Parametric properties of semi-nonparametric distributions, with applications to option valuation
AbstractWe 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.
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Bibliographic InfoPaper provided by Banco de Espa�a in its series Banco de Espa�a Working Papers with number 0707.
Length: 60 pages
Date of creation: Mar 2007
Date of revision:
kurtosis; density expansions; gram-charlier; skewness; s&p index options;
Other versions of this item:
- LeÃ³n, Ãngel & MencÃa, 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.
- León, Ángel & Mencía, Javier & Sentana, Enrique, 2005. "Parametric Properties of Semi-Nonparametric Distributions, With Applications to Option Valuation," CEPR Discussion Papers 5435, C.E.P.R. Discussion Papers.
- Ángel León & Javier Mencía & Enrique Sentana, 2005. "Parametric Properties Of Semi-Nonparametric Distributions, With Applications To Option Valuation," Working Papers wp2005_0509, CEMFI.
- 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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