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Title: Estimating the variance-gamma distribution: A comparison of algorithms and of estimated option prices Authors:  Marco Bee - University of Trento (Italy) [presenting]
Maria Michela Dickson - University of Trento (Italy)
Flavio Santi - University of Trento (Italy)
Abstract: The variance-gamma (VG) process has been proposed in the theory of option pricing as an alternative to the geometric Brownian motion for modeling the underlying of financial derivatives. The VG distribution is the marginal distribution of this process and has the capability of capturing skewness and kurtosis of the underlying asset's distribution. We exploit the fact that the VG distribution is a special case of the generalized hyperbolic distribution to develop maximum likelihood estimation (MLE) via the EM algorithm. Two main conclusions are reached. First, according to extensive simulation experiments, the EM-based estimators are preferable to the MLEs obtained via standard numerical optimization routines implemented in the {\tt VarianceGamma} and {\tt ghyp R} packages. Second, given the availability of closed-form formulas for computing the prices of the European-style options with VG-distributed underlying, the simulated distributions of the estimators are used to study the precision of estimated option prices. Besides shedding some light on the controversy about the estimated values of the parameters of the VG distribution, these outcomes permit to assess the impactof the errors associated to the different estimation procedures on the prices of options.