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Dynamics of state price densities

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  • Härdle, Wolfgang Karl
  • Hlávka, Zdeněk

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.

Suggested Citation

  • Härdle, Wolfgang Karl & Hlávka, Zdeněk, 2005. "Dynamics of state price densities," SFB 649 Discussion Papers 2005-021, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2005-021
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    References listed on IDEAS

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    1. Yatchew, Adonis & Hardle, Wolfgang, 2006. "Nonparametric state price density estimation using constrained least squares and the bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 579-599, August.
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    5. Huynh, Kim & Kervella, Pierre & Zheng, Jun, 2002. "Estimating state-price densities with nonparametric regression," SFB 373 Discussion Papers 2002,40, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Ait-Sahalia, Yacine & Wang, Yubo & Yared, Francis, 2001. "Do option markets correctly price the probabilities of movement of the underlying asset?," Journal of Econometrics, Elsevier, vol. 102(1), pages 67-110, May.
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    Cited by:

    1. Hans Buehler, 2006. "Expensive martingales," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 207-218.
    2. Matthias Fengler, 2009. "Arbitrage-free smoothing of the implied volatility surface," Quantitative Finance, Taylor & Francis Journals, vol. 9(4), pages 417-428.
    3. repec:hum:wpaper:sfb649dp2005-019 is not listed on IDEAS

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    Keywords

    option pricing; state price density estimation; nonlinear least squares; confidence intervals;
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