Abstract
Abstract Although the Black–Scholes model lays the foundation to the modern option pricing theory, its empirical performance is rather unsatisfactory as manifested in the phenomenon known as volatility smile . This article explains what volatility smile is, and describes some nonparametric techniques and parametric models that may be used to deal with volatility smile for pricing and/or hedging purposes. Kernel regression and the GARCH option pricing model are chosen to be the nonparametric technique and parametric model, respectively, in our demonstration involving a sample of S&P 500 index options. Kernel regression is found to perform better than the GARCH model, but its applicability is limited to pricing the same type of options. Without providing a dynamic for the underlying asset price, kernel regression is also ill‐suited for hedging purposes. In contrast, the GARCH model is not subject to the same application limitations even though its performance on the same type of options is poorer. Thus, both nonparametric techniques and parametric models serve useful purposes in dealing with derivative contracts.
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