Journal
JOURNAL OF BUSINESS & ECONOMIC STATISTICS
Volume 27, Issue 2, Pages 176-192Publisher
AMER STATISTICAL ASSOC
DOI: 10.1198/jbes.2009.0013
Keywords
Density expansions; Gram-Charlier; Kurtosis; Skewness
Funding
- Fundacion Ramon Areces (Mencia)
- Spanish Ministry of Education and Science [SEJ 2005-09372, SEJ 2005-08880]
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We derive the statistical properties of the semi-nonparametric (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 analyze 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 Generalized Beta and Variance Gamma models.
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