Maximum Likelihood Estimation in Nonlinear Fractional Stochastic Volatility Model
Jaya P. N. Bishwal *
Department of Mathematics and Statistics, University of North Carolina at Charlotte, University City Blvd, Charlotte, NC 28223, USA.
*Author to whom correspondence should be addressed.
Abstract
We study the strong consistency and asymptotic normality of the maximum likelihood estimator (MLE) of a drift parameter in a stochastic volatility model when both the asset price process and the stochastic volatility are driven by independent fractional Brownian motions. Long memory in volatility is a stylized fact. We compute the nonlinear filter in the MLE using Kitagawa algorithm.
Keywords: Fractional Brownian motion, stochastic volatility model, maximum likelihood estimate, strong consistency, asymptotic normality, nonlinear ltering, long-range dependence.