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.

Mercuri, L., Loregian, A., Rroji, E. (2011). Approximation of the variance gamma model with a finite mixture of normals [Working paper del dipartimento].

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

MERCURI, LORENZO;LOREGIAN, ANGELA;RROJI, EDIT
2011

Abstract

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.
Working paper del dipartimento
Scientifica
Variance Gamma distribution; Finite Mixture; EM algorithm; Option pricing
English
Mercuri, L., Loregian, A., Rroji, E. (2011). Approximation of the variance gamma model with a finite mixture of normals [Working paper del dipartimento].
Mercuri, L; Loregian, A; Rroji, E
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/21102
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