Maximum Likelihood Estimation in Nonlinear Fractional Stochastic Volatility Model

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.