The linkages,persistence, asymmetry in the volatility,the price discovery and efficiency,and the effect of the US subprime mortgage financial crisis on the spot and the futures market’s returns: the case of India

This article examines the effects of persistence, asymmetry and the US subprime mortgage crisis on the volatility of the returns and also the price discovery, efficiency and the linkages and causality between the spot and futures volatility by using various classes of the ARCH and GARCH models, and through the Granger’s causality. We have used two indices: one for spot and the other for futures, for the daily data from 12 June 2000 to 30 September 2013 from Nifty stock indices. We have then tested for ARCH effects, and subsequently employed various models of the ARCH and GARCH conditional volatility. The GARCH(1,1) model is found to be significant, and it implies that the returns are not autocorrelated and have ‘short memory’. It supports the hypothesis of the efficiency of the markets. The negative ‘news’ has more significant effect on volatility, corroborating the ‘leverage impact’ in finance on market volatility. We have also tested the volatility spillover effects. The two methods we employed support the spillover effects and the causality is bidirectional. We also have used the dummy variable for the US subprime mortgage financial crisis and found that they are statistically significant. Indian stock market is thus integrated to the world stock markets.     

Modelling the risk–return relation for the S&P 100: The role of VIX

A significantly positive risk–return relation for the S&P 100 market index is detected if the implied volatility index (VIX) is allowed for as an exogenous variable in the conditional variance equation. This result holds for 4 alternative GARCH specifications, irrespective of the conditional distribution, and regardless of whether the conditional mean equation includes a constant term. This finding is robust to sub-samples, and to using VIX innovations to control for dividend yield and trading volume effects. Monte Carlo evidence suggests that if VIX is not included, the risk–return relation is more likely to be negative or weak, in line with several previous studies. If VIX is included, the distribution of the risk–return parameter has more than 99% of its mass in the area of positive values. We conclude that VIX carries important forward-looking information which improves the precision of the conditional variance estimation and, subsequently, reveals a significantly positive relation.     

Examining the relationship between stock return volatility and trading volume: new evidence from an emerging economy

Using daily stock return data for individual stocks from an emerging economy, this article examines the relationship between return volatility and trading volume under the theoretical postulate of the mixture of distributions hypothesis. The results suggest that the contemporaneous trading volume as a proxy for latent information arrival to the market did not contribute to the removal of significant ARCH or Generalized Autoregressive Conditional Heteroscedasticity effects that are found in stocks at the first stage of the investigation. The same holds for the lagged volume except for one case. This, perhaps, suggests that the trading volume (contemporaneous or lagged) is not adequately conveying information to induce traders’ views of the desirability of trade and, therefore, points to the need for searching for other micro and macro variables to be used as potential proxy for information arrival to the stock market of the emerging economy.     

A general model for short-term interest rates

A general one-factor model for short-term interest rates is proposed. Besides the long memory fractionally integrated mean process, the model also consists of a power function of the interest rate as well as the GARCH effect in the conditional variance. The estimation results show that, while there is no evidence for fractional integration in the mean beyond the well-known martingale property, both the power function of the interest rate and the GARCH effect (but not the ARCH effect) are highly significant in the formation of the conditional variance. Test results also confirm a structure change in October 1979 due to the shift in the Federal Reserve monetary policy.     

我国CPI波动的GARCH效应

CPI一直以来是政府和民众十分关注的指标。通过检验得到了CPI变动具有ARCH效应,利用GARCH(1,1)模型对波动性进行了分析。提出应对CPI波动的政策建议。     

German stock market dynamics

This article estimates generalized ARCH (GARCH) models for German stock market indices returns, using weekly and monthly data, various GARCH specifications and (non)normal error densities, and a variety of diagnostic checks. German stock return series exhibit significant levels of second-order dependence. Our results clearly demonstrate that for both weekly as well as monthly return series the Student-t distribution is superior to the standard normal distribution. In particular, the estimated GARCH-t models appear to be reasonably successful in accounting for both observed leptokurtosis and conditional heteroskedasticity from German stock return movements.     

