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State price density estimation via nonparametric mixtures

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  • Ming Yuan
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    Abstract

    We consider nonparametric estimation of the state price density encapsulated in option prices. Unlike usual density estimation problems, we only observe option prices and their corresponding strike prices rather than samples from the state price density. We propose to model the state price density directly with a nonparametric mixture and estimate it using least squares. We show that although the minimization is taken over an infinitely dimensional function space, the minimizer always admits a finite dimensional representation and can be computed efficiently. We also prove that the proposed estimate of the state price density function converges to the truth at a ``nearly parametric'' rate.

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    File URL: http://arxiv.org/pdf/0910.1430
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0910.1430.

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    Date of creation: Oct 2009
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    Publication status: Published in Annals of Applied Statistics 2009, Vol. 3, No. 3, 963-984
    Handle: RePEc:arx:papers:0910.1430

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    1. Yacine Ait-Sahalia & Jefferson Duarte, 2002. "Nonparametric Option Pricing under Shape Restrictions," NBER Working Papers 8944, National Bureau of Economic Research, Inc.
    2. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
    3. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, American Finance Association, vol. 49(3), pages 771-818, July.
    4. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-51.
    5. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 51(4), pages 621-51, October.
    6. Joshua Rosenberg & Robert F. Engle, 2000. "Empirical Pricing Kernels," New York University, Leonard N. Stern School Finance Department Working Paper Seires, New York University, Leonard N. Stern School of Business- 99-014, New York University, Leonard N. Stern School of Business-.
    7. Buchen, Peter W. & Kelly, Michael, 1996. "The Maximum Entropy Distribution of an Asset Inferred from Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 31(01), pages 143-159, March.
    8. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers, University of California at Berkeley RPF-232, University of California at Berkeley.
    9. René Garcia & Eric Ghysels & Éric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers, CIRANO 2004s-04, CIRANO.
    10. Hutchinson, James M & Lo, Andrew W & Poggio, Tomaso, 1994. " A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks," Journal of Finance, American Finance Association, American Finance Association, vol. 49(3), pages 851-89, July.
    11. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, Elsevier, vol. 94(1-2), pages 9-51.
    12. Banz, Rolf W & Miller, Merton H, 1978. "Prices for State-contingent Claims: Some Estimates and Applications," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 51(4), pages 653-72, October.
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    Cited by:
    1. Wolfgang Karl Härdle & Brenda López-Cabrera & Huei-Wen Teng, 2013. "State Price Densities implied from weather derivatives," SFB 649 Discussion Papers SFB649DP2013-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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