GARCH Family Models Research Articles

Modelling volatility during the current financial crisis: an empirical analysis of the US and the UK stock markets

The overarching aim of the present paper is to investigate the pattern of returns and volatility in the US and the UK stock markets prior and subsequent to the current financial crisis. For that reason, the family of GARCH models is utilised; specifically, GARCH, GARCH in Mean, threshold GARCH and exponential GARCH specifications are applied on daily data from July 2004 to April 2009. The advanced fitness of TGARCH specifications after the crisis outbreak indicates significant asymmetric behaviour and increased nervousness and uncertainty in both markets. Indeed, the financial crisis forms a risky environment where the effects of shocks are more persistent. However, contradictive empirical findings arise for the required risk premium between the examined capital markets, although it would be expected that higher risk is compensated with additional returns.

Volatility Forecasts Based on Data Sampled at Different Frequencies

Measuring and modeling unobservable volatility is one of the key issues in finance and risk management. Value at Risk (VaR) is a natural application of volatility estimates and therefore allows to differentiate between volatility estimation approaches. In this paper we consider daily VaR measures for WIG20 index using one-step-ahead forecasts of volatility in a crisis period. We compare forecasts from GARCH family models based on daily data with forecasts from HAR-RV and ARFIMA models for realized volatility based on intraday returns. Both VaR forecasts obtained from models that use intraday information in defining volatility and simple models based on daily returns deliver similar results. However, when loss functions are considered, HAR-RV models allow to minimize opportunity cost of capital.

A Study on the Behavior of Volatility in Saudi Arabia Stock Market Using Symmetric and Asymmetric GARCH Models

Problem statement: This study examines several stylized facts (heavy-tailedness, leverage effect and persistence) in volatility of stock price returns exploiting symmetric and asymmetric GARCH family models for Saudi Arabia. Approach: This study is carried out using closing stock market prices over 15 years covering the period 1 January 1994 to 31 March 2009. The sample period is divided into three sub-periods according to the local crisis in 2006. Results: The results reveal that asymmetric models with heavy tailed densities improve overall estimation of the conditional variance equation. Moreover, we find that AR (1)-GJR GARCH model with Student-t outperform the other models during and before the local crisis in 2006, while AR (1)-GARCH model with GED exhibits a better performance after the crisis. Furthermore, the findings reveal the existence of leverage effect at 1 percent significance level. Conclusion/Recommendations: Finally, the volatility persistent in the samples during and after crises decreases in all models under various distribution assumptions.

The Indian exchange rate and Central Bank action: An EGARCH analysis

We analyze the impact of conventional monetary policy measures such as interest rates, intervention, and other quantitative measures, on exchange rate level and volatility, and compare these to the impact of Central Bank communication using dummy variables in the best of a family of GARCH models estimated with daily and monthly Indian data. Since India has a managed float, we also test if the measures affect the level of the exchange rate. We find variations in the Euro/Dollar rate strongly affect the Rupee/Dollar level and volatility. The interest rate differential has strong perverse effects, tending to increase variance and depreciate the Indian currency. News decreases volatility as it adds to scarce information. Domestic policy variables affect both level and volatility, and persist at the monthly frequency, but sometimes work at cross-purposes. Communication channels have potential but were not used effectively.

A hybrid modeling approach for forecasting the volatility of S&P 500 index return

Forecasting volatility is an essential step in many financial decision makings. GARCH family of models has been extensively used in finance and economics, particularly for estimating volatility. The motivation of this study is to enhance the ability of GARCH models in forecasting the return volatility. We propose two hybrid models based on EGARCH and Artificial Neural Networks to forecast the volatility of S&P 500 index. The estimates of volatility obtained by an EGARCH model are fed forward to a Neural Network. The input to the first hybrid model is complemented by historical values of other explanatory variables. The second hybrid model takes as inputs both series of the simulated data and explanatory variables. The forecasts obtained by each of those hybrid models have been compared with those of EGARCH model in terms of closeness to the realized volatility. The computational results demonstrate that the second hybrid model provides better volatility forecasts.

