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

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  • Ángel León
  • Javier Mencía
  • Enrique Sentana

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 general than the truncated Gram-Charlier expansions of Jondeau and Rochinger (2001), who impose parameter restrictions to ensure positivity. We also use the SNP densities for option valuation. We relate real and risk-neutral measures, obtain closed-form prices for European options, and study the “Greeks”. We show that SNP densities generate wider option price ranges than the truncated expansions. In an empirical application to S&P 500 index options, we find that the SNP model beats the standard and Practitioner’s Black-Scholes formulas, and truncated expansions.

Suggested Citation

  • Ángel León & Javier Mencía & Enrique Sentana, 2005. "Parametric Properties of Semi-Nonparametric Distributions, with Applications to Option Valuation," Working Papers wp2005_0509, CEMFI.
    • Handle: RePEc:cmf:wpaper:wp2005_0509
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    References listed on IDEAS

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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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