Modelling Stock Returns in the G-7 and in Selected CEE Economies: A Non-linear GARCH Approach

This paper investigates conditional variance patterns in daily return series of stock market indices in the G-7 and 6 selected economies of Central and Eastern Europe. For this purpose, various linear and asymmetric GARCH models are employed. The analysis is conducted for Canada, France, Germany, Italy, Japan, the UK and the US for which the TSX, CAC-40, DAX-100, BCI, Nikkei-225, FTSE-100 and DJ-30 indices are respectively considered over the period 1987 to 2002. Furthermore, the official indices of Czech, Hungarian, Polish, Russian, Slovak and Slovene stock markets are also studied, i.e. the PX-50, BUX, WIGI, RFS, SAX-16 and SBI, respectively, over 1991/1995 to 2002. The estimation results reveal that the selected stock returns for the G-7 can be reasonably well modelled using linear specifications whereas the overwhelming majority of the stock indices from Central and Eastern Europe can be much better characterised using asymmetric models. In other words, stock markets of the transition economies exhibit much more asymmetry because negative shocks hit much harder these markets than positive news. It also turns out that these changes do not occur in a smooth manner but happen pretty brusquely. This corroborates the usual observation that emerging stock markets may collapse much more suddenly and recover more slowly than G-7 stock markets.http://deepblue.lib.umich.edu/bitstream/2027.42/40049/3/wp663.pd

Parameterizing Unconditional Skewness in Models for Financial Time Series

In this paper we consider the third-moment structure of a class of nonlinear time series models. Empirically it is often found that the marginal distribution of financial time series is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate for unconditional skewness. We consider modelling the unconditional mean and variance using models which respond nonlinearly or asymmetrically to shocks. We investigate the implications these models have on the third moment structure of the marginal distribution and different conditions under which the unconditional distribution exhibits skewness as well as nonzero third-order autocovariance structure. With this respect, the asymmetric or nonlinear specification of the conditional mean is found to be of greater importance than the properties of the conditional variance. Several examples are discussed and, whenever possible, explicit analytical expressions are provided for all third order moments and cross-moments. Finally, we introduce a new tool, shock impact curve, that can be used to investigate the impact of shocks on the conditional mean squared error of the return.asymmetry; GARCH; nonlinearity; stock impact curve; time series; unconditional skewness

Modelling Stock Returns in the G-7 and in Selected CEE Economies: A Non-linear GARCH Approach

This paper investigates conditional variance patterns in daily return series of stock market indices in the G-7 and 6 selected economies of Central and Eastern Europe. For this purpose, various linear and asymmetric GARCH models are employed. The analysis is conducted for Canada, France, Germany, Italy, Japan, the UK and the US for which the TSX, CAC-40, DAX-100, BCI, Nikkei-225, FTSE-100 and DJ-30 indices are respectively considered over the period 1987 to 2002. Furthermore, the official indices of Czech, Hungarian, Polish, Russian, Slovak and Slovene stock markets are also studied, i.e. the PX-50, BUX, WIGI, RFS, SAX-16 and SBI, respectively, over 1991/1995 to 2002. The estimation results reveal that the selected stock returns for the G-7 can be reasonably well modelled using linear specifications whereas the overwhelming majority of the stock indices from Central and Eastern Europe can be much better characterised using asymmetric models. In other words, stock markets of the transition economies exhibit much more asymmetry because negative shocks hit much harder these markets than positive news. It also turns out that these changes do not occur in a smooth manner but happen pretty brusquely. This corroborates the usual observation that emerging stock markets may collapse much more suddenly and recover more slowly than G-7 stock markets.volatility modelling, conditional variance, non-linearity, asymmetric GARCH, G-7, transition economies

Value at Risk models with long memory features and their economic performance

We study alternative dynamics for Value at Risk (VaR) that incorporate a slow moving component and information on recent aggregate returns in established quantile (auto) regression models. These models are compared on their economic performance, and also on metrics of first-order importance such as violation ratios. By better economic performance, we mean that changes in the VaR forecasts should have a lower variance to reduce transaction costs and should lead to lower exceedance sizes without raising the average level of the VaR. We find that, in combination with a targeted estimation strategy, our proposed models lead to improved performance in both statistical and economic terms

