Model risk of the implied GARCH-normal model

Abstract

Model risk causes significant losses in financial derivative pricing and hedging. Investors may undertake relatively risky investments due to insufficient hedging or overpaying implied by flawed models. The GARCH model with normal innovations (GARCH-normal) has been adopted to depict the dynamics of the returns in many applications. The implied GARCH-normal model is the one minimizing the mean square error between the market option values and the GARCH-normal option prices. In this study, we investigate the model risk of the implied GARCH-normal model fitted to conditional leptokurtic returns, an important feature of financial data. The risk-neutral GARCH model with conditional leptokurtic innovations is derived by the extended Girsanov principle. The option prices and hedging positions of the conditional leptokurtic GARCH models are obtained by extending the dynamic semiparametric approach of Huang and Guo [Statist. Sin., 2009, 19, 1037–1054]. In the simulation study we find significant model risk of the implied GARCH-normal model in pricing and hedging barrier and lookback options when the underlying dynamics follow a GARCH-t model.