Hedging Volatility Risk

Volatility derivatives are becoming increasingly popular as means for hedging unexpected changes in volatility. Although pricing volatility derivatives demands extreme care in modeling the underlying volatility process, not much attention has been devoted to the complete specification of the autonomous process that volatility follows in continuous time. Despite the fact that jumps are widely considered as a salient feature of volatility, their implications for pricing and hedging volatility options and futures are not yet fully understood. This thesis addresses two principal issues: a) modeling volatility, and b) hedging volatility risk. With respect to the modeling of volatility, the thesis assesses the ability of the most commonly used processes (diffusion and jump -diffusion) to capture the dynamics of implied volatility. The assessment of these processes is performed both analytically and empirically using data from the implied volatility index VIX for a period of 15 years. The empirical analysis produces new evidence concerning stationarity, long-memory, nonnormality and jump behavior. Furthermore, the empirical fit of diffusion processes can be significantly improved by the addition of jumps. If jumps are conditioned on the level of the index, model performance is further enhanced. With respect to hedging volatility risk, the thesis assesses the hedging effectiveness of volatility derivatives. The comparative evaluation attests that the most “naïve” volatility option pricing model can be reliably used for pricing and hedging purposes. Finally, the thesis develops new closed-form models for pricing volatility futures and European volatility options, when the underlying volatility index displays mean reversion and jumps. The results from these new models demonstrate that incorrectly omitting jumps may cause severe problems to both pricing and hedging.