An essay on option prices

I study cross-sectional S&P 500 option prices using a jump-diffusion model that allows for negative correlation between price jumps and volatility jumps. Exploiting the information on integrated volatility and price jumps from high-frequency intraday data, I propose a GMM estimator for the model. I analytically derive closed-form moments for measures from high-frequency data, daily index returns, and cross-sectional option prices. My model relaxes Eraker's (2004) assumption of zero volatility jump risk premium and Broadie et al.'s (2007) assumption of independent price and volatility jump sizes. My results contrast with their findings of a limited role in volatility jumps. I find that price jumps and volatility jumps are both necessary. They play different roles in generating sufficient volatility smirks and in improving the fit for volatility term structures. I find a significantly positive risk premium for price jumps and a negative premium for volatility jumps. Volatility smirks are due primarily to large jumps rather than to small diffusive shocks.