Estimation of Continuous-Time Models with an Application to Equity Volatility Dynamics

Abstract

The treatment of this article renders closed-form density approximation feasible for univariate continuous-time models. Implementation methodology depends directly on the parametric-form of the drift and the diffusion of the primitive process and not on its transformation to a unit-variance process. Offering methodological convenience, the approximation method relies on numerically evaluating one-dimensional integrals and circumvents existing dependence on intractable multidimensional integrals. Density-based inferences can now be drawn for a broader set of models of equity volatility. Our empirical results provide insights on crucial outstanding issues related to the rank-orderings of continuous-time stochastic volatility models, the absence/presence of non-linearities in the drift function, and the desirability of pursuing more flexible diffusion function specifications.

Keywords: Continuous-time models, Maximum-likelihood estimation, Density approximation

JEL Classification: G10, G11, G12, G13, C15, C32, C52