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Zbl 0937.91052
Madan, Dilip B.; Carr, Peter P.; Chang, Eric C.
The variance gamma process and option pricing. (English)
[J] Eur. Finance Rev. 2, No.1, 79-105 (1998). ISSN 1382-6662

Summary: A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. The process is obtained by evaluating Brownian motion with drift at a random time given by a gamma process. The two additional parameters are the drift of the Brownian motion and the volatility of the time change. These additional parameters provide control over the skewness and kurtosis of the return distribution. Closed forms are obtained for the return density and the prices of European options. The statistical and risk neutral densities are estimated for data on the S\&P500 Index and the prices of options on this Index. It is observed that the statistical density is symmetric with some kurtosis, while the risk neutral density is negatively skewed with a larger kurtosis. The additional parameters also correct for pricing biases of the Black-Scholes model that is a parametric special case of the option pricing model developed here.

MSC 2000:: *91B24 Price theory and market structure
91B82 Statistical methods in economics

Keywords: variance gamma process; Brownian motion; pricing

Cited in: Zbl 1229.91367 Zbl 1180.91160 Zbl 1103.62103 Zbl 1092.91022

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