Minimum Disparity Estimator in Continuous Time Stochastic Volatility Model

Abstract

In the study of finance, likelihood based or moment based methods are frequently

used to estimate parameters for various kinds of models given the sampled return

data. While the former method is not robust, the latter one suffers from loss of

efficiency and high noise-to-signal ratio in the data. In this paper, we investigate the

ergodic behavior of the bivariate series described by the Barndorff-Nielsen and

Shephard (BN-S) stochastic volatility model. In particular, we study its beta-mixing

property and the differentiability of its stationary distribution. A robust and efficient

estimation scheme for continuous models called the Negative Exponential Disparity

Estimator (NEDE) is studied. We apply this method and the classical Method of

Moments (MOM) to the BN-S model. Asymptotic properties of the NEDE and the

MOM estimator are proved, implementation details are provided.