What Jump Process to use to Model S&P500 Returns?

This article estimates stochastic volatility jump-diffusion processes using the continuous empirical characteristic function method based on the Joint characteristic function and the Marginal characteristic function. The emphasis is on the specification of jumps in the asset log-price. Out of the models considered, stochastic volatility with normal jumps in the asset log-price fits the best the S&P500 index for the period from January 1980 to December 1999. Empirical characteristic unction estimation procedure based on the Marginal unconditional characteristic function is found to be more efficient when applied to the stochastic volatility models with jumps in the asset log-price. Joint unconditional characteristic function estimation is preferred in case of stochastic volatility model and stochastic volatility with jumps in both the asset log-prices and variance process.