IDEAS home Printed from https://ideas.repec.org/p/prg/jnlwps/v3y2021id3.002.html
   My bibliography  Save this paper

Variance Gamma process in the option pricing model

Author

Listed:
  • Jakub Drahokoupil

Abstract

Aim of this paper is to use Variance Gamma process in the option pricing model and compare it with the well-known and the most widely used option pricing model, the Black-Scholes model. The Variance Gamma model is, in contrast to the one-parameter Black-Scholes model, a three-parameter model. In addition, these two parameters, which are included in the Variance Gamma model, serve to model the skewness and kurtosis of the empirical distribution of the logarithmic returns of the underlying asset. An important part of this work is also a comparison of suitable valuation algorithms for calculation of the option price using the Variance Gamma model. The comparison of both models will be performed primarily on historical empirical distributions of logarithmic returns of selected stocks. Then, performance and pricing error of both models will be tested when estimating implied coefficients based on market data of the option. The performance of both models will be measured by traditional statistical-econometric methods such as RMSE, Likelihood ratio, Akaike information criterion and last but not least by the Natural spline regression model, which estimates the effect of the variable "Moneyness" (distance between the strike price and the current asset value) on the pricing error. All tests performed in this work suggest that the Variance Gamma model is a more accurate model for calculating the price of options.

Suggested Citation

  • Jakub Drahokoupil, 2020. "Variance Gamma process in the option pricing model," FFA Working Papers 3.002, Prague University of Economics and Business, revised 31 Jan 2021.
    • Handle: RePEc:prg:jnlwps:v:3:y:2021:id:3.002
    as

    Download full text from publisher

    File URL: http://wp.ffu.vse.cz/artkey/wps-202101-0002_variance-gamma-process-in-the-option-pricing-model.php
    Download Restriction: free of charge
    File URL: http://wp.ffu.vse.cz/pdfs/wps/2021/01/02.pdf
    Download Restriction: free of charge
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. Rama Cont & Ekaterina Voltchkova, 2005. "Integro-differential equations for option prices in exponential Lévy models," Finance and Stochastics, Springer, vol. 9(3), pages 299-325, July.
    3. Rama Cont & Ekaterina Voltchkova, 2005. "A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models," Post-Print halshs-00445645, HAL.
    4. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    5. Fiorani, Filo, 2004. "Option Pricing Under the Variance Gamma Process," MPRA Paper 15395, University Library of Munich, Germany.
    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. Kyriakos Georgiou & Athanasios N. Yannacopoulos, 2023. "Probability of Default modelling with L\'evy-driven Ornstein-Uhlenbeck processes and applications in credit risk under the IFRS 9," Papers 2309.12384, arXiv.org.
    2. 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.
    3. Ricardo Crisóstomo, 2017. "Speed and biases of Fourier-based pricing choices: Analysis of the Bates and Asymmetric Variance Gamma models," CNMV Working Papers CNMV Working Papers no. 6, CNMV- Spanish Securities Markets Commission - Research and Statistics Department.
    4. 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).
    5. Liming Feng & Vadim Linetsky, 2008. "Pricing Options in Jump-Diffusion Models: An Extrapolation Approach," Operations Research, INFORMS, vol. 56(2), pages 304-325, April.
    6. Martin Kegnenlezom & Patrice Takam Soh & Antoine-Marie Bogso & Yves Emvudu Wono, 2019. "European Option Pricing of electricity under exponential functional of L\'evy processes with Price-Cap principle," Papers 1906.10888, arXiv.org.
    7. Lukas Gonon & Christoph Schwab, 2021. "Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models," Finance and Stochastics, Springer, vol. 25(4), pages 615-657, October.
    8. Yun, Jaeho, 2014. "Out-of-sample density forecasts with affine jump diffusion models," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 74-87.
    9. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    10. Ricardo Crisóstomo, 2021. "Estimating real‐world probabilities: A forward‐looking behavioral framework," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(11), pages 1797-1823, November.
    11. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    12. Lam, K. & Chang, E. & Lee, M. C., 2002. "An empirical test of the variance gamma option pricing model," Pacific-Basin Finance Journal, Elsevier, vol. 10(3), pages 267-285, June.
    13. Martijn Pistorius & Johannes Stolte, 2012. "Fast computation of vanilla prices in time-changed models and implied volatilities using rational approximations," Papers 1203.6899, arXiv.org.
    14. Oscar Gutierrez, 2008. "Option valuation, time-changed processes and the fast Fourier transform," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 103-108.
    15. Tobias Behrens & Gero Junike & Wim Schoutens, 2023. "Failure of Fourier pricing techniques to approximate the Greeks," Papers 2306.08421, arXiv.org, revised Sep 2024.
    16. 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.
    17. Peter K. Friz & Stefan Gerhold & Marc Yor, 2013. "How to make Dupire's local volatility work with jumps," Papers 1302.5548, arXiv.org.
    18. Calvet, Laurent E. & Fisher, Adlai J., 2008. "Multifrequency jump-diffusions: An equilibrium approach," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 207-226, January.
    19. Jimin Lin & Guixin Liu, 2024. "Neural Term Structure of Additive Process for Option Pricing," Papers 2408.01642, arXiv.org, revised Oct 2024.
    20. 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.

    More about this item

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:prg:jnlwps:v:3:y:2021:id:3.002. 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: Stanislav Vojir (email available below). General contact details of provider: https://edirc.repec.org/data/uevsecz.html .

    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.