DP5435 Parametric Properties of Semi-Nonparametric Distributions, With Applications to Option Valuation
Author(s): | Ángel León, Javier Mencía, Enrique Sentana |
Publication Date: | December 2005 |
Keyword(s): | density expansions, Gram-Charlier, Kurtosis, S&P index options, skewness |
JEL(s): | C16, G13 |
Programme Areas: | Financial Economics |
Link to this Page: | cepr.org/active/publications/discussion_papers/dp.php?dpno=5435 |
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 Rockinger (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 the truncated expansions.