Understanding Jumps in the High-Frequency VIX

This thesis provides a comprehensive nonparametric study of volatility jumps and the leverage effect by examining high-frequency data on the VIX and S&P 500 from 1992 to 2010. The data are analyzed within the theoretical framework of a classical jump-diffusion stochastic volatility model while remaining completely nonparametric about jumps and leverage effect dynamics. The model is considered in a very general form: independent and dependent jumps in price and volatility along with the leverage effect specified through diffusive and jump components. The jumps are detected using a nonparametric test similar to the test of Lee and Mykland (2008). The first part of the data (1992 - 1998) is found to be too noisy for the inference about jumps because of the monotonic time trend in several features, such as the leverage effect, annual occurrence of jumps, and microstructure noise. This time trend is independent of market conditions but is consistent with the overall improvement of the quality of the option data. In the second, stationary part of the dataset (1999 - 2010), the high-frequency dynamics of VIX jumps challenges standard stochastic volatility models. First, such jumps rarely correspond to any economic event. Second, the time series of these jumps has a strong negative autocorrelation, which seems to be a characteristic of noise. Moreover, the smaller the time period between such jumps the stronger is the negative autocorrelation. Third, these jumps are not followed by the change in the spot volatility. Interestingly, the more counterintuitive are the properties of these jumps the less strong is the leverage effect transferred by these types of movements. Noteworthy, such controversial features belong only to the independent volatility jumps, while the dependent volatility jumps seem to agree with the model. These controversial features of extreme movements in the VIX coupled with the overall lower quality of the dataset lead to the hypothesis of “pseudo-jumps” in the VIX. These are jumps, which take place in the observable VIX but do not represent real movements in its fundamental value. These results confirm the existing critique of the VIX in the literature.