Parametric Properties of Semi-Nonparametric Distributions, with Applications to Option Valuation

52 Pages Posted: 17 Apr 2006

See all articles by Javier Mencia

Javier Mencia

Banco de España

Enrique Sentana

Centro de Estudios Monetarios y Financieros (CEMFI); Financial Markets Group; Centre for Economic Policy Research (CEPR)

Angel Leon

Universidad de Alicante

Multiple version iconThere are 2 versions of this paper

Date Written: December 2005

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.

Keywords: Kurtosis, density expansions, Gram-Charlier, skewness, S&P index options

JEL Classification: C16, G13

Suggested Citation

Mencia, Javier and Sentana, Enrique and Leon, Angel, Parametric Properties of Semi-Nonparametric Distributions, with Applications to Option Valuation (December 2005). CEPR Discussion Paper No. 5435. Available at SSRN: https://ssrn.com/abstract=897351

Javier Mencia

Banco de España ( email )

Alcala 50
Madrid 28014
Spain
+34 91 338 5414 (Phone)
+34 91 338 6104 (Fax)

HOME PAGE: http://www.bde.es/investigador/staff/66.htm

Enrique Sentana (Contact Author)

Centro de Estudios Monetarios y Financieros (CEMFI) ( email )

Casado del Alisal 5
28014 Madrid
Spain
+34 91 429 0551 (Phone)
+34 91 429 1056 (Fax)

HOME PAGE: http://www.cemfi.es/~sentana/

Financial Markets Group

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London School of Economics & Political Science (LSE)
London WC2A 2AE
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+44 20 7955 7002 (Phone)
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Centre for Economic Policy Research (CEPR)

London
United Kingdom

Angel Leon

Universidad de Alicante ( email )

Campus de San Vicente
Carretera San Vicente del Raspeig
San Vicente del Raspeig, 03690
Spain

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