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Parametric Properties of Semi-Nonparametric Distributions, with Applications to Option Valuation

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  • León, à ngel
  • Mencía, Javier
  • Sentana, Enrique

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 Nempirical 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.
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Suggested Citation

  • León, à ngel & Mencía, Javier & Sentana, Enrique, 2009. "Parametric Properties of Semi-Nonparametric Distributions, with Applications to Option Valuation," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 176-192.
    • Handle: RePEc:bes:jnlbes:v:27:i:2:y:2009:p:176-192
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    JEL classification:

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

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