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Option Pricing Under the Variance Gamma Process

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  • Fiorani, Filo

Abstract

In this dissertation we price European and American vanilla and barrier options assuming that the underlying follows the variance gamma process. We solve numerically the problem implementing a finite difference algorithm and we present numerical experiments on the option pricing. This dissertation includes detailed algorithms as well as programming code in C++ to price European and American vanilla and barrier options under variance gamma.

Suggested Citation

  • Fiorani, Filo, 2004. "Option Pricing Under the Variance Gamma Process," MPRA Paper 15395, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:15395
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    References listed on IDEAS

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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. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components1," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 39-55, October.
    3. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Working Paper 1159, Economics Department, Queen's University.
    4. 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.
    5. 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.
    6. Geman, Helyette, 2002. "Pure jump Levy processes for asset price modelling," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1297-1316, July.
    7. 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.
    8. Thierry Ané & Hélyette Geman, 2000. "Order Flow, Transaction Clock, and Normality of Asset Returns," Journal of Finance, American Finance Association, vol. 55(5), pages 2259-2284, October.
    9. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    10. 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.
    11. repec:dau:papers:123456789/1392 is not listed on IDEAS
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    Citations

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    Cited by:

    1. 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.
    2. Marwa Belhaj Salem & Mitra Fouladirad & Estelle Deloux, 2021. "Prognostic and Classification of Dynamic Degradation in a Mechanical System Using Variance Gamma Process," Mathematics, MDPI, vol. 9(3), pages 1-25, January.
    3. John Angle, 2023. "Generalizing the Inequality Process’ gamma model of particle wealth statistics," The Journal of Mathematical Sociology, Taylor & Francis Journals, vol. 47(3), pages 227-243, July.
    4. 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.
    5. 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).
    6. Takayuki Sakuma & Yuji Yamada, 2014. "Application of Homotopy Analysis Method to Option Pricing Under Lévy Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(1), pages 1-14, March.
    7. Filippo Fiorani & Elisa Luciano, 2006. "Credit risk in pure jump structural models," ICER Working Papers - Applied Mathematics Series 6-2006, ICER - International Centre for Economic Research.
    8. Ulze, Markus & Stadler, Johannes & Rathgeber, Andreas W., 2021. "No country for old distributions? On the comparison of implied option parameters between the Brownian motion and variance gamma process," The Quarterly Review of Economics and Finance, Elsevier, vol. 82(C), pages 163-184.
    9. Hitaj, Asmerilda & Mercuri, Lorenzo & Rroji, Edit, 2015. "Portfolio selection with independent component analysis," Finance Research Letters, Elsevier, vol. 15(C), pages 146-159.

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    More about this item

    Keywords

    Variance Gamma Process; Option Pricing Under Variance Gamma; Numerical Solution of Option Prices Under Variance Gamma; Numerical Solution of Variance Gamma PIDE; Numerical Solutions of Variance Gamma Partial Differential Equation; Programming Code for Variance Gamma Option Pricing;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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