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|Title||The Pricing of VIX Derivatives: Theory and Empirical Performance|
|Institution||University of Zurich|
|Faculty||Faculty of Economics, Business Administration and Information Technology|
|Number of Pages||70|
|Abstract Text||This Master’s thesis studies the pricing of options and futures written on the CBOE Volatility Index (VIX). To this end, the definition of the VIX as well as the characteristics of the derivatives are reviewed in detail. After an evaluation of almost model-free valuation bounds for VIX futures, a comparison of two fundamentally different modelling approaches is conducted and comes to the conclusion that a class of models based on a mean-reverting Ornstein-Uhlenbeck process for the logarithm of the VIX is an adequate starting point. Two extensions and a combination thereof are presented to include the empirically observed stochastic volatility and jumps that shape the time series of the VIX. Stochastic volatility is modelled by a Cox-Ingersoll-Ross process and jumps are assumed to be exponentially distributed and the arrival times of jumps follow an homogeneous Poisson process. To price VIX derivatives under these model assumptions, their conditional characteristic functions are derived and require solving a system of ordinary differential equations and numerical integration. The pricing performance of the logarithmic model and its extensions for VIX futures and options is tested by market calibration using historical data from 2007 to 2016. In this period, we test the capabilities of four models in- and out-of-sample. We find that stochastic volatility is an essential factor for pricing both VIX derivatives and that an additional jump component improves the result for VIX options even further.|