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Estimating state price densities by Hermite polynomials: theory and application to the Italian derivatives market

  • Paolo Guasoni

    ()

    (Universita' di Pisa)

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    We study the problem of extracting the state price densities from the market prices of listed options. Adapting a model of Madan and Milne to a multiple expiration setting, we present an estimation method for the risk-neutral probability at a moving horizon of fixed length. With the exception of volatility, all model parameters can be estimated by linear regression and their number can be chosen arbitrarily, depending on the size of the dataset. We discuss empirical issues related to the application of this model to real data and show results on listed options on the Italian MIB30 equity index.

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    File URL: http://www.bancaditalia.it/pubblicazioni/temi-discussione/2004/2004-0507/tema_507.pdf
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    Paper provided by Bank of Italy, Economic Research and International Relations Area in its series Temi di discussione (Economic working papers) with number 507.

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    Date of creation: Jul 2004
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    Handle: RePEc:bdi:wptemi:td_507_04
    Contact details of provider: Postal: Via Nazionale, 91 - 00184 Roma
    Web page: http://www.bancaditalia.it

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    1. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    2. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
    3. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
    4. Frank Milne & Dilip Madan, 1994. "Contingent Claims Valued And Hedged By Pricing And Investing In A Basis," Working Papers 1158, Queen's University, Department of Economics.
    5. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
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