Estimation of Continuous Time Processes Via the Empirical Characteristic Function

This paper examines a particular class of continuous-time stochastic processes commonly known as af¿ne diffusions (AD) and af¿ne jump-diffusions (AJD) in which the drift, the diffusion and the jump coef¿cients are all af¿ne functions of the state variables. By deriving the joint characteristic function associated with a vector of observed state variables for such models, we are able to examine the statistical properties of these diffusions and jump-diffusions as well as develop an ef¿cient estimation technique based on empirical characteristic functions (ECF) and a GMM estimation procedure based on exact moment conditions. The estimators developed in this paper are in stark contrast to those available in the literature in the sense that our methods require neither discretization nor simulation. We demonstrate that our methods are in particular useful for the AD and AJD models with latent variables, i.e. the case where some of the state variables are unobserved. We illustrate our approach with a detailed examination of the continuous-time square-root stochastic volatility (SV) model, along with an empirical application using S&P 500 index returns.