The effects of multilateral trading systems on risk and return in equity markets

The event study methodology of Brown and Warner (1985) is adopted and augmented to evaluate the effect of the launch of multilateral trading systems on risk and return in equity markets. The methodology is supplemented with various techniques, such as the nonparametric ranking test and kernel regression, to find out if announcements about the introduction of Chi-X Australia generated abnormal returns (ARs). Asset pricing models are fitted with interaction variables, while GARCH, threshold ARCH (TARCH), exponential GARCH (EGARCH) and power-ARCH (PARCH) are used to determine changes in systematic risk. We find evidence in favour of Fisher’s separation theorem and detect a new market anomaly, which we call the ‘Fisher market anomaly’. Our results show that Chi-X system testings affect ARs. Consistent with the adaptive expectations theory, we confirm that the first announcement about the launch of Chi-X affected systematic risk the most. In addition, we identify industry and firm effects in risk analysis.     

Modelling conditional heteroskedasticity: Application to the “IBEX-35” stock-return index

This paper compares alternative time-varying volatility models for daily stock-returns using data from Spanish equity index IBEX-35. Specifically, we estimate a parametric family of models of generalized autoregressive heteroskedasticity (which nests the most popular symmetric and asymmetric GARCH models), a semiparametric GARCH model, the generalized quadratic ARCH model, the stochastic volatility model, the Poisson Jump Diffusion model and, finally, a nonparametric model. Those models which use conditional standard deviation (specifically, TGARCH and AGARCH models) produce better fits than all other GARCH models. We also compare the within sample predictive power of all models using a standard efficiency test. Our results show that the asymmetric behaviour of responses is a statistically significant characteristic of these data. Moreover, we observe that specifications with a distribution which allows for fatter tails than a normal distribution do not necessarily outperform specifications with a normal distribution.     

Volatility and trading activity in Short Sterling futures

The objective of the present study is to examine the interplay between information, trading volume and volatility in Short Sterling futures. More specifically, the paper concentrates on the role of liquidity variables as conduits of information arrival and whether such variables could be an exclusive platform of the market's information set. The analytical framework employed to examine the interaction among those factors is based on the conditional volatility family of techniques. The approach is well suited as it naturally leads to examine the interaction among volatility and sources of information. In an attempt to identify proxies of information and their role in determining volatility, four main conclusions have emerged. First, the empirical findings suggest that both volume and open interest exhibit a positive correlation with volatility. Second, based on the current methodology, one can observe the persistence and importance of GARCH effects after accounting for liquidity. Third, the liquidity variables remain significantly exogenous compared with other studies. Finally, although both liquidity variables are found significant, their role as vehicles of transmitting information is proved to be weak with respect to the information itself.     

Has the EMS reduced member-country exchange rate volatility?

Using tests for unit roots, serial correlation, and conditional heteroskedasticity, we find that the stochastic structure of the percentage changes in both the Franc/DM and Lira/DM rates is well described by a low order autoregression with ARCH disturbances. While this assertion is not rejected in either the Pre-EMS or the EMS period, we present evidence indicating a structural shift between sub-periods. In particular, while ARCH is present in each sub-period, its explicit parameterization changes dramatically.Likelihood-ratio tests indicate the desirability of a bivariate analysis, and significant ARCH effects are found in the conditional variances and covariances over both subperiods. Likelihood ratio tests also indicate substantial structural change between the subperiods. The conditional variances of exchange rate innovations are used as natural measures of exchange rate volatility; it is found that volatility decreases substantially for both rates in the EMS period. Furthermore, the Franc shows a relatively greater volatility decrease with the move to the EMS, a result consistent with the narrower parity bands established for the Franc. Finally, the covariation of shocks to the two intra-EMS rates is shown to decrease between the Pre-EMS and EMS periods.     

The risk-return relation and VIX: evidence from the S&P 500

A significantly positive risk-return relation for the S&P 500 market index is detected if the squared implied volatility index (VIX) is allowed for as an exogenous variable in the conditional variance equation of the parsimonious GARCH(1,1) model. This result holds for both daily and weekly observations, for extended conditional mean and variance specifications, and is robust to sub-samples. We show that the conditional variance obtained from the GARCH model with VIX has better predictive ability for realized volatility than the conditional variance from GARCH without VIX and VIX itself, thereby documenting an important information content of VIX for conditional variance. The results are interpreted as evidence that adding VIX squared in the conditional variance equation yields a better measure of conditional variance which, subsequently, uncovers a strong risk-return relation.     

