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A GARCH Option Pricing Model in Incomplete Markets

Author

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  • Giovanni Barone-Adesi

    (University of Lugano and Swiss Finance Institute)

  • Robert F. Engle

    (New York University, Leonard Stern School of Business)

  • Loriano Mancini

    (University of Zurich and Swiss Banking 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.

Suggested Citation

  • Giovanni Barone-Adesi & Robert F. Engle & Loriano Mancini, 2004. "A GARCH Option Pricing Model in Incomplete Markets," Swiss Finance Institute Research Paper Series 07-03, Swiss Finance Institute, revised Feb 2007.
  • Handle: RePEc:chf:rpseri:rp0703
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    Cited by:

    1. Juan-Pablo Ortega, 2012. "GARCH options via local risk minimization," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 1095-1110, May.

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