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

60 Pages Posted: 29 Mar 2007

See all articles by Angel Leon

Angel Leon

Universidad de Alicante

Javier Mencia

Banco de España

Enrique Sentana

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

Multiple version iconThere are 2 versions of this paper

Date Written: 03/27/2007

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 flexible than truncated Gram-Charlier expansions with positivity restrictions. We use the SNP densities for financial derivatives valuation. We relate real and risk-neutral measures, obtain closed-form prices for European options, and analyse the semiparametric properties of our pricing model. In an empirical application to S&P500 index options, we compare our model to the standard and Practitioner's Black-Scholes formulas, truncated expansions, and the Generalised Beta and Variance Gamma models.

Keywords: kurtosis, density expansions, gram-charlier, skewness, s&p index options

JEL Classification: G13, C16

Suggested Citation

Leon, Angel and Mencia, Javier and Sentana, Enrique, Parametric Properties of Semi-Nonparametric Distributions, with Applications to Option Valuation (03/27/2007). Banco de España Research Paper No. WP-0707. Available at SSRN: https://ssrn.com/abstract=976595 or http://dx.doi.org/10.2139/ssrn.976595

Angel Leon (Contact Author)

Universidad de Alicante ( email )

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

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

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

Houghton Street
London School of Economics & Political Science (LSE)
London WC2A 2AE
United Kingdom
+44 20 7955 7002 (Phone)
+44 20 7852 3580 (Fax)

Centre for Economic Policy Research (CEPR)

London
United Kingdom

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