Long-Memory,Asymmetry and Fat-Tailed GARCH Models in Value-at-Risk Estimation: Empirical Evidence from the Global Real Estate Markets

In this paper, we address the question of whether long memory, asymmetry, and fat-tails in global real estate markets volatility matter when forecasting the two most popular measures of risk in financial markets, namely Value-at-risk (VaR) and Expected Shortfall (ESF), for both short and long trading positions. The computations of both VaR and ESF are conducted with three long memory GARCH-class models including the Fractionally Integrated GARCH (FIGARCH), Hyperbolic GARCH (HYGARCH), and Fractionally Integrated Asymmetric Power ARCH (FIAPARCH). These models are estimated under three alternative innovation’s distributions: normal, Student, and skewed Student. To test the efficacy of the forecast, we employ various backtesting methodologies. Our empirical findings show that considering for long memory, fat-tails, and asymmetry performs better in predicting a one-day-ahead VaR and ESF for both short and long trading positions. In particular, the forecasting ability analysis points out that the FIAPARCH model under skewed Student distribution turns out to improve substantially the VaR and ESF forecasts. These results may have several potential implications for the market participants, financial institutions, and the government.

     

Using monthly returns to model conditional heteroscedasticity

This empirical study examines the extent of non–linearity in a multivariate model of monthly financial series. To capture the conditional heteroscedasticity in the series, both the GARCH(1,1) and GARCH(1,1)–in–mean models are employed. The conditional errors are assumed to follow the normal and Student– t distributions. The non–linearity in the residuals of a standard OLS regression are also assessed. It is found that the OLS residuals as well as conditional errors of the GARCH models exhibit strong non–linearity. Under the Student density, the extent of non–linearity in the GARCH conditional errors was generally similar to those of the standard OLS. The GARCH–in–mean regression generated the worse out–of–sample forecasts.     

Further empirical evidence on the forecasting of volatility with smooth transition exponential smoothing

Smooth transition exponential smoothing (STES) uses a logistic function of a user-specified transition variable as adaptive time varying smoothing parameter. This paper empirically addresses three aspects of the use of STES for volatility forecasting. Previous empirical results showed the method performing well in comparison with fixed parameter exponential smoothing and a variety of GARCH models. However, those results related only to forecasting weekly volatility. In this paper, we address the use of STES for forecasting daily volatility. A second issue that we evaluate is the robustness of STES in the presence of extreme outlying observations. The third aspect that we consider is the use of trading volume within a transition variable in the STES method. Our simulation results suggest that STES performs well in terms of robustness, when compared with standard methods and several alternative robust methods. Analysis using stock return data shows that STES has the potential to outperform standard and robust forms of fixed parameter exponential smoothing and GARCH models. The results suggest the use of the sign and size of past shocks as STES transition variables, and provide no clear support for the incorporation of trading volume in a transition variable.     

A comparison of two methods for estimating income uncertainty with an application to aggregate consumption behaviour

Econometric theory now provides various techiniques for estimating the variance of a variable for which only a single. Observation is available at each sample point. This paper compares the autoregressive conditional heteroskedastic (ARCH) and linear moment (LM) estimated of the variance of disposable labour income as measures of income uncertainty. Consumer theory postulates a negative relationship between uncertainty about future income and current consumption. Using quarterly post-world war II data with income modelled as a random walk with drift, both ARCH and LM estimates of the variance of income are included in a standard specification of the consumption function. It is found that while noth the ARCH and LM estimates of income uncertainty provide essentially the same predicted reduction in consumption growth as uncertainty increases the LM estimates yield a statistically significant influence on consumption while the ARCH estimated do not. However, both uncertainty measures provide a statistically significant imporvement in the specification of the consumption function relative to estimating the equation in the absence on an uncertainty measure. Thus, recent advances in estimation techniques, for post-world waf II data, show that the uncertainty theorists of over two decades ago were correct, that is estimation of a consumption function in the absence of an uncertainty measure relults in an equation with a biased estimate of the marginal propensity to consume as well as biased estimates of coefficients for all other included variables (see e.g. Leland, 1968, PP. 470-472).     

Rolling-sampled parameters of ARCH and Levy-stable models

In this article an asymmetric autoregressive conditional heteroskedasticity (ARCH) model is applied to some well-known financial indices (DAX30, FTSE20, FTSE100 and SP500), using a rolling sample of constant size, in order to investigate whether the values of the estimated parameters of the model change over time. Although, there are changes in the estimated parameters reflecting that structural properties and trading behaviour alter over time, the ARCH model adequately forecasts the one-day-ahead volatility. A simulation study has been carried out to investigate whether the time-variant attitude holds in the case of a generated ARCH data process revealing that either in that case the rolling-sampled parameters are time varying. The rolling analysis is also applied to estimate the parameters of a Levy-stable distribution. The empirical findings support that the stable parameters are also time variant.     

