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A GARCH Option Pricing Model in Incomplete Markets

Giovanni Barone-Adesi, Robert Engle and Loriano Mancini
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Giovanni Barone-Adesi: University of Lugano and Swiss Finance Institute
Loriano Mancini: University of Zurich and Swiss Banking Institute

No 07-03, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework we allow for different distributions of the historical and the pricing return dynamics enhancing the model flexibility to fit market option prices. An extensive empirical analysis based on S&P 500 index options shows that our model outperforms other competing GARCH pricing models and ad hoc Black-Scholes models. Using our GARCH model and a nonparametric approach we obtain decreasing state price densities per unit probability as suggested by economic theory, validating our GARCH pricing model. Implied volatility smiles appear to be explained by the negative asymmetry of the filtered historical innovations. A new simplified delta hedging scheme is presented based on conditions usually found in option markets, namely the local homogeneity of the pricing function. We provide empirical evidence and we quantify the deterioration of the delta hedging in the presence of large volatility shocks.

New Economics Papers: this item is included in nep-ecm and nep-fmk
Date: 2007-02
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