Forward variance dynamics : Bergomi's model revisited

Sidi Mohamed Ould Aly (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

In this article, we propose an arbitrage-free modeling framework for the joint dynamics of forward variance along with the underlying index, which can be seen as a combination of the two approaches proposed by Bergomi. The difference between our modeling framework and the Bergomi models (2008), is mainly the ability to compute the prices of VIX futures and options by using semi-analytic formulas. Also, we can express the sensitivities of the prices of VIX futures and options with respect to the model parameters, which enables us to propose an efficient and easy calibration to the VIX futures and options. The calibrated model allows to Delta-hedge VIX options by trading in VIX futures, the corresponding hedge ratios can be computed analytically

Mots clés: Variance-swap; forward variance; VIX; VIX futures; VIX options; Implied volatility; Skew; Hedging

Domaines: Probabilités [math.PR]

Sidi Mohamed Ould Aly. Forward variance dynamics : Bergomi's model revisited. 2011. ⟨hal-00624812⟩