Terrorism and capital markets: The effects of the Madrid and London bomb attacks

Using event study methodology and GARCH family models, the paper investigates the effects of two terrorist incidents – the bomb attacks of 11th March 2004 in Madrid and 7th July 2005 in London – on equity sectors. Significant negative abnormal returns are widespread across the majority of sectors in the Spanish markets but not so in the case of London. Furthermore, the market rebound is much quicker in London compared to the Spanish markets where the attackers were not suicide bombers. Nevertheless, the overall findings point to only a transitory impact on return and volatility that does not last for a long period.

TIME‐VARYING VOLATILITY MODELLING OF BALTIC STOCK MARKETS

As time‐varying volatility has found applications in roughly all time series modelling in economics, it largely draws attention in the areas of financial markets. This study also examines the characteristics of conditional volatility in the Baltic Stock Markets (Estonia, Latvia and Lithuania) by using a broad range of GARCH volatility models. Correctly forecasting the volatility leads to better understanding and managing financial market risk. Daily returns from four Baltic stock indexes are used; Estonia (TALSE index), Latvia (RIGSE index), Lithuania (VILSE index) and synthetic BALTIC benchmark index. We test a large family of GARCH models, including; the basic GARCH model, GARCH‐in‐mean model, asymmetric exponential GARCH and GJR GARCH, power GARCH and component GARCH model. We find strong evidence that daily returns from Baltic Stock Markets can be successfully modelled by GARCH‐type models. For all Baltic markets, we conclude that increased risk will not necessarily lead to a rise in the returns. All of the analysed indexes exhibit complex time series characteristics involving asymmetry, long tails and complex autoregression in the returns. Results from this study are firmly recommended to financial officers and international investors. Santrauka Straipsnyje analizuojamas salyginis Baltijos vertybiniu popieriu rinku (Estijos, Latvijos ir Lietuvos) nepastovumas, taikant eile GARCH kintamumo modeliu. Pažymetina, kad tinkamai prognozuojant nepastovuma, galima geriau suvokti ir valdyti finansiniu rinku rizika. Straipsnyje remiamasi keturiu Baltijos šaliu kasdienemis akciju indeksu gražomis; Estijos (TALSE indeksu), Latvijos (RIGSE indeksu), Lietuvos (VILSE indeksu) ir sintetiniu palyginamuoju BALTIC indeksu. Pritaikius eile GARCH kintamumo modeliu, galima teigti, kad didejanti rizika Baltijos šaliu rinkose nebūtinai itakos vertybiniu popieriu gražos augima. Tyrimo metu gauti rezultatai rekomenduojami finansu specialistams ir investuotojams.

The day-of-the-week effects on the volatility: The role of the asymmetry

In this paper, we propose to evaluate whether asymmetry influences the day-of-the-week effects on volatility. We also investigate empirically the impact of the day-of-the-week effect in major international stock markets using GARCH family models from a forecast framework. Indeed the existence of calendar effects might be interesting only if their incorporation in a model results in better volatility forecasts.

Stock Volatility in the Segmented Chinese Stock Markets: A SWARCH Approach

This study adopts the Markov-switching ARCH (hereafter SWARCH) model to examine the volatility nature and volatility linkages of four segmented Chinese stock indices (SHA, SZA, SHB, and SZB). Our empirical findings are consistent with the following notions. First, we find strong evidence of regime shift in the volatility of four segmented markets and SWARCH model appears to outperform standard GARCH family models. Second, although there are some common features of volatility switch in segmented markets, there exist a few difference: (i)compared with the A-share markets, B-share markets are more volatile and shift more frequently between high- and low-volatility states; (ii) B-share markets have longer stays at high volatility state than the A-share markets; (iii) the relative magnitude of the high volatility compared with that of the low volatility is much greater than the case in two A-share markets. Third, B-share markets are found to be more sensitive to international shocks, while the A-share markets seem immune to international spillovers of volatility. Finally, analyses of volatility spillover effect among the four stock markets indicate that the A-share markets play a dominant role in volatility in Chinese stock markets.

