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Parametric properties of semi-nonparametric distributions, with applications to option valuation

Author

Listed:
  • Ángel León

    (Universidad de Alicante)

  • Javier Mencía

    (Banco de España)

  • Enrique Sentana

    (Centro de Estudios Monetarios y Financieros (CEMFI))

Abstract

We derive the statistical properties of the SNP densities of Gallant and Nychka (1987). We show that these densities, which are always positive, are more flexible than truncated Gram-Charlier expansions with positivity restrictions. We use the SNP densities for financial derivatives valuation. We relate real and risk-neutral measures, obtain closed-form prices for European options, and analyse the semiparametric properties of our pricing model. In an empirical application to S&P500 index options, we compare our model to the standard and Practitioner's Black-Scholes formulas, truncated expansions, and the Generalised Beta and Variance Gamma models.

Suggested Citation

  • Ángel León & Javier Mencía & Enrique Sentana, 2007. "Parametric properties of semi-nonparametric distributions, with applications to option valuation," Working Papers 0707, Banco de España.
    • Handle: RePEc:bde:wpaper:0707
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    References listed on IDEAS

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    More about this item

    Keywords

    kurtosis; density expansions; gram-charlier; skewness; s&p index options;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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