Applying volatility and EVT models to U.S., Chinese and Russian stock markets

Abstract

Purpose: The purpose of this study is to explore the ability of EWMA, GARCH (1,1) and EGARCH (1,1) to forecast volatilities of S&P500, SSEC and MICEX, reference to two time periods in the timeframe of the Syrian war. VaR is derived using the HS approach which incorporates in its calculation the volatility of the best chosen model. The added value is the application of EVT in order to determine VaR results, which are compared and analyzed to the results of the HS approach, to define the most accurate approach. Methodology of Work: Returns of the in-sample period prices are used in estimating the parameters of the three applied models. The calculated in-sample parameters are used to estimate the in-sample and out-of-sample volatilities. RMSE, MAE and MAPE are the error statistics applied in comparing volatility results, to obtain the most accurate volatility model, for both sample periods. VaR derived from the Historical Simulation volatility is calculated using the chosen model’s parameters. On the other hand, VaR results are also obtained when applying the Extreme Value Theory using Matlab. EVT VaR and HS VaR are compared to the realized VaR to analyze the accuracy of the models. Findings: Analysis and comparison of results show that the EVT VaR approach outperformed the HS VaR approach through providing more accurate results as compared to the realized VaR. On the other hand, the GARCH (1, 1) model outperforms EGARCH (1, 1) model for S&P 500, for both the in-sample and out-of-sample period. Moreover, our results show that EGARCH (1, 1) among the asymmetric models outperformed symmetric models used. Limitations and implications of the research: One limitation relates to the limited number of countries chosen in the portfolio tested; which comprises of only three indices. This is mainly due to the strong influence of the chosen counties on the world’s military production. Moreover, the chosen in-sample period extending from January 2015 till December 2016 might not be the ideal period, since it did not witness the burst of the Syrian war. However, if an earlier time period was to be chosen to entail former years of war, then the studied results would be obsolete. Finally, it would be interesting to derive a panel of daily EVT VaR results over a specific period to assess the trend of variations in these results, instead of deriving the results on a one-day basis. Practical implications: Results concluded in this study are helpful for decision makers (investors, firms, governments, etc.) willing to invest in any of U.S., China and Russia. Results depict the degree of influence of the Syrian war on the studied countries’ economies based on their high degree of intervention. Accordingly, investors can forecast and manage their risk exposure to limit any possible future losses. Originality/value: This study tackles a combination of three stock market indices to form a portfolio of the three most powerful military countries of the world; U.S., China and Russia. Specifically, this is done to study the impact of the intervention of the chosen countries in the Syrian war.

Purpose – The purpose of this study is to explore the ability of EWMA, GARCH (1, 1) and EGARCH (1, 1) to forecast volatilities of S&P500, SSEC and MICEX, reference to two time periods in the timeframe of the Syrian war. VaR is derived using the HS approach which incorporates in its calculation the volatility of the best chosen model. The added value is the application of EVT in order to determine VaR results, which are compared and analyzed to the results of the HS approach, to define the most accurate approach. Methodology of Work – Returns of the in-sample period prices are used in estimating the parameters of the three applied models. The calculated in-sample parameters are used to estimate the in-sample and out-of-sample volatilities. RMSE, MAE and MAPE are the error statistics applied in comparing volatility results, to obtain the most accurate volatility model, for both sample periods. VaR derived from the Historical Simulation volatility is calculated using the chosen model’s parameters. On the other hand, VaR results are also obtained when applying the Extreme Value Theory using Matlab. EVT VaR and HS VaR are compared to the realized VaR to analyze the accuracy of the models. Findings – Analysis and comparison of results show that the EVT VaR approach outperformed the HS VaR approach through providing more accurate results as compared to the realized VaR. On the other hand, the GARCH (1, 1) model outperforms EGARCH (1, 1) model for S&P 500, for both the in-sample and out-of-sample period. Moreover, our results show that EGARCH (1, 1) model outperforms GARCH (1, 1) model for the out-of-sample period; which prove that EGARCH (1, 1) among the asymmetric models outperformed symmetric models used. Limitations and implications of the research – One limitation relates to the limited number of countries chosen in the portfolio tested; which comprises of only three indices. This is mainly due to the strong influence of the chosen counties on the world’s military production. Moreover, the chosen in-sample period extending from January 2015 till December 2016 might not be the ideal period, since it did not witness the burst of the Syrian war. However, if an earlier time period was to be chosen to entail former years of war, then the studied results would be obsolete. Finally, it would be interesting to derive a panel of daily EVT VaR results over a specific period to assess the trend of variations in these results, instead of deriving the results on a one-day basis. Practical implications – Results concluded in this study are helpful for decision makers (investors, firms, governments, etc.) willing to invest in any of U.S., China and Russia. Results depict the degree of influence of the Syrian war on the studied countries’ economies based on their high degree of intervention. Accordingly, investors can forecast and manage their risk exposure to limit any possible future losses. Originality/value – This study tackles a combination of three stock market indices to form a portfolio of the three most powerful military countries of the world; U.S., China and Russia. Specifically, this is done to study the impact of the intervention of the chosen countries in the Syrian war.