Variance gamma process - Wikipedia

There is no diffusion component in the VG process and it is thus a pure jump process. The increments are independent and follow a Variance-gamma distribution , which is a generalization of the Laplace distribution.

There are several representations of the VG process that relate it to other processes.

An alternative way of stating this is that the variance gamma process is a Brownian motion subordinated to a Gamma subordinator. Since the VG process is of finite variation it can be written as the difference of two independent gamma processes: Alternatively it can be approximated by a compound Poisson process that leads to a representation with explicitly given independent jumps and their locations.

This last characterization gives an understanding of the structure of the sample path with location and sizes of jumps. On the early history of the variance-gamma process see Seneta The VG process can be advantageous to use when pricing options since it allows for a wider modeling of skewness and kurtosis than the Brownian motion does. As such the variance gamma model allows to consistently price options with different strikes and maturities using a single set of parameters.

Madan and Seneta present a symmetric version of the variance gamma process. Hirsa and Madan show how to price American options under variance gamma. The variance gamma process has been successfully applied in the modeling of credit risk in structural models. The pure jump nature of the process and the possibility to control skewness and kurtosis of the distribution allow the model to price correctly the risk of default of securities having a short maturity, something that is generally not possible with structural models in which the underlying assets follow a Brownian motion.

Fiorani, Luciano and Semeraro [8] model credit default swaps under variance gamma. In an extensive empirical test they show the overperformance of the pricing under variance gamma, compared to alternative models presented in literature.

Call Option Strategies ~ Best Option Strategy

Monte Carlo methods for the variance gamma process are described by Fu Under this assumption it is possible to derive closed form vanilla option prices and their associated Greeks. For a comprehensive description see. From Wikipedia, the free encyclopedia. The Laplace distribution and generalizations: Advances in Mathematical Finance.

Model for Share Market Returns". Journal of Computational Finance. Option Pricing Under the Variance Gamma Process.

Option Pricing under the Variance Gamma Process by Filo Fiorani :: SSRN

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