In this paper we consider a general ...rst-order power ARCH process and, in particular, a special case in which the power parameter approaches zero. These considerations give us the autocorrelation function of the logarithms of the squared observations for ...rstorder exponential and logarithmic GARCH processes. These autocorrelations decay exponentially with the lag and may be used for checkin...

Volatility modelling of asset returns is an important aspect for many financial applications, e.g., option pricing and risk management. GARCH models are usually used to model the volatility processes of financial time series. However, multivariate GARCH modelling of volatilities is still a challenge due to the complexity of parameters estimation. To solve this problem, we suggest using Independ...

Considering alternative models for exchange rates has always been a central issue in applied research. Despite this fact, formal likelihood-based comparisons of competing models are extremely rare. In this paper, we apply the Bayesian marginal likelihood concept to compare GARCH, stable, stable GARCH, stochastic volatility, and a new stable Paretian stochastic volatility model for seven major c...

A simple iterative algorithm for nonparametric 1rst-order GARCH modelling is proposed. This method o4ers an alternative to 1tting one of the many di4erent parametric GARCH speci1cations that have been proposed in the literature. A theoretical justi1cation for the algorithm is provided and examples of its application to simulated data from various stationary processes showing stochastic volatili...

We develop a misspecification test for the multiplicative two-component GARCHMIDAS model suggested in Engle et al. (2013). In the GARCH-MIDAS model a short-term unit variance GARCH component fluctuates around a smoothly timevarying long-term component which is driven by the dynamics of a macroeconomic explanatory variable. We suggest a Lagrange Multiplier statistic for testing the null hypothes...

We are interested in estimation of stationary GARCH models. In simulation studies, we assess the performance of the maximum likelihood estimator and Yule-Walker estimator of the GARCH (1, 1) model. Finally we attempt to fit the dynamics of daily stock returns on Nordea by a GARCH model.

GARCH model has gained popularity during the last two decades, because of their ability to capture non-linear dynamics in the real life data which we often observe especially in financial markets. This paper discuss four common information criteria (AIC, AICc, BIC and HQ) and their ability of correct selection in the presence of GARCH effect, based on their probability of correct selection as a...

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...

In this paper, we take the advantage of high frequency data to develop option pricing model and select the Realized GARCH model to describe the volatility of assets, use NIG distribution to describe the distribution of underlying assets, and also build the Realized-GARCH-NIG model to price the option. Finally, we obtain the dynamic option pricing model based on the Realized-GARCH-NIG approach. ...

This paper presents an effective way of combining two popular, yet distinct approaches used in the hedging literature – dynamic programming (DP) and time-series (GARCH) econometrics. Theoretically consistent yet realistic and tractable models are developed for traders interested in hedging a portfolio. Results from a bootstrapping experiment used to construct confidence bands around the competi...