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 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.
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Bibliographic InfoPaper provided by CEMFI in its series Working Papers with number wp2005_0509.
Date of creation: Dec 2005
Date of revision:
Kurtosis; density expansions; Gram-Charlie; 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.
- Ángel León & Javier Mencía & Enrique Sentana, 2007. "Parametric properties of semi-nonparametric distributions, with applications to option valuation," Banco de Espaï¿½a Working Papers 0707, Banco de Espa�a.
- 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.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-09-11 (All new papers)
- NEP-FIN-2006-09-11 (Finance)
- NEP-FMK-2006-09-11 (Financial Markets)
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