Dynamics of state price densities

Wolfgang Härdle , Zdeněk Hlávka

State price densities (SPDs) are an important element in applied quantitative finance. In a Black-Scholes world they are lognormal distributions but in practice volatility changes and the distribution deviates from log-normality. In order to study the degree of this deviation, we estimate SPDs using EUREX option data on the DAX index via a nonparametric estimator of the second derivative of the (European) call pricing function. The estimator is constrained so as to satisfy no-arbitrage constraints and corrects for the intraday covariance structure in option prices. In contrast to existing methods, we do not use any parametric or smoothness assumptions.

Mots clés: C13; C14; G13; Option pricing; State price density; Nonlinear least squares; Constrained estimation

Wolfgang Härdle, Zdeněk Hlávka. Dynamics of state price densities. Econometrics, 2009, 150 (1), pp.1. ⟨10.1016/j.jeconom.2009.01.005⟩. ⟨hal-00556046⟩