Parameter Estimation for a Fractional Black-Scholes Model with Jumps from Discrete Time Observations

We consider a stochastic differential equation (SDE) governed by a fractional Brownian motion (B-t(H)) and a Poisson process (N-t) associated with a stochastic process (A(t)) such that: dX(t) = mu X(t)dt + sigma X(t)dB(t)(H) + A(t)X(t)-dN(t), X-0 = x(0) > 0. The solution of this SDE is analyzed and properties of its trajectories are presented. Estimators of the model parameters are proposed when the observations are carried out in discrete time. Some convergence properties of these estimators are provided according to conditions concerning the value of the Hurst index and the nonequidistance of the observation dates.