Working Paper: CEPR ID: DP5435
Authors: ngel Len; Javier Menca; Enrique Sentana
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: density expansions; Gram-Charlier; kurtosis; SP index options; skewness
JEL Codes: C16; G13
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| SNP distributions (C46) | prevention of arbitrage opportunities (F31) |
| SNP model (C59) | wider option price ranges (G13) |
| SNP model (C59) | improved performance over Black-Scholes model (C58) |
| SNP model (C59) | improved performance over truncated expansions (C34) |