Dynamics of state price densities

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SFB 649 Discussion Paper ; No. 2005,021

Classification and Topics

• Classification: Wirtschaft
• Subject: option pricing ; state price density estimation ; nonlinear least squares ; confidence intervals

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Härdle, Wolfgang Karl ; Hlávka, Zdeněk
• Event: Veröffentlichung
• (who): Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
• (where): Berlin
• (when): 2005

Further information

• Handle: http://hdl.handle.net/10419/25040
• Last update: 10.03.2025, 11:43 AM CET