Approximation of the variance gamma model with a finite mixture of normals

Several authors have shown the ability of the variance gamma model to correct some biases of the Black-Scholes model. The variance gamma distribution has two additional parameters that allow to capture the skewness and kurtosis observed in financial data. However its density has not got a simple form formula and this implies numerical issues for historical estimation and option pricing. This paper investigates the possibility of approximating the variance gamma distribution to a finite mixture of normals. Therefore, we apply this result to derive a simple historical estimation procedure by means of the Expectation Maximization algorithm and we obtain a simple formula to price a European call option.