Minimum Disparity Estimator in Continuous Time Stochastic Volatility Model
Minimum Disparity Estimator in Continuous Time Stochastic Volatility Model
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Date
2010
Authors
Li, Ziliang
Advisor
Slud, Eric V.
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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.