements in the pricing of equity options," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 1-46.
    20. Jean-Philippe Aguilar & Jan Korbel & Nicolas Pesci, 2021. "On the Quantitative Properties of Some Market Models Involving Fractional Derivatives," Mathematics, MDPI, vol. 9(24), pages 1-24, December.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1903.07519. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.