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Title:Dynamics of state price densities PDF Logo
Authors:Härdle, Wolfgang Karl
Hlávka, Zdeněk
Issue Date:2005
Series/Report no.:SFB 649 discussion paper 2005,021
Abstract:State price densities (SPD) are an important element in applied quantitative finance. In a Black-Scholes model they are lognormal distributions with constant volatility parameter. In practice volatility changes and the distribution deviates from log-normality. We estimate SPDs using EUREX option data on the DAX index via a nonparametric estimator of the second derivative of the (European) call price function. The estimator is constrained so as to satisfy no-arbitrage constraints and it corrects for intraday covariance structure. Given a low dimensional representation of this SPD we study its dynamic for the years 1995-2003. We calculate a prediction corridor for the DAX for a 45 day forecast. The proposed algorithm is simple, it allows calculation of future volatility and can be applied to hedging exotic options.
Subjects:option pricing
state price density estimation
nonlinear least squares
confidence intervals
Document Type:Working Paper
Appears in Collections:SFB 649 Discussion Papers, HU Berlin

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