Dynamics of state price densities

Wolfgang Härdle and Zdeněk Hlávka

No 2005-021, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

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.

Keywords: option pricing; state price density estimation; nonlinear least squares; confidence intervals (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb649:sfb649dp2005-021

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