This dissertation contains two essays empirically exploring the equity option markets. Chapter 1 studies the role played by institutional investors in determining equity option returns. In this chapter, I study whether institutional stock holdings predict equity option returns. I find that institutional concentration in the underlying stock negatively predicts the cross-section of corresponding option returns. Evidence is consistent with a hedging and demand pressure channel: For stocks with

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... e concentrated ownership, some institutional holders are more likely to overweight them and demand more of their options to hedge. To absorb the order imbalances, dealers sell options and charge higher prices, leading to lower option returns. Using option holdings of U.S. equity mutual funds, I document a positive correlation between funds' stock concentration and their option share in the same firms. In Chapter 2 (joint with Steven Heston), we improve continuous-time variance swap approximation formulas to derive exact returns on benchmark VIX option portfolios. The new methodology preserves the variance swap interpretation that decomposes returns into realized variance and option implied-variance. We apply this new methodology to explore return momentum on option portfolios across different S&P 500 stocks. We find that stock options with high historical returns continue to outperform options with low returns. This predictability has a quarterly pattern, resembling the pattern of stock momentum found by Heston and Sadka (2008). In contrast to stock momentum, option momentum lasts for up to five years, and does not reverse.