Asymmetry Effects in Chinese Stock Markets Volatility: A Generalized Additive Nonparametric Approach

The unique characteristics of Chinese stock markets give rise to the difficulty of assuming innovation distributions and the specification form of the volatility process when modelling volatility with the parametric GARCH family models. This paper examines the Chinese stock market volatility and the asymmetric effects in the Chinese stock volatility by a generalized additive nonparametric (GAM NP) smoothing technique. The empirical results indicates that the asymmetric effect exists in the Chinese stock market. However, the News Impact Curve from the GAM NP model indicates that limited amounts of good news are needed in order to to keep the market calm. Further, compared with other parametric and nonparametricmodels, the empirical result from the GAMNP model demonstrates better performance for the volatility forecasts, particularly in the out-of-sample forecast. This GAM NP technique should have wide applications to other merging stock markets which are similarly imperfect and incomplete.

GARCH Models for Forecasting Volatility and Determining Arbitrage in Options

Derivatives have become widely accepted as tools for hedging and risk-management, and also to some extent for speculation. A more recent trend has been gaining some ground, that of arbitrage in derivatives. The critical parameter in derivatives pricing is the volatility of the underlying asset. Exchanges often overestimate volatility in order to cover for any sudden changes in market behavior, leading to systematic overpricing of derivatives. Accurate forecasting of volatility would expose this systematic overpricing. Unfortunately, volatility is not an easy phenomenon to predict or forecast. One class of models which have proved successful in forecasting volatility in many situations is the GARCH family of models. The objective of the present study is to analyze systematic mispricing of options derivatives. In order to perform the analysis, data was collected for a sample of NSE-traded stock options and for their underlying stocks for the period of one year prior to the contract. The study uses GARCH models to forecast underlying stock volatility, and uses this forecasted volatility in the Black-Scholes model in order to determine whether the corresponding options are fairly priced. The motivation behind the research was to find systematic mispricing that would provide evidence for arbitrage opportunities.

Corporate governance and volatility in the capital markets: Brazil case study

n 2001, with the São Paulo Stock Exchange (Bovespa) creation of the “New Market and Governance Levels I and II”, Brazil became a unique country for corporate governance studies. From this date on it became possible to distinguish, in the same macroeconomic and institutional environment, companies that formally adopt good practices of corporate governance from those that don’t. This article objective, considering Brazil as a case study, was to assess the impact of higher levels of governance on the volatility term structure of the stocks. In methodological terms, it were developed two indexes of daily returns in the Brazilian stock market called IEPG-I and IEPG-S, and it was analyzed the volatility term structure with adjustments on the GARCH family models. The results were statistically surprisingly, highlighting: 1) higher levels of governance had positive effect in the reduction of the short and long term volatility; 2) the volatility of the companies with the worst practices of corporate governance seems to be more reactive to the market; 3) the persistence of the volatility of the companies with good practices is higher than that of the companies with worse practices; 4) the convergence speed of the volatility of the companies with good practices is lower than that of the companies with worse practices; and 5) the presence of information asymmetry or leverage effect in companies with worse practices of corporate governance and absence in companies with better practices of governance.

Improving forecasts of GARCH family models with the artificial neural networks: An application to the daily returns in Istanbul Stock Exchange

In the study, we discussed the ARCH/GARCH family models and enhanced them with artificial neural networks to evaluate the volatility of daily returns for 23.10.1987–22.02.2008 period in Istanbul Stock Exchange. We proposed ANN-APGARCH model to increase the forecasting performance of APGARCH model. The ANN-extended versions of the obtained GARCH models improved forecast results. It is noteworthy that daily returns in the ISE show strong volatility clustering, asymmetry and nonlinearity characteristics.

