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The Variance Gamma (V.G.) Model for Share Market Returns

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  • Madan, Dilip B
  • Seneta, Eugene

Abstract

A new stochastic process, termed the variance gamma process, is proposed as a model for the uncertainty underlying security prices. The unit period distribution is normal conditional on a variance that is distributed as a gamma variate. Its advantages include long tailedness, continuous-time specification, finite moments of all orders, elliptical multivariate unit period distributions, and good empirical fit. The process is pure jump, approximable by a compound Poisson process with high jump frequency and low jump magnitudes. Applications to option pricing show differential effects for options on the money, compared to in or out of the money. Copyright 1990 by the University of Chicago.

Suggested Citation

  • 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.
  • Handle: RePEc:ucp:jnlbus:v:63:y:1990:i:4:p:511-24
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    References listed on IDEAS

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    1. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-987, December.
    2. Nelson, Charles R & Startz, Richard, 1990. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 58(4), pages 967-976, July.
    3. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-1286, September.
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