Three Essays on Equity, Volatility and Commodity Derivatives
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This thesis provides a comprehensive study on option markets, with a focus on Leveraged Exchange Traded Fund (LETF) options, volatility options and crude oil options. Study of LETF option market is carried out using a parametric framework. A stochastic volatility framework for the LETFs is proposed and a systematic pricing formula for options on equity and volatility LETFs is further developed by employing Fast Fourier Transform (FFT). In contrast, research on volatility and crude oil option markets is conducted under a nonparametric framework. We extract variance and skew risk premiums from VIX options, which the first study on higher moment risk premiums for the volatility market and explains how they are related to VIX index returns as well as to S&P 500 index returns. When analysing higher moment risk premiums in the crude oil market, we decompose the risk premiums conditional on the market return sign. One key finding is that the decomposed risk premiums contain more predictive information about market excess returns. All the results contribute to a better understanding of the option market, and provide comparison with equity market.