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

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.

Number of Pages in PDF File: 60

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

JEL Classification: G13, C16

working papers series