Asymmetric GARCH and the financial crisis: a preliminary study

The paper deals with estimation of both general GARCH as well as asymmetric EGARCH and TGARCH models, used to model the leverage effect of good news and bad news on market volatility. We estimate the models using daily returns of S&P 500 stock index and describe the news impact curves (NICs) for these models. When estimating the crisis series, we show the possibility of using a news impact surface to describe the results from models of higher orders.volatility modeling, financial crisis, asymmetric GARCH class models, news impact curve

Alternative Asymmetric Stochastic Volatility Models

The stochastic volatility model usually incorporates asymmetric effects by introducing the negative correlation between the innovations in returns and volatility. In this paper, we propose a new asymmetric stochastic volatility model, based on the leverage and size effects. The model is a generalization of the exponential GARCH (EGARCH) model of Nelson (1991). We consider categories for asymmetric effects, which describes the difference among the asymmetric effect of the EGARCH model, the threshold effects indicator function of Glosten, Jagannathan and Runkle (1992), and the negative correlation between the innovations in returns and volatility. The new model is estimated by the efficient importance sampling method of Liesenfeld and Richard (2003), and the finite sample properties of the estimator are investigated using numerical simulations. Four financial time series are used to estimate the alternative asymmetric SV models, with empirical asymmetric effects found to be statistically significant in each case. The empirical results for S&P 500 and Yen/USD returns indicate that the leverage and size effects are significant, supporting the general model. For TOPIX and USD/AUD returns, the size effect is insignificant, favoring the negative correlation between the innovations in returns and volatility. We also consider standardized t distribution for capturing the tail behavior. The results for Yen/USD returns show that the model is correctly specified, while the results for three other data sets suggest there is scope for improvement.Stochastic volatility; asymmetric effects; leverage; threshold; indicator function; importance sampling; numerical simulations

"Alternative Asymmetric Stochastic Volatility Models"

The stochastic volatility model usually incorporates asymmetric effects by introducing the negative correlation between the innovations in returns and volatility. In this paper, we propose a new asymmetric stochastic volatility model, based on the leverage and size effects. The model is a generalization of the exponential GARCH (EGARCH) model of Nelson (1991). We consider categories for asymmetric effects, which describes the difference among the asymmetric effect of the EGARCH model, the threshold effects indicator function of Glosten, Jagannathan and Runkle (1992), and the negative correlation between the innovations in returns and volatility. The new model is estimated by the efficient importance sampling method of Liesenfeld and Richard (2003), and the finite sample properties of the estimator are investigated using numerical simulations. Four financial time series are used to estimate the alternative asymmetric SV models, with empirical asymmetric effects found to be statistically significant in each case. The empirical results for S&P 500 and Yen/USD returns indicate that the leverage and size effects are significant, supporting the general model. For TOPIX and USD/AUD returns, the size effect is insignificant, favoring the negative correlation between the innovations in returns and volatility. We also consider standardized t distribution for capturing the tail behavior. The results for Yen/USD returns show that the model is correctly specified, while the results for three other data sets suggest there is scope for improvement.

Markov-Switching GARCH Modelling of Value-at-RisK

This paper proposes an asymmetric Markov regime-switching (MS) GARCH model to estimate value-at-risk (VaR) for both long and short positions. This model improves on existing VaR methods by taking into account both regime change and skewness or leverage effects. The performance of our MS model and single-regime models is compared through an innovative backtesting procedure using daily data for UK and US market stock indices. The findings from exceptions and regulatory-based tests indicate the MS-GARCH specifications clearly outperform other models in estimating the VaR for both long and short FTSE positions and also do quite well for S&P positions. We conclude that ignoring skewness and regime changes has the effect of imposing larger than necessary conservative capital requirements