It is important to improve volatility models and accurate forecasting in the research of financial markets. Improved forecasts will improve risk management and pricing of financial assets. At this moment America, China, Japan, Germany, India, The United Kingdom, and France are the top seven economies in the globe. In this study, we have selected only one stock market index from America, Japan, Germany, India, The United Kingdom, and France. Those indices are The National Association of Securities Dealers Automated Quotations Stock Market or Nasdaq (America), Nikkei 225 (Japan), Deutscher Aktienindex or DAX Performance Index (Germany), Nifty Fifty (India), Financial Times Stock Exchange or FTSE 100 (United Kingdom, Cotation Assistée en Continu or CAC 40 (France).

Earlier much research has been done in this area both nationally and internationally. Some of them are mentioned here to have a deep insight into the objective of this study.

Goudarzi And Ramnarayanan(2011) discussed the volatility  of the BSE 500 index using the ARCH model over 10 years time. The findings demonstrate that the Indian stock market exhibits persistent volatility and a mean-reverting tendency. BSE500 also showed persistent conditional volatility. In addition, they found it, to explain volatility, clustering volatility, and mean reverting in chosen data series GARCH (1,1) model is more effective than any other model.

Sriram(2015) examined the return volatility for crude oil for the time period from 05.03.07 to 27.02.15. The conditional variances are studied using the GARCH (1,1) model, and it was observed that volatility shocks persist over a long time. They used EGARCH (1,1) to analyze the leverage effect and news asymmetry and discovered that the impact of negative news is noticeably more significant on crude oil returns than the impact of positive news.

Som Sankar And Tanmay(2018) aimed to investigate the characteristics of the BSE SENSEX's daily returns and conditional volatility. They discovered that there is a cluster in volatility during the research period and it lasts in this market for a very long time.

Gunasekaran and Rajamohan (2022) analyzed the Sensex price's historical volatility from 1997 to 2016 for a period of 20 years. The model calculates changes in an underlying security's price over various time periods.

Mehta and Sharma (2011) inspected the time-varying volatility of the Indian stock market and focused on the Nifty from March 2001 to October 2010—roughly a decade. They provided an indication of the generality of the time-varying volatility in the Indian equity market, with the past volatility having a greater influence on the present volatility.

Singhania and Prakash (2014) studied the conditional volatility and unconditional volatility of stock markets, the cross-correlation in the stock returns of the SAARC countries, and the efficient market hypothesis (EMH). Research results indicate there is a serial autocorrelation in stock market returns, which implies the dependency of the current stock prices on the past prices and makes the EMH invalid. A significant correlation between unconditional volatility and stock market returns suggests that in any unforeseen changes in the stock market, investors are anticipated to pay an additional risk premium. According to cross-correlation, with the global market, South Asian economies have a high degree of amalgamation.

Singhania and Anchalia (2013) did research on the effect of the globally occurring financial crisis on the stock returns volatility in the Asian Stock Market; this study can assist in enhanced policy formulation and execution in the occurrence of a financial crisis. They observed that there is a favorable impact of the subprime crisis on the return volatility of Japan, China, and India yet a minimal effect on the volatility of return of Hong Kong. The Eurozone debt crisis has a damaging effect on the already extremely volatile stock returns of Asian nations such as India and China. However, the volatility of stock market returns in Japan or Hong Kong was unaffected by the European crisis. In addition, they noticed persistence, clustering of volatility, leverage, and asymmetry in the stock return series of Japan, China, India, and Hong Kong.

M. Muthukamu(2018) evaluated the performance generated by the stocks of the banking industry and the volatility attributed to that performance between 2008 and 2018. The GARCH family model was employed. He observed that while public sector banks experienced less volatility over the study period than private sector stocks but at the same time private sector banks delivered higher returns. 

The Objective of the Study:

• Empirical investigation of the volatility experienced by different countries in the period of study.
• To manage risk in an efficient way for the investors.

We have selected six indices from six different countries for our study. Those indices are Nasdaq, Nikkei 225, Dax Performance Index, Nifty 50, FTSE 100, and CAC 40. The period of study spans from April 2012 to March 2022. The daily closing price data consisting of around 2500 daily observations of the said indices from the period 1^st April 2012 to 31 March 2022 were obtained from finance.yahoo.com. we applied the following formula to calculate the return.

R_x=[log P_x – log P_x-1] × 100,

Where R_x denotes the logarithmic daily return of stock at time X,

P_x denotes the closing price of that stock at time X.

P_x-1 is the corresponding price in the period at time X-1.

To check the stationarity of the time series data Augmented Dickey-Fuller (ADF) Tests have been done. ARCH model has been done to check is there any heteroskedasticity exists or not. Finally, the GARCH model is applied to estimate the volatility. ‘R’ software is used to analyze the data.

Findings of Augmented Dickey-Fuller (Adf) Test

The stationarity of the data series is determined by applying the Augmented Dickey-Fuller (ADF) unit root test. A stationary time series is one whose statistical characteristics, such as mean, variance, etc., do not alter over time. The stationarity of the returns of the six indices that were chosen for the study was examined using the Augmented Dickey-Fuller (ADF) test. The null hypothesis is that stationarity is absent in the returns series of the chosen indices.

Table 1: Augmented Dickey-Fuller(Adf) Test.

ADF unit root tests result on the original dataset are shown in Table 1. We reject the non-stationarity hypothesis because the statistics of the ADF test are bigger in absolute values than the critical values. The stock returns of the chosen indexes were thus found to be stationary at their level form.

Auto-Regressive Conditional Heteroskedasticity(Arch):

 The ARCH-LM test was applied to determine the conditional heteroscedasticity (ARCH effect) on the time series data. The assumption of the null hypothesis is that FMCG stocks do not exhibit an ARCH impact in the residuals of the return series.

Table 2: ARCH-LM TEST.

LM test has been applied to examine the ARCH effects in the residuals of the data sets. The Lagrange Multiplier (LM) test results for ARCH disturbances showed there is strong evidence of ARCH effects all across data sets. Observed R - squared values are lower than calculated F statistics values for all the return series of the chosen indices, and at the 1% level the P values are significant . This implies that the series considered for the investigation exhibits the ARCH effect.

Findings of Generalised Auto Regressive Conditional Heteroskedasticity (GARCH)

The GARCH (1,1) model is applied to estimate the level of volatility experienced by the chosen indices. The means of volatility return to its long-run price level at a rate that is determined by the sum of the ARCH and GARCH coefficients, which is often close to one for financial time series data. We estimate the half-life of the volatility shock wave by the formula-

 L_half = (ln (1/2)) / (ln (α+β )), where α and β are the computed ARCH and GARCH coefficients, which is basically the average amount of time it takes to return to its long-run price level. Table 3 displayed the outcomes.

Table 3: GARCH TEST.

The degree of volatility that the chosen indices from various nations experienced throughout the study period has been explained by applying the GARCH (1,1) model. From table 3 we have seen that for all the indices the estimated sum of the ARCH and GARCH coefficients (α+β) is closer to one (1), indicating that the world's top economies witnessed high volatility in that period of study.

Limitations and Future Scope:

Also, this study has several drawbacks. The most significant restriction is that the intraday price behavior of the stocks within the chosen indices is not calculated. In order to understand the immediate impact of any event-specific or sector-specific phenomenon, in the future, any researcher should use the intraday price behavior of the stocks within each of the selected indices. This could result in an entirely different conclusion.

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