Dynamic semiparametric factor models in risk neutral density estimation

Dynamic semiparametric factor models (DSFM) simultaneously smooth in space and are parametric in time, approximating complex dynamic structures by time invariant basis functions and low dimensional time series. In contrast to traditional dimension reduction techniques, DSFM allows the access of the dynamics embedded in high dimensional data through the lower dimensional time series. In this paper, we study the time behavior of risk assessments from investors facing random financial payoffs. We use DSFM to estimate risk neutral densities from a dataset of option prices on the German stock index DAX. The dynamics and term structure of risk neutral densities are investigated by Vector Autoregressive (VAR) methods applied on the estimated lower dimensional time series.