Bias in the Estimate of a Mean Reversion Parameter for a Fractional Ornstein-Uhlenbeck Process

Abstract

In this thesis we studied the estimation bias of the least squares estimate of the mean reversion parameter, when the underlying dynamics is governed by fractional Brownian motions. Fractional Brownian motion is a continuous-time model with long-range dependency features. Least squares estimate for the mean reversion parameter under standard Brownian motion framework has been shown to be positively biased. Using an approximate bias formula, we show that the estimation bias in the fractional Brownian case behaves differently from the standard Brownian motion case, and in fact can be negative depending on the Hurst parameter and the true value of the mean reversion. We conclude the thesis by looking into the implication of these results from the perspective of risk management.