A scaled version of the double-mean-reverting model for VIX derivatives

As the Heston model is not consistent with VIX data in real market, alternative stochastic volatility models including the double-mean-reverting model of Gatheral have been developed to overcome its limitation. The... [ view full abstract ]

As the Heston model is not consistent with VIX data in real market, alternative stochastic volatility models including the double-mean-reverting model of Gatheral have been developed to overcome its limitation. The double-mean-reverting model is a three factor model reflecting the empirical dynamics of the variance but there is no closed form solution for VIX derivatives and thus calibration may be slow. In this paper, we propose a fast mean-reverting version of the double-mean-reverting model. We obtain a closed form approximation for VIX derivatives and show how it is effective by comparing it with the Heston model and the double-mean-reverting model.