Empirical VaR&ES Study On GEM Market Risk Based On ARME-GARCH Model

In this paper we mainly discuss the basic principle of ES, a new method for riskmeasurement, and the empirical VaR&ES study on GEM (Growth EnterprisesMarket) index market risk based on ARMA-GARCH models. In addition, we applythe vector autoregressive model (VAR) to explore the mutual influence betweenGEM and SME, deeply analyzing the risk factors of GEM. The whole paper includes5chapters.In the first chapter, we come up with some backgrounds for the main topic ofthis paper, i.e. the GEM market risk. And then we introduce some related literaturesabout VaR and ES methods.In the second chapter, based on loss variables describing correspondingfinancial portfolios’ risk and-quantile (upper tail) of loss distribution, thedefinitions of Expected Shortfall (ES) and Conditional Value at Risk (CVaR) are setup. Under general loss distributions, it has been proved by some direct calculationsthat the definition of ES is independent on the choice of-quantile for any lossvariable; also by some direct calculations the equivalence between ES and CVaR hasbeen checked; and furthermore by constructing a set of probability measures withwhich ES can be represented for any loss variable, the coherence of ES as a riskmeasure has been discovered.In the third chapter, based on ARMA-GARCH model, we use VaR and ES riskmeasurement methods to carry on the empirical analysis with GEM index marketrisk (sample:2010.6.1-2014.2.1), including the calculation of VaR and ES, and thecomparative analysis about the empirical results, etc. First by some basic statisticalanalysis about GEM day’s closing price of logarithmic rate of return, we found thatthe sequence has the feature of aiguilles and fat-tail. Then we determine the lag orderfor each model by using AIC+SC criteria, and estimate the parameters of themodels, and hence get the residual sequence. Afterwards, by the calculation of VaRvalue of the residual sequence we can then get the VaR and ES value of our riskmodel. Finally we use failure test method to test the model. The empirical resultsshow that ES is more accurately estimate the exception case actual loss when VaRestimates is failure; ES can be used to make up for the shortcoming of the VaRmodel; ES is more steady and conservative than VaR risk measurement methods.In the fourth chapter, we apply VAR (vector autoregressive) model to explorethe mutual influence between GEM and SME. Using co-integration and granger causality test to analysis the internal relationship between GEM and SME, we try tolook for the external factors that may be influencing the risk of GEM. Empiricalresults show that the volatility of the two markets is relatively consistent, and therehas no long-term equilibrium relationship between them. The results further showthat GME have greater influence on SME.The fifth chapter is a summary of the full text and points out the shortages ofthis paper, and also come up with the future prospect of the research direction.