In this papeT we study the performance of the GARCH model and two of its non-linear modifications to forecast weekly stock market volatility. The models are the Quadratic GARCH (Engle and Ng. 1993) and the Glosten. Jagannathan and Runkle (1992) models which have been proposed to describe, for example, the often observed negative skewness in stock market indices. We find that the QGARCH model is...

The univariate Generalised Autoregressive Conditional Heterscedasticity (GARCH) model has successfully captured the symmetric conditional volatility in a wide range of time series financial returns. Although multivariate effects across assets can be captured through modelling the conditional correlations, the univariate GARCH model has two important restrictions in that it: (1) does not accommo...

The paper develops two Dynamic Conditional Correlation (DCC) models, namely the Wishart DCC (WDCC) model and the Matrix-Exponential Conditional Correlation (MECC) model. The paper applies the WDCC approach to the exponential GARCH (EGARCH) and GJR models to propose asymmetric DCC models. We use the standardized multivariate t-distribution to accommodate heavy-tailed errors. The paper presents a...

The objective of this study is to investigate the predictability of model based forecasts and the VIX index on forecasting future volatility of S&P 500 index daily returns. The study period is from January 1990 to December 2010, including 5291 observations. A variety of time series models were estimated, including random walk model, GARCH (1,1), GJR(1,1) and EGARCH (1,1) models. The study resul...

The main purpose of this paper is to estimate the volatility in global fertilizer prices. The endogenous structural breakpoint unit root test and alternative volatility models, including the generalized autoregressive conditional heteroskedasticity (GARCH) model, Exponential GARCH (EGARCH) model, and GJR model are estimated for six global fertilizer prices and the crude oil price. Weekly data f...

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...

Over the past years, cryptocurrencies have drawn substantial attention from media while attracting many investors. Since then, cryptocurrency prices experienced high fluctuations. In this paper, we forecast high-frequency 1 min volatility of four widely traded cryptocurrencies, i.e., Bitcoin, Ethereum, Litecoin, and Ripple, by modeling to select best model. We propose various generalized autore...

When using trees to price options, the standard practice is to increase the number of partitions per day, n, to improve accuracy. But increasing n incurs computational overhead. In fact, raising n makes the popular Ritchken-Trevor tree under non-linear GARCH (NGARCH) grow exponentially when n exceeds a typically small threshold. Worse, when this happens, the tree cannot grow beyond a certain ma...

The skewness in physical distributions of equity index returns and the implied volatility skew in the risk neutral measure are subjects of extensive academic research. Much attention is now being focused on models that are able to capture time-varying conditional skewness and kurtosis. For this reason normal mixture GARCH(1,1) models have become very popular in financial econometrics. We introd...