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Discussion Paper Details

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Title: Parametric Properties of Semi-Nonparametric Distributions, With Applications to Option Valuation

Author(s): �ngel Le�n, Javier Menc�a and Enrique Sentana

Publication Date: December 2005

Keyword(s): density expansions, Gram-Charlier, Kurtosis, S&P index options and skewness

Programme Area(s): Financial Economics

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 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.

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Bibliographic Reference

Le�n, �, Menc�a, J and Sentana, E. 2005. 'Parametric Properties of Semi-Nonparametric Distributions, With Applications to Option Valuation'. London, Centre for Economic Policy Research. https://cepr.org/active/publications/discussion_papers/dp.php?dpno=5435