Parametric properties of semi-nonparametric distributions, with applications to option valuation
- León Valle, Angel
- Mencía, Javier
- Sentana Iváñez, Enrique
ISSN: 0213-2710
Year of publication: 2007
Issue: 7
Pages: 5-62
Type: Working paper
More publications in: Documentos de trabajo - Banco de España
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.