This paper investigates the forecasting ability of four different GARCH models and the Kalman filter method. The four GARCH models applied are the bivariate GARCH, BEKK GARCH, GARCH-GJR and the GARCH-X model. The paper also compares the forecasting ability of the non-GARCH model the Kalman method. Forecast errors based on twenty UK company weekly stock return (based on timevary beta) forecasts ...

We derive analytically the first four conditional moments of the integrated variance implied by the GARCH diffusion process. From these moments we obtain an analytical closed-form approximation formula to price European options under the GARCH diffusion model. Using Monte Carlo simulations, we show that this approximation formula is accurate for a large set of reasonable parameters. Finally, we...

After the so-called Asia crisis in the summer of 1997 the nancial markets were shaken by increased volatility transmission around the world. Therefore, in this paper we will analyse the daily exchange rates in New York, Germany, and Japan for the period of 2 years (June 21, 1996 to June 22, 1998). We estimate a VAR-GARCH in mean model and estimate the multivariate volatility e ects between the ...

In this paper we combine the appealing properties of the stable Paretian distribution to model the heavy tails and the GARCH model to capture the phenomenon of the volatility clustering. We assume the asset-returns to have a particular multivariate stable distribution, i.e., to be sub-Gaussian random vectors. In this way the characteristic function has a tractable expression and the density fun...

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...

This article establishes a family of models for pricing interest rate sensitive claims when the underlying interest rate is driven by a two state variable GARCH process. Analytical solutions are established for the case when the innovations in the short rate are combinations of a normal and chi-squared random variables and the volatility of rates takes on a special GARCH form. GARCH models that...