There is a vast amount of literature on modeling as well as measuring the volatility of asset returns all over the world. Since our focus is mainly on the ARCH family of models, most of the literature reviewed in this section dealt with these models. The study relating to the estimation of volatility either in spot or derivatives markets includes Choudhury (1997), Speight et al. (2000), Lin B.H. et al (2000), Duarte (2001), Fung et al (2001), Peters (2001), Claessen and Mittnik (2002), Jacobsena and Dannenburg (2003), Bresczynski and Weife (2004), Malmsten and Terasvirta (2004) etc. All these studies are dealt with the modeling and estimation of volatility either in spot or in derivatives markets or in both.
Choudhury (1997) had attempted to investigate the return volatility in the spot and stock index futures markets. By applying GARCH-X model, they had tried to study the effects of the short run deviations between the cash and futures prices on the stock return volatility. The short run deviations between the two price series were indicated by the error correction term from the co-integration test between two prices. His results had indicated a significant volatility clustering in the stated markets and a strong interaction between the spot and futures markets. The study also had found a significant positive effect of the deviation on the volatility of spot and futures markets.
In order to examine the intraday volatility component of stock index futures, the authors Speight et al. (2000) had empirically tested for explicit volatility decomposition using the variance component model of Engle and Lee (1993) on the intraday data of FTSE 100 futures index. They had reported a direct evidence for the existence of such volatility decomposition in intraday futures return data at frequencies of one hour and higher. Though the transitory component to volatility exhibits a rapid decay, within the half day, the permanent component has been found to be highly persistent, that decays over a much longer horizon.
Lin and Yeh (2000) had studied the distribution and conditional heteroskedasticity in stock returns on Taiwan stock market. Apart from the normal distribution, in order to explain the leptokurtosis and skewness observed in the stock return distribution, they had also examined the student -t, the Poisson-normal, and the mixed normal distributions, which are essentially a mixture of normal distributions, as conditional distributions in the stock return process. They had also used the ARMA (1,1) model to adjust the serial correlation, and adopt the GJR-GARCH (1,1) model to account for the conditional heteroskedasticity in the return process. Their empirical results had shown that GARCH model is the most probable specification for Taiwan stock returns. The results also showed that skewness seems to be diversifiable through portfolio. Thus the normal GARCH or the student-t-GARCH model which involves symmetric conditional distribution might be a reasonable model to describe the stock portfolio return process.
The results of research by Duarte (2001) lead to the conclusion that GARCH volatility is the series that provides the better forecast of the PSI-20 series volatility. Under these circumstances, the Black and Scholes formula has not been found to be the most adequate to evaluate options on the PSI-20 futures, which is clearly proved by the difficulties in an attempt of modeling implied volatility. Modeling volatility with ARCH models is one among several alternatives to the Black and Scholes model. Within the ARCH family, their results revealed that the GARCH (1,1) model is the most adequate for the series under analysis.
By studying the behaviour of return volatility in relation to the timing of information flow under different market conditions influenced by trading volume and market depth, Fung and Patterson (2001) had tried to emphasise on the information flow during trading and non-trading periods that may represent domestic and offshore information in the global trading of currencies. Their results reveal that volatility was negatively related to market depth; that is, deeper markets had relatively less return volatility, and the effect that market depth had on volatility was superceded by information within trading volume. Their test results focusing on the timing of information flow revealed that in low volume markets, the volatility of non-trading periods return exceeded the volatility of trading period return. However, when trading volume is high, this pattern was reversed. They also observed a trend towards greater integration between foreign and U.S. financial markets; the U.S. market increasingly emphasized information from non-trading periods to supplement information arriving during trading periods.
Peters (2001) had tried to examine the forecasting performance of Four GARCH (1,1) models (GARCH, E-GARCH, GJR-GARCH, APARCH) used with three distributions (Normal, Student-t and Skewed Student-t). They explored and compared different possible sources of forecast improvements: asymmetry in conditional variance, fat tailed distributions and skewed distributions. Two major European stock indices (FTSE-100 and DAX-30) were studied using daily data over a 15 years period. Their results suggested that improvements of the overall estimation were achieved when asymmetric GARCH were used and when fat tailed densities were taken into account in the conditional variance. Moreover, it was found that GJR and APARCH give better forecasts than symmetric GARCH. Finally, increased performance of the forecasts was not clearly observed while using non-normal distributions.
Alternative strategies for predicting stock market volatility are examined by Claessen and Mittnik ( 2002). GARCH class of models were investigated to determine if they are more appropriate for predicting future return volatility. Employing German DAX index return data it was found that past returns do not contain useful information beyond the volatility expectations already reflected in option prices. This supports the Efficient Market Hypothesis for the DAX-index options market.
Jacobsen and Dannenburg (2003) had investigated volatility clustering using a modeling approach based on temporal aggregation results for GARCH models in Drost and Nijman (Econometrica 61 (1993). Their findings highlighted that volatility clustering, contrary to widespread belief, is not only present in high frequency financial data. Monthly data also found to exhibit significant serial dependence in the second moments. They have shown that the use of temporal aggregation to estimate low frequency models reduce parameter uncertainty substantially.
Bresczynski and Weife (2004) in their paper have presented the factor and predictive GARCH (1,1) models of the Warsaw Stock Exchange (WSE) main index WIG. An approach where the mean equation of the GARCH model includes a deterministic part was applied. The models incorporated such explanatory variables as volume of trade and major international stock market indices. Their paper exploits the direction quality measure that can be used as alternative measures to evaluate model goodness of fit. Finally, the in sample versus the out of sample forecasts from the estimated models were compared and forecasting performance was discussed.
Malmsten and Terasvirta (2004) had considered three well- known and frequently applied first order models viz. standard GARCH, Exponential GARCH and Autoregressive Stochastic Volatility model for modeling and forecasting volatility in financial series such as stock and exchange rate returns. They had focused on finding out how well these models are able to reproduce characteristic features of such series, also called stylized facts. Finally, it was pointed out that non of these basic models can generate realizations with a skewed marginal distribution. A conclusion that emerged from their observation, largely based on results on the moment structure of these models, was that none of the models dominates the other when it comes to reproducing stylized facts in typical financial time series.