GARCH-VaR Model Comparative Study On Different Residual Distribution Using Euro-Dollar Exchange Rate

As a result of the ongoing outbreak of the European debt crisis, the EUR/USD as the main currency pairs of the foreign exchange market is therefore greatly affected. The risk management technology of foreign exchange market is necessary to carry out the research. It can be seen that the necessary risk management controls must be actively involved in the foreign exchange market transactions, and the identification and measurement of financial risks has become the focus of attention of the financial institutions and regulatory authorities. So far, in the many risk measurement tools, VAR has become an important tool for measuring market risk in variety of financial institutions, non-financial institutions and regulatory authorities.Probability distribution of assets yield has a fat tail characteristics and volatility clustering, and does not meet the normal distribution assumption, but the prediction accuracy of VaR model is inseparable from the yield leptokurtic characteristics. GARCH model has a wide range of applications in the financial sector, using GARCH model in portfolio choice and risk management, has been widely appreciated in the financial markets. GARCH-VaR model is an important tool of foreign exchange risk management, but the model of risk measurement will produce significant differences results because of the different residuals distributions. Using GED generalized error distribution instead of the standard normal distribution, GARCH model and GED distribution combined with VaR methodology is a good choice for portfolio and risk management. It can improve the accuracy of the model and applicability comparing the only simple application of VAR method.For example, Euro/U.S. Dollar is the main currency of the foreign exchange market and needs to research as the representative of the foreign exchange market risk management techniques. In this paper, I use the euro-dollar exchange rate as an example to compare he GARCH-VaR model that the residual distribution is a normal distribution, or t distribution and GED distribution. The specific structure is as following:The first chapter is the introduction of this article, this article clarify the research background, significance and the stage of research status at home and abroad, while I point out that the innovation and shortcomings.The second chapter introduces the VaR principles and various calculation methods, do the aforementioned prepare for later.The third Chapter introduces GARCH model, GARCH-VaR model distribution based on different residuals, the model parameter estimation and VaR Backtesting inspection.The fourth chapter is the core of this argument, the data sequence features stationary test to verify the return series and ARCH effect. On this basis, by comparing the model sample forecast results, intuitively compare the pros and cons of the residual distribution as a normal distribution, t distribution and GED distribution GARCH-VaR model risk management. At the same time gives the model backtesting test results to prove that the results of the model’s demonstration is reasonable and correct.Chapter V of this article describes the first four chapters, and makes the conclusions of this study.On the95%confidence level for the management of the VaR under the GARCH model, the residual distribution has the high failure rate under the normal distribution, it also proves the normal distribution underestimated the risk of foreign currency fluctuations. The failure rate under the t-distribution model is obviously unreasonable on the99%confidence level, and it proves that the t distribution overestimated the risk of foreign exchange fluctuations. In contrast, VaR forecasts of the GARCH model whose residuals distribution is the GED distribution are relatively stable on95%and99%confidence level, particularly it is suitable for the higher confidence level, it is Instructive for the return risk management of the foreign exchange market, the characteristics of return is fat tail and high kurtosis.The innovation of this paper is to: (1) With respect to the traditional VaR model, This paper assets takes leptokurtic characteristics into consideration according to GARCH-GED function.(2) In the empirical analysis, this paper does not just apply GARCH-GED function, but a function of the GARCH-N, GARCH-t function resulting VaR. It’s more persuasive.(3) Before researching GARCH-GED model, the EGARCH model is also studied, and my article deny the empirical analysis of asymmetries of foreign exchange gains rate. In view of this situation, I give my own interpretation. Of course, due to my limited level, there are many deficiencies:(1) Application GARCH model for volatility forecast, the implicit assumptions that assume that history will repeat itself, the historical data can reflect the future. But relative to the stress tests, scenario simulation method, this assumption has been limited to predict the future on the basis of historical data.(2) GARCH model parameters estimated using only local optimization method, but not the more accurate global optimization methods, such as simulated annealing method.(3) This article during three model comparisons did not consider the random method and historical simulation VaR model and Monte Carlo simulation method, it will be better able to explain the problem if it also included the comparison. As well as an empirical analysis on the data selected insufficient daily data greatly reduce market volatility authenticity that is due to the market news and economic data, foreign exchange data daily can influence market sentiment. It can be considered daily data to high-frequency data for research.