To date in literature, GARCH model has been described not suitable for non-linear foreign exchange series and therefore this paper proposes an Augmented GARCH model that could capture both linear and non-linear behavior of data. The properties of this new model is derived and found to have a minimum variance compared with GARCH model. We employ the use of Brock-DechertScheinkman (BDS) test stat...

We introduce a new family of processes that include the long memory (power law) in the volatility correlation. This is achieved by measuring the historical volatilities on a set of increasing time horizons and by computing the resulting effective volatility by a sum with power law weights. The processes have 2 parameters (linear processes) or 4 parameters (affine processes). In the limit where ...

In this paper, we propose a bounded influence estimation (BIE) and outlier detection procedure for GARCH models. Previous studies show that maximum likelihood estimates of GARCH models are sensitive to outliers and financial time series present a heavy tail due to outliers. The proposed BIE limits the influence of a small subset of the data and is asymptotically normal. Its robustness against o...

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset returns and volatilities. Our model nests Duan’s GARCH option models where conditional returns are constrained to being normal, as well as extends Merton’s jump-diffusion model by allowing return volatility to exhibit GARCH-like behavior. Empirical analysis on the S&P 500 index r...

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 paper estimates the dynamic conditional correlations in the returns on Tapis oil spot and onemonth forward prices for the period 2 June 1992 to 16 January 2004, using recently developed multivariate conditional volatility models, namely the Constant Conditional Correlation Multivariate GARCH (CCCMGARCH) model of Bollerslev [1990], Vector Autoregressive Moving Average – GARCH (VARMAGARCH) m...

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...

It is well-known that causal forecasting methods that include appropriately chosen Exogenous Variables (EVs) very often present improved forecasting performances over univariate methods. However, in practice, EVs are usually difficult to obtain and in many cases are not available at all. In this paper, a new causal forecasting approach, called Wavelet Auto-Regressive Integrated Moving Average w...

How persistent is volatility? In other words, how quickly do financial markets forget large volatility shocks? Figure 1.1, Shephard (attached) shows that daily squared returns on exchange rates and stock indices can have autocorrelations which are significant for many lags. In any stationary ARCH or GARCH model, memory decays exponentially fast. For example, if {εt } are ARCH (1), the {εt} have...