Y.-N. Lin and K. Hung (Taiwan)
Derivatives, implied volatility tree, kernel regression, risk-neutral distribution
This paper implements an algorithm to infer, from the implied volatility tree, the risk-neutral density that is directly comparable to the risk-neutral density implicit in the kernel-regression volatility surface on which the tree is constructed. The equity between the tree-based and kernel-regression-based risk-neutral densities becomes an empirical issue on the validity of the implied volatility tree model in option pricing. Three different tests, consisting of the moment comparison, Kolmogorov Smirnov statistic, and relative differences in skewness and kurtosis premiums, are performed for the S&P 500 index options over the period, January 1990-December 1995. Our comparison reveals that the market prices S&P 500 options with an overly skewed and leptokurtic risk-neutral density. The matches between these two distributions for 30 and 100 days to expiry are found. The inaccuracy for 300-day options is remarkably stable with respect to different period choices. Out-of-sample fit and hedging effectiveness are examined to investigate the implied volatility tree's applicability to pricing S&P 500 index options of various maturities. The tree model appears to produce better results for call options with maturity equal to 30 and 100 days.
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