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


  • Paolo Guasoni

    () (Universita' di Pisa)


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.

Suggested Citation

  • Paolo Guasoni, 2004. "Estimating state price densities by Hermite polynomials: theory and application to the Italian derivatives market," Temi di discussione (Economic working papers) 507, Bank of Italy, Economic Research and International Relations Area.
  • Handle: RePEc:bdi:wptemi:td_507_04

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    References listed on IDEAS

    1. Dilip B. Madan & Frank Milne, 1994. "Contingent Claims Valued And Hedged By Pricing And Investing In A Basis," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 223-245.
    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 727-752.
    3. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    4. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    5. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
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    Cited by:

    1. Albert Ando & Sergio Nicoletti-Altimari, 2004. "A micro simulation model of demographic development and households' economic behavior in Italy," Temi di discussione (Economic working papers) 533, Bank of Italy, Economic Research and International Relations Area.

    More about this item


    option pricing; state-price densities; orthogonal polynomials; risk-neutral valuation; calibration;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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