Estimating state price densities by Hermite polynomials: theory and application to the Italian derivatives market
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.
|Date of creation:||Jul 2004|
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- Dilip B. Madan & Frank Milne, 1994.
"Contingent Claims Valued And Hedged By Pricing And Investing In A Basis,"
Wiley Blackwell, vol. 4(3), pages 223-245.
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- Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
- Rosenberg, Joshua V. & Engle, Robert F., 2002.
"Empirical pricing kernels,"
Journal of Financial Economics,
Elsevier, vol. 64(3), pages 341-372, June.
- Joshua Rosenberg & Robert F. Engle, 2000. "Empirical Pricing Kernels," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-014, New York University, Leonard N. Stern School of Business-.
- 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.
- Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
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