The variance-gamma distribution is a continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the gamma distribution. The most widely used option pricing model is the Black-Scholes model.
We motivate an alternative option pricing model called the Variance Gamma (VG) model and demonstrate its implementation in the Bloomberg system. The tails of the distribution decrease more slowly than the normal distribution. It is therefore suitable to model phenomena where numerically large values are more probable than is the case for the normal distribution. Examples are returns from financial assets and turbulent wind speeds. The distribution was introduced in the financial literature by Madan and Seneta. The variance-gamma distributions form a subclass of the generalised hyperbolic distributions.
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. Madan, Carr and Chang extend the model to allow for an asymmetric form and present a formula to price European options under the variance gamma process.
Fiorani presents numerical solutions for European and America barrier options under variance gamma process. He also provides computer programming code to price vanilla and barrier European and American barrier options under variance gamma process.