Approximate Maximum Likelihood Estimates for Stock and Index Returns with Stochastic Volatility, Stochastic Jump Intensity, and Infinite-Activity Jumps

The Bates (2006) Approximate Maximum Likelihood (AML) method is considered from a practical point of view. Application of the AML method is undertaken using FFT with splines for integration. Results are validated by both simulation and comparison to MCMC literature. The SVJ model is estimated with infinite-activity jumps, and the SVSJ model is treated exclusively with Merton jumps. We maximize the likelihood unconstrained by the Feller condition, finding that certain data is unsuitable for infinite-activity jumps. But, infinite-activity jumps in the SVJ model describe some technology stocks particularly well. The Bates (2006) SVSJ Merton model often outperforms, and the Feller condition appears unlikely to fail with Merton jumps