Generalized Parameter Functions for Option Pricing
Journal of Banking & Finance, Volume 34, Issue 3, March 2010, Pages 633-646
Posted: 17 Mar 2008 Last revised: 19 Jul 2015
Date Written: November 3, 2008
We extend the benchmark nonlinear deterministic volatility regression functions of Dumas et al. (1998) to provide a semi-parametric method where an enhancement of the implied parameter values is used in the parametric option pricing models. Besides volatility, skewness and kurtosis of the asset return distribution can also be enhanced. Empirical results, using closing prices of the S&P 500 index call options (in one day ahead out-of-sample pricing tests), strongly support our method that compares favorably with a model that admits stochastic volatility and random jumps. Moreover, it is found to be superior in various robustness tests. Our semi-parametric approach is an effective remedy to the curse of dimensionality presented in nonparametric estimation and its main advantage is that it delivers theoretically consistent option prices and hedging parameters. The economic significance of the approach is tested in terms of hedging, where the evaluation and estimation loss functions are aligned.
Keywords: implied parameters, deterministic volatility functions, hedging, semi-parametric approach
JEL Classification: G13, G14
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