Trading asymmetric trend and volatility by leverage trend GARCH in Taiwan stock index

This article develops a leverage trend Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model by incorporating asymmetric trend of returns of the exponential autoregressive and asymmetric volatility of GARCH models to study the asymmetric effects. Using in-sample daily data of Taiex over the period 4 January 1980 to 25 August 1997 and postsample daily data over the period 26 August 1997 to 10 September 2007, the evidence reveals that a curvaceous risk–return relationship and both asymmetric volatility and asymmetric trend of returns are significant in Taiex. The episode of asymmetric trend of returns is that the positive information creates a higher return trend than the negative information of the same amount, while similarly to most studies, the evidence of asymmetric volatility appears that the negative information makes a higher volatility than the positive information of the same size. Most remarkably, we evidence that the volatility asymmetry effect is a conservative trading factor and the return trend asymmetry effect is an active trading factor. In comparison of post-sample performance using rolling-window technique, the leverage trend GARCH model indeed outperforms the other three models with single asymmetry adjusted or without asymmetry adjusted, while the asymmetry nonadjusted model performs the worst. It implies that the return trend asymmetry (active trading) and the volatility asymmetry effects (conservative trading) tend to compensate, but not offset each other.     

FINANCIAL CRISES AND INTERNATIONAL STOCK MARKET VOLATILITY TRANSMISSION

This paper examines the interplay between stock market returns and their volatility, focusing on the Asian and global financial crises of 1997–98 and 2008–09 for Australia, Singapore, the UK, and the US. We use a multivariate generalised autoregressive conditional heteroskedasticity (MGARCH) model and weekly data (January 1992–June 2009). Based on the results obtained from the mean return equations, we could not find any significant impact on returns arising from the Asian crisis and more recent global financial crises across these four markets. However, both crises significantly increased the stock return volatilities across all of the four markets. Not surprisingly, it is also found that the US stock market is the most crucial market impacting on the volatilities of smaller economies such as Australia. Our results provide evidence of own and cross ARCH and GARCH effects among all four markets, suggesting the existence of significant volatility and cross volatility spillovers across all four markets. A high degree of time‐varying co‐volatility among these markets indicates that investors will be highly unlikely to benefit from diversifying their financial portfolio by acquiring stocks within these four countries only.     

ASYMMETRIC INFORMATION IMPACTS: EVIDENCE FROM THE AUSTRALIAN TREASURY-BOND FUTURES MARKET

Abstract.  The effect of information flows on the return volatility of Australian 3-year Treasury bond futures is examined using linear and non-linear GARCH models. Results show significant asymmetric information effects, where bad news has a greater impact on volatility than good news and a non-linear Threshold ARCH(1,1) in mean model provides the most accurate estimation of return volatility. Diagnostic tests confirm this finding and out of sample forecasting error statistics verify that the Threshold ARCH(1,1) in mean model yields the lowest forecasting error. The Threshold ARCH(1,1)-M model is best at capturing the asymmetric information impact on the Australian three-year T-Bond futures return volatility.     

Volatility spill-overs in commodity spot prices: New empirical results

The classical rational expectations model of commodity markets implies that expected spot price risk is an explanatory variable in spot price regressions; and also that inventory carryover, which is reduced by a larger price variance, creates autoregressive conditional heteroscedastic processes in spot prices. In order to falsify/verify this theory, it has typically been assumed that the square root of the conditional variance of spot prices, a proxy for spot price risk, enters the conditional mean function of spot prices. Based on this simple representation, a typical but counter intuitive outcome has been that spot price risk has an insignificant impact on spot prices, see, e.g., Beck (Beck, S., 1993. A Rational Expectations Model of Time Varying Risk Premia in Commodities Futures Markets: Theory and Evidence. International Economic Review 34, 149–168, Beck, S., 2001. Autoregressive Conditional Heteroskedasticity in Commodity Spot Prices. Journal of Applied Econometrics 16, 115–132). In this paper, we propose an alternative functional relationship (from GARCH(1,1) to GARCH(1,1)-AR(m)) between spot price risk and spot prices that is fully supported by the classical rational expectations model, and based on this new representation we are able to provide stronger empirical support for Muth's rational expectation theory.