Essays on equity index options and VIX

Abstract

This dissertation consists of three essays on studies of equity index options and VIX. The first essay shows thejump-GARCH option pricing model requires both variance premium and jump premium in order to generatemodel-implied VIX consistent with CBOE VIX. The jumps in the dynamics of equity prices and variances, andthe variance premium in investors’ preference is required, and conventional GARCH option pricing models notincluding both have limitations in capturing the variation of CBOE VIX. However, even the most flexible modelwith both premiums cannot generate the unbiased indicator for the future CBOE VIX and the model-impliedvariance of VIX is much less volatile than CBOE VIX. The second essay suggests various tail risk indexes usingthe notion of a Value-at-Risk swap whose payoff depends on a prescribed tail risk event. To capture the asymmetrybetween downside risks and upside uncertainty, alternative swaps using upside uncertainty are devised. Withthose tail risk swaps, several tail risk indexes that are model-free and implied from equity index option pricesare proposed. Tail risk indexes are decomposed into tail risk premiums and conditional tail risk components,and their predictabilities for future returns of various characteristic-sorted portfolios are assessed. The last essayempirically compares machine learning algorithms in predicting implied volatility changes. Decision tree, randomforest, extremely randomized trees, gradient boosting trees, k-nearest neighbors and neural networks are comparedwith respect to 3-parameters model of Hull and White (2017). Neural network has the highest predictability, andthe predictability is higher in times of market crash or surge, and high sentiment periods.