Option Pricing in a Dynamic Variance-Gamma Model

Journal of Financial Decision Making, Vol. 7, 2011

25 Pages Posted: 16 Oct 2010 Last revised: 29 May 2014

See all articles by Lorenzo Mercuri

Lorenzo Mercuri

University of Milan

Fabio Bellini

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Date Written: March 29, 2010

Abstract

We present a discrete time stochastic volatility model in which the conditional distribution of the logreturns is a Variance-Gamma, that is a normal variance-mean mixture with Gamma mixing density. We assume that the Gamma mixing density is time varying and follows an affine Garch model, trying to capture persistence of volatility shocks and also higher order conditional dynamics in a parsimonious way.

We select an equivalent martingale measure by means of the conditional Esscher transform as in Buhlmann et al. (1996) and show that this change of measure leads to a similar dynamics of the mixing distribution. The model admits a recursive procedure for the computation of the characteristic function of the terminal logprice, thus allowing semianalytical pricing as in Heston and Nandi (2000).

From an empirical point of view, we check the ability of this model to calibrate SPX option data and we compare it with the Heston and Nandi (2000) model and with the Christoffersen, Heston and Jacobs (2006) model, that is based on Inverse Gaussian innovations.

Keywords: Variance-Gamma Distribution, Garch Processes, Affine Stochastic Volatility Models, Semianalytical Formula, Esscher Transform

JEL Classification: C00, C63, C65, G12, G13

Suggested Citation

Mercuri, Lorenzo and Bellini, Fabio, Option Pricing in a Dynamic Variance-Gamma Model (March 29, 2010). Journal of Financial Decision Making, Vol. 7, 2011 , Available at SSRN: https://ssrn.com/abstract=1692683

Lorenzo Mercuri (Contact Author)

University of Milan ( email )

Via Festa del Perdono, 7
Milan, 20122
Italy

Fabio Bellini

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi ( email )

Milano, Milan
Italy

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