Essays in empirical finance

Much asset and derivative pricing theory is based on diffusion models for primary securities. However, prescriptions for practical applications derived from these models typically produce disappointing results. The objective of this dissertation is to investigate a general class of continuous-time diffusions that can be used for modeling equity returns and provide a more satisfactory basis for asset pricing applications.; In the first essay, I exploit data on S&P500 returns and option prices to estimate two common asymmetric stochastic volatility diffusion models, the log-variance specification of Melino and Turnbull (1990) and the square-root representation of Heston (1993). Stochastic volatility greatly enhances the models' performance. For instance, both models are able to capture asymmetries in stock returns, and to reduce option pricing errors. Suggestive diagnostic tools are developed based on the concept of “SV implied volatilities,” variance estimates computed from option prices. Big discrepancies are observed between SV implied volatilities and other return-based variance estimates, indicative of the presence of inconsistencies in the joint model of option prices and stock returns. The volatility risk is priced by the market: the risk premium is statistically significant and has a big impact on option prices. A non-zero risk premium reduces the pricing errors considerably and affects the state-price densities (SPDs) significantly, by fattening their tails. Finally, I use SPDs to compare and interpret the (mis)pricing of the two models.; In the second essay, joint work with Torben Andersen and Jesper Lund, I extend the class of stochastic volatility diffusions to encompass Poisson jumps of time-varying intensity. We find that any reasonably descriptive continuous-time model for equity-index returns must allow for discrete jumps as well as stochastic volatility with a pronounced negative relationship between return and volatility innovations. We also find that the dominant empirical characteristics of the return process appear to be priced by the option market. Our analysis indicates a general correspondence between the evidence extracted from daily equity-index returns and the stylized features of the corresponding options market prices.