In this paper a method is developed and implemented to provide the simulated maximum likelihood estimation of latent diffusions based on discrete data. The method is applicable to diffusions that either have latent elements in the state vector or are only observed at discrete time with a noise....

A new algorithm is developed to provide a simulated maximum likelihood estimation of the GARCH diffusion model of Nelson (1990) based on return data only. The method combines two accurate approximation procedures, namely, the polynomial expansion of Aït-Sahalia (2008) to approximate the...