Essays in Volatility Modeling and Option Pricing

The common thread that runs through my research is the implication of volatility dynamics for option pricing. In the first chapter of this thesis, my co-authors and I study the presence of a factor structure in equity options. A principal component analysis of equity options reveals a strong factor structure. Guided by this finding, we develop an equity option valuation model that captures this factor structure. The model allows for stochastic volatility in the market return and also in the idiosyncratic component of equity returns. The model has a series of predictions relating individual firm's beta to patterns in implied volatilities. The equity option data support the cross-sectional implications of the estimated model. In the second chapter, I focus on the impact of intermediaries' risk sharing capacity on index options. I examine how inventory risk and market-maker wealth jointly determine the value of index options through their effects on the variance risk premium. My analysis shows that part of the variance risk premium compensates option market-makers for their exposure to market variance. Based on these findings, I develop a theoretical model in which market variance is stochastic and the representative market-maker accumulates inventory over time by absorbing end-users' net demand for index options. Starting from the market-maker's optimal trading strategy, I derive an explicit formula linking the variance risk premium to inventory risk and market-maker wealth. The model predicts that the variance risk premium is influenced by the ratio of inventory risk to the market-maker's wealth. Estimating the model on S 500 index returns and options, I find that it performs well.Ph.D