In this paper, we consider a general family of asymmetric volatility models with stationary and ergodic coefficients. This family can nest several non-linear asymmetric GARCH models with stochastic parameters into its ambit. It also generalizes Markovswitching GARCH and GJR models. The geometric ergodicity of the proposed process is established. Sufficient conditions for stationarity and existe...

Traditional GARCH models fail to explain at least two of the stylized facts found in financial series: the asymmetry of the distribution of errors and the leverage effect. The leverage effect stems from the fact that losses have a greater influence on future volatilities than do gains. Asymmetry means that the distribution of losses has a heavier tail than the distribution of gains. We test whe...

In this paper the class of BL-GARCH (Bilinear General AutoregRessive Conditional Heteroskedasticity) models is introduced. The proposed model is a modification to the BL-GARCH model proposed by Storti and Vitale (2003). Stationary conditions and autocorrelation structure for special cases of these new models are derived. Maximum likelihood estimation of the model is also considered. Some simula...

The use of GARCH models with stable Paretian innovations in financial modeling has been recently suggested in the literature. This class of processes is attractive because it allows for conditional skewness and leptokurtosis of financial returns without ruling out normality. This contribution illustrates their usefulness in predicting the downside risk of financial assets in the context of mode...

Distributional theory for Quasi-Maximum Likelihood estimators in long memory conditional heteroskedastic models is not formally defined, even asympotically. Because of that, this paper analyses the performance of the Likelihood Ratio and the Lagrange Multiplier misspecification tests for Periodic Long Memory GARCH models. The real size and power of these tests are studied by means of Monte Carl...

It is a well-known fact that financial returns exhibit conditional heteroscedasticity and fat tails. While the GARCH-type models are very popular in depicting the conditional heteroscedasticity, the α-stable distribution is a natural candidate for the conditional distribution of financial returns. The α-stable distribution is a generalization of the normal distribution and is described by four ...

Discrete-time stochastic volatility (SV) models have generated a considerable literature in financial econometrics. However, carrying out inference for these models is a difficult task and often relies on carefully customized Markov chain Monte Carlo techniques. Our contribution here is twofold. First, we propose a new SV model, namely SV–GARCH, which bridges the gap between SV and GARCH models...

In this paper we test for (Generalized) AutoRegressive Conditional Heteroskedasticity [(G)ARCH] in daily data on 22 exchange rates and 13 stock market indices using the standard Lagrange Multiplier [LM] test for GARCH and a LM test that is resistant to patches of additive outliers. The data span two samples of 5 years ranging from 1986 to 1995. Using asymptotic arguments and Monte Carlo simulat...

In this paper, we quantify market risk at an intraday time horizon using normal GARCH, Student GARCH, RiskMetrics and high-frequency duration (Log-ACD) models set in the framework of the conditional VaR methodology. Because of the small time horizon of the intraday returns (15 and 30 minute returns in this paper), an evaluation of intraday market risk can be useful to market participants (trade...

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...