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The Variance-Gamma Process for Option Pricing

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  • Rohan Shenoy
  • Peter Kempthorne

Abstract

This paper explores the concept of random-time subordination in modelling stock-price dynamics, and We first present results on the Laplace distribution as a Gaussian variance-mixture, in particular a more efficient volatility estimation procedure through the absolute moments. We generalise the Laplace model to characterise the powerful variance gamma model of Madan et al. as a Gamma time-subordinated Brownian motion to price European call options via an Esscher transform method. We find that the Variance Gamma model is able to empirically explain excess kurtosis found in log-returns data, rejecting a Black-Scholes assumption in a hypothesis test.

Suggested Citation

  • Rohan Shenoy & Peter Kempthorne, 2025. "The Variance-Gamma Process for Option Pricing," Papers 2510.14093, arXiv.org.
    • Handle: RePEc:arx:papers:2510.14093
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    References listed on IDEAS

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    1. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components1," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 39-55, October.
    2. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Working Paper 1159, Economics Department, Queen's University.
    3. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    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. 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.
    6. Pena, Ignacio & Rubio, Gonzalo & Serna, Gregorio, 1999. "Why do we smile? On the determinants of the implied volatility function," Journal of Banking & Finance, Elsevier, vol. 23(8), pages 1151-1179, August.
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