The Methods And Empirical Researches Of The CAViaR Model

VaR was proposed by Morgan bank in1994. It is still a main method to calculate the risk by measuring the maximum possible loss under a certain confidence level. Many major institutions have adopted VaR to measure and manage their risks. The huge advantages in the management of the risks of VaR have been affirmed by the institutions. VaR has been used widely in the world.The quantile regression is a semi-parametric method for calculating VaR. The quantile regression is proposed by Koenker Roger in1978for solving optimization problems of expected loss functions. Since then a large number of scholars have conducted the researches. The various QR models have been generated. CAViaR is a milestone in all methods of the quantile regression. It is the most widely used. The idea of CAViaR breaks through the general idea by building the VaR directly. CAViaR was proposed by Engle and Manganelli in2004. It does not need to estimate the tail of the distribution. