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 InfoArticle provided by American Statistical Association in its journal Journal of Business and Economic Statistics.
Volume (Year): 27 (2009)
Issue (Month): 2 ()
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Other versions of this item:
- Ángel León & Javier Mencía & Enrique Sentana, 2005. "Parametric Properties Of Semi-Nonparametric Distributions, With Applications To Option Valuation," Working Papers wp2005_0509, CEMFI.
- 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, 2007. "Parametric properties of semi-nonparametric distributions, with applications to option valuation," Banco de Espaï¿½a Working Papers 0707, Banco de Espa�a.
- 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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