A GARCH Option Pricing Model in Incomplete Markets
AbstractWe 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.
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Bibliographic InfoPaper provided by Swiss Finance Institute in its series Swiss Finance Institute Research Paper Series with number 07-03.
Length: 50 pages
Date of creation: Oct 2004
Date of revision: Feb 2007
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-10-20 (All new papers)
- NEP-ECM-2007-10-20 (Econometrics)
- NEP-FMK-2007-10-20 (Financial Markets)
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