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Confidence Intervals for State Price Densities

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  • Hlávka, Zdeněk

Abstract

The state price density is a second derivative of the discounted European options prices with respect to the strike price. We use Maximum Likelihood method to derive a simple estimator of the curve such that it is decreasing, convex and its second derivative integrates to one. Confidence intervals for this estimator can be constructed using standard Maximum Likelihood theory. The method works well in praxis as illustrated on the DAX option prices data.

Suggested Citation

  • Hlávka, Zdeněk, 2003. "Confidence Intervals for State Price Densities," SFB 373 Discussion Papers 2003,34, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:200334
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    References listed on IDEAS

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    1. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    2. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    3. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
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