Covariance stationary GARCH-family models with long memory property

We propose simple models which extend GARCH model and find regions of coefficients on which the given process is nonnegative covariance stationary and has long memory property.

Change in unconditional foreign exchange rate volatility: an analysis of the GBP and USD price of the Euro from 2002 to 2003

Unconditional foreign exchange rate variance is generally assumed to be constant in analysis of foreign exchange rates. It is noted that there is evidence of a change in unconditional foreign exchange rate variance during the two-year period surrounding the Iraq war, January 2002 to December 2003, for the GBP price of the Euro, although not for the USD price of the Euro. This has implications for the indiscriminate use of models that assume constant unconditional variance, such as the GARCH family of models, in the analysis of foreign exchange rates.

Analysis of economic time series: effects of extremal observations on testing heteroscedastic components

AbstractMacroeconomic and financial time series are often tested for the presence of non‐linearity effects. Sometimes, small patches of extremal observations may wrongly influence non‐linearity tests. In this paper, a robust analysis of the Lagrange multiplier (LM) test for GARCH components is suggested. With Monte‐Carlo simulation we show that extreme observations might cause over‐estimation of the number of GARCH components, with the main contribution consisting by introducing the forward search method into the GARCH model family. Using robust estimators of regression coefficients and graphical displays of results, the effect of influential observations on estimates can be efficiently monitored. Analysing macroeconomic and financial time series we show that identifying the order of a GARCH model can be unduly influenced by a few isolated large values, and extremal observations affect p‐values and t‐statistics in an unexpected manner. Copyright © 2004 John Wiley & Sons, Ltd.

Leveraging profit from the fixed-variable cost ratio: the case of new hotels in Spain

The aim of this paper is to detect the variations in the risk of a hotel chain's performance derived from opening a new lodging establishment. Investments requiring huge fixed costs have a direct effect on the operating leverage of a firm; consequently, the analysis of the changes in the operating leverage derived from strategic decisions is a crucial aspect since it allows to shed some light on the degree of sensitivity of the firm to variations in demand. In order to operationalise the assessment of the risk, the volatility of returns is used. For this purpose, it is employed, for the first time in the hotel industry, a methodology based on GARCH-family models to detect such changes.

Long-Memory versus Option-Implied Volatility Predictions

Volatility is a critical parameter in virtually all option pricing models. But the closer we look at volatility, the harder it seems to be to model it correctly. The constant volatility assumption of early pricing models is clearly inadequate. GARCH family models make volatility a function of the asset price process, and stochastic volatility models bring in a second stochastic factor that affects volatility movements. These approaches make sense in theory, but empirically volatility shocks seem to be too persistent to be consistent with them. A further confounding factor is that implied volatilities extracted from option prices in the market are widely thought to give more accurate predictions of future realized volatility, but don9t obey any of these models exactly. In this article, Li examines a volatility model with “long memory,” meaning that it can be made to fit the slow-decay feature of market volatilities. He also introduces a much more extensive data series, with intraday observations every five minutes. Using such a dense price series, realized volatility becomes observable, and the vast number of data points allows precise estimation of model parameters. For exchange rates on the deutsche mark, the yen and the British pound, the ARFIMA (“Autoregressive Fractionally Integrated Moving Average”) model is shown to give a better fit to volatility behavior than the alternative model, and it beats implied volatility substantially in the standard tests of forecasting performance.

Modeling the Volatility of the Heath-Jarrow-Morton Model: A Multi-factor GARCH Analysis

Based on the nonparametric study of Pearson and Zhou (1999), a parametric HJM model is developed for the forward rate volatility. It allows the volatility of the forward rate with different maturities to react in a different way with the level of forward rate and the forward spread. Specifically, the proposed forward rate volatility function is imbedded into GARCH family models and compared with several widely used HJM volatility specifications. It is shown that the proposed volatility specification performs the best. It is also confirmed that the volatility of forward rate with different maturities depends on the forward rate and the forward spread in a different way.