A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for economics and finance. GARCH models are typically estimated by the Quasi-Maximum Likelihood (QML) method, which works under mild statistical assumptions. Here...

This paper proposes a simple test for threshold nonlinearity in either the mean or volatility equation, or both, of a heteroskedastic time series. Our proposal adopts existing Bayesian Markov chain Monte Carlo methods to fit a general double threshold GARCH model, which may have an explosive regime, then forms posterior credible intervals on model parameters to detect and specify threshold nonl...

We propose a method of estimating the Pareto tail thickness parameter of the unconditional distribution of a financial time series by exploiting the implications of a GJR-GARCH volatility model. The method is based on some recent work on the extremes of GARCH-type processes. We show that the estimator of tail thickness is consistent and converges at rate √ T to a normal distribution (where T is...

This paper investigates the statistical relationship of the GARCH model and its di usion limit. Regarding the two types of models as two statistical experiments formed by discrete observations from the models, we study their asymptotic equivalence in terms of Le Cam's de ciency distance. To our surprise, we are able to show that the GARCH model and its di usion limit are asymptotically equivale...

The issue of finite-sample inference in GARCH-like models has seldom been explored in the theoretical literature, although its potential relevance for practitioners is self-evident. In some cases, asymptotic theory may provide a very poor approximation to the actual distribution of the estimators in finite samples. The aim of this paper is to propose the application of the socalled double lengt...

The main objective of this paper is to propose an alternative valuation framework for pricing foreign currency and cross-currency options, which is capable of accommodating existing empirical regularities. The paper generalizes the GARCH option pricing methodology of Duan (1995) to a two-country setting. Specifically, we assume a bivariate nonlinear GARCH system for the exchange rate and the fo...

This paper attempts to model the behavior of 1-minute high frequency exchange rate data of 5 currencies : the Japanese Yen, the Australian Dollar, the Canadian Dollar, the Euro, the Pound sterling against the US Dollar, on 21 July 2005 when the Chinese Yuan was revaluated. The data shows the following distinctive features: (1) There is a large jump at the time of the Yuan revaluation, (2) Large...

In recent decades, the momentum of global environmental protection has culminated in the Kyoto Agreement of 1998, placing the limelight on “green” issues. This paper argues that the protection of environmental systems involves a fragile balance between the costs of environment preservation and the profit motivations of industrialists. In particular, one of the issues that needs to be addressed ...

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...