Title: Modelling VIX and VIX derivatives with reducible diffusions

Authors: Zhigang Tong

Addresses: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

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.

Keywords: volatility index; VIX; VIX derivatives; reducible diffusions; CIR; 3/2 model; CEV model; nonlinear model.

DOI: 10.1504/IJBD.2017.084927

International Journal of Bonds and Derivatives, 2017 Vol.3 No.2, pp.153 - 175

Received: 15 Jun 2016
Accepted: 21 Jun 2016

Published online: 27 Jun 2017 *

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