Nonlinear Filtering and Parameter Estimation for an Affine Jump Diffusion Process
ABSTRACT: I consider a nonlinear ﬁltering problem for the generalized Hawkes process, with applications to portfolio credit risk. The investors in the market have access to the credit history of ﬁrms with correlated default risk, but the observations of default times are only available at ﬁxed time intervals. The intensity driving the default counting process is exposed to an unobservable risk factor in the market, but also reacts to a jump in the counting process itself. Thus, a default of a name in the portfolio directly impacts the survival rate of the remaining ﬁrms. I will present some of the properties of the non-linear ﬁlter constructed for this hidden Markov model in discrete time, and its sensitivity with respect to the parameters of the model. I will also address the estimation of parameters in this context, and discuss the implementation of the Expectation Maximization Algorithm for this affine jump diffusion model in an incomplete information set-up.