We reveal that in the estimation of univariate GARCH or multivariate generalized orthogonal GARCH (GO-GARCH) models, maximizing the likelihood is equivalent to making the standardized residuals as independent as possible. Based on that, we propose three factor GARCH models in the framework of GO-GARCH: independent-factor GARCH exploits factors that are statistically as independent as possible; ...

4 GARCH Models 7 4.1 Basic GARCH Specifications . . . . . . . . . . . . . . . . . . . 8 4.2 Diagnostic Checking . . . . . . . . . . . . . . . . . . . . . . . 11 4.3 Regressors in the Variance Equation . . . . . . . . . . . . . . . 12 4.4 The GARCH–M Model . . . . . . . . . . . . . . . . . . . . . . 12 4.5 The Threshold GARCH (TARCH) Model . . . . . . . . . . . . 12 4.6 The Exponential GARCH (EG...

Applying the Cherny-Shiryaev-Yor invariance principle, we introduce a generalized Jarrow-Rudd (GJR) option pricing model with uncertainty driven by skew random walk. The GJR tree exhibits skewness and kurtosis in both natural risk-neutral world. We construct implied surfaces for parameters determining tree. Motivated Merton’s incorporating transaction costs, extend to include hedging cost. demo...

To capture the missed information in the standardized errors by parametric multivariate generalized autoregressive conditional heteroskedasticity (MV-GARCH) model, we propose a new semiparametric MV-GARCH (SM-GARCH) model. This SM-GARCH model is a twostep model: firstly estimating parametric MV-GARCH model, then using nonparametric skills to model the conditional covariance matrix of the standa...

The augmented GARCH model is a unification of numerous extensions of the popular and widely used ARCH process. It was introduced by Duan and besides ordinary (linear) GARCH processes, it contains exponential GARCH, power GARCH, threshold GARCH, asymmetric GARCH, etc. In this paper, we study the probabilistic structure of augmented GARCH(1,1) sequences and the asymptotic distribution of various ...

This brief note offers an explicit algorithm for a multivariate GARCH model, called PC-GARCH, that requires only univariate GARCH estimation. It is suitable for problems with hundreds or even thousands of variables. PC-GARCH is compared to two other techniques of getting multivariate GARCH using univariate estimates.

Abstract This study investigated the reaction of German stock market volatility (Dax index) to European Central Bank (ECB)’s unconventional monetary policy (UMP) announcements. The financial crisis 2008 proved that traditional policy’s tool (the short -term interest rate) has lost its effectiveness meet new challenges. So, key central banks, ECB included, had implement new, untested and nonstan...