A Comparative Study On The ES Measure Of China And The UK Stock Market Risk Based On The Bayesian MS-GARCH Model

Economic globalization has linked the national financial markets together and has played a significant role in economic development.However,once a financial crisis occurs,it may trigger a global chain reaction.This essay studies the China Shanghai Composite Index and the UK FTSE100 index and establishes Markov –switching Bayesian GARCH models respectively.Based on volatility and VaR,we further measure the risk of China and UK stock markets via ES followed by a comparative study.The main work of this essay focuses on three parts.The first part is the establishment of Markov –switching Bayesian GARCH models to study the volatility of China and UK stock markets.Through the log-returns and statistical characteristics of Shanghai Composite Index and FTSE100 index,we find both of them have heteroscedasticity and structural changes.Thus we set the model as Markov –switching GARCH models;Bayesian MCMC method of the Metropolis-Hasting sampler is used to get more accurate estimation results.Therefore,Markov –switching Bayesian GARCH models are established.In order to verify the rationality of the model,we use the model to predict the volatility of the out-of-sample 20 trading days and compare the actual results with the predictions.If the errors are in the reasonable range,models are rational.The conclusions are as follows: China stock market has a longer fluctuation period(166.2 days)and mainly medium-low fluctuations(165 days),while the UK market cycle(121 days)is slightly short and dominated by high-medium fluctuations(109 days).In addition,this essay also predicts the volatility of the stock market in the eight trading days in the future which prepares for the predictions of VaR.The second part is the study of the VaR in the China and UK stock markets based on the first part.According to the former established volatility models,the daily in-sample VaR is calculated separately,and Kupiec failure test is applied to test the results.The conclusions are as follows: under the 99% confidence level,the mean VaR of the Shanghai Composite Index(3.925)is higher than that of the FTSE100 Index(2.76)which shows that the risk of China stock market is higher than that of UK stock market.In addition,we also forecast VaR of eight trading days in the future based on the predictions in the first part.The third part is about ES based on the VaR in the second part.Since ES can measure the tail-risk better than VaR and has consistency,ES is applied to measure the risks of China and UK stock market.The conclusions are as follows: under the 99% confidence level,the mean ES of Shanghai Composite Index(4.923)is higher than that of the FTSE 100 Index(3.412),which also shows that the risk of the China stock market is greater.Furthermore,when the VaR fails in forecasting the volatility,the loss value of the failed part is closer to the ES measure,indicating that ES is a better risk measure.Moreover,we also forecast ES of eight trading days in the future based on the predictions in the second part.