Dr. Alexandra Chronopoulou (PSTAT-UCSB)

Title: Parameter Estimation for Fractional SDEs

Abstract: We consider the parameter estimation problem for a multidimensional stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H > 1/2, with non-linear random drift and diffusion coefficients. Due to the intractability of the likelihood function, we propose the maximizer of a partial likelihood as the estimator of the parameters of the model. We show how to compute this estimator using Malliavin calculus techniques and approximation results. We study the computational efficiency of our method and we provide rates of convergence for the approximation task. For a particular class of fractional SDEs, we establish consistency of the proposed estimator. We apply our methodology to the estimation of the parameters of the fractional Black-Scholes model using S&P 500 data.