Modelling VIX and VIX derivatives with reducible diffusions
by Zhigang Tong
International Journal of Bonds and Derivatives (IJBD), Vol. 3, No. 2, 2017

Abstract: Starting from the tractable basic diffusion processes, we obtain a one-factor diffusion model for VIX and VIX derivatives through a nonlinear transformation. The new model encompasses many existing models such as square root, 3/2 and logarithmic Ornstein-Uhlenbeck models as special cases. We obtain the analytical solutions for VIX futures and options. We estimate the parameters in the models using the historical data from the time series of VIX index and VIX options and compare this model with some of the nested others. The results indicate that the elasticity of volatility with respect to the underlying VIX is statistically and economically different from 1/2 or 3/2 as specified in the popular models.

Online publication date: Sun, 09-Jul-2017

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