This paper extends the class of stochastic volatility diffusions for asset returns to include time-varying intensity Poisson jumps. The authors find that any reasonable continuous-time model for equity-index returns must account for both discrete jumps and stochastic volatility, with a pronounced negative relationship between return and volatility innovations. They also find that the dominant empirical characteristics of the return process are priced by the option market. The analysis suggests a general correspondence between the evidence from daily equity-index returns and the stylized features of corresponding options market prices. The paper uses a simulated method of moments (SMM) technique to estimate the model parameters, focusing on the adequacy of the model under the "physical" measure. The results indicate that both stochastic volatility and discrete jump components are critical for capturing the skewness and leptokurtosis in S&P500 returns. The estimated model parameters are similar to those obtained from previous studies using only equity options, and the model produces option pricing implications that correspond qualitatively to those from actual derivatives data. The paper avoids using derivatives prices for estimation to focus on the underlying asset return dynamics, which is crucial for practical hedging, risk management, portfolio allocation, and asset pricing decisions.This paper extends the class of stochastic volatility diffusions for asset returns to include time-varying intensity Poisson jumps. The authors find that any reasonable continuous-time model for equity-index returns must account for both discrete jumps and stochastic volatility, with a pronounced negative relationship between return and volatility innovations. They also find that the dominant empirical characteristics of the return process are priced by the option market. The analysis suggests a general correspondence between the evidence from daily equity-index returns and the stylized features of corresponding options market prices. The paper uses a simulated method of moments (SMM) technique to estimate the model parameters, focusing on the adequacy of the model under the "physical" measure. The results indicate that both stochastic volatility and discrete jump components are critical for capturing the skewness and leptokurtosis in S&P500 returns. The estimated model parameters are similar to those obtained from previous studies using only equity options, and the model produces option pricing implications that correspond qualitatively to those from actual derivatives data. The paper avoids using derivatives prices for estimation to focus on the underlying asset return dynamics, which is crucial for practical hedging, risk management, portfolio allocation, and asset pricing decisions.