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 GARCHnormal 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.

A network autoregressive model with GARCH effects and its applications

“…Moreover,ε h;tÀ d j h À kþ1 denotes the corresponding lag-k standardized residual of the h-th index for the j-th index at date t with the definition of d j h . The NAR model defined in ( 9) is a special case of model (6). Since the standardized residual process of each index obtained in Step 1 has a mean of zero and does not have autocorrelation, we remove the first two terms on the right-hand side (RHS) of (6).…”

“…The NAR model defined in ( 9) is a special case of model (6). Since the standardized residual process of each index obtained in Step 1 has a mean of zero and does not have autocorrelation, we remove the first two terms on the right-hand side (RHS) of (6). The 4th term on the RHS of ( 6) is also removed since we did not include any covariate yet in this study.…”

“…In addition, many empirical findings indicate that the return process of a stock index usually has the features of potential autocorrelation, conditional heteroscedasticity, volatility clustering, asymmetry, and heavy-tailed distribution. To characterize these features, GARCH-type models are commonly used in economics, finance, and statistics (see [1,[4][5][6][7][8] and the references therein). Therefore, to simultaneously consider the joint effects among multiple return processes and the above features contained in each financial time series, a VAR model with the de-GARCH technique is widely used for modeling multivariate time series (see [9][10][11] and the references therein).…”

An Empirical Study on Implied GARCH Models

“…Unlike the result in Proposition 2.1 for the GARCH-N model, the change of measure processes Λ ess t and Λ egp t in Proposition 2.2 are no longer equal. Huang and Guo (2011) established the derivation of the risk-neutral GARCH models under Q egp in a general setting. Hence, by applying Proposition 3.1 of Huang and Guo (2011), the risk-neutral GARCH models with double exponential innovations considered in this study under Q egp can be obtained.…”

“…Thus researchers have considered GARCH models with leptokurtic innovations. For example, the GARCH model with standardized t innovations (Bollerslev, 1987), generalized exponential innovations (Nelson, 1991), shifted-gamma innovations (Siu, Tong and Yang, 2004) and double-exponential innovations (Huang, 2011;Huang and Guo, 2011) have been discussed. To evaluate the financial derivatives in GARCH models with leptokurtic innovations, the Esscher transform (Gerber and Shiu, 1994) and the extended Girsanov principle (Elliott and Madan, 1998) are two popular change of measure processes used in practice (Badescu and Kulperger, 2008).…”