A GARCH Option Pricing Model with Filtered Historical Simulation
Swiss Finance Institute at the University of Lugano; Ecole Polytechnique Fédérale de Lausanne - Swiss Finance Institute
Robert F. Engle
New York University - Leonard N. Stern School of Business - Department of Economics; New York University (NYU) - Department of Finance; National Bureau of Economic Research (NBER)
Ecole Polytechnique Fédérale de Lausanne; Ecole Polytechnique Fédérale de Lausanne - Swiss Finance Institute
Review of Financial Studies, 2008
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 historical and 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. We show that the flexible change of measure, the asymmetric GARCH volatility and the nonparametric innovation distribution induce the accurate pricing performance of our model. Using a nonparametric approach, we obtain decreasing state price densities per unit probability as suggested by economic theory and corroborating our GARCH pricing model. Implied volatility smiles appear to be explained by asymmetric volatility and negative skewness of filtered historical innovations.
Number of Pages in PDF File: 54
Keywords: Option pricing, GARCH model, state price density, Monte Carlo simulation
JEL Classification: G13
Date posted: October 15, 2004 ; Last revised: April 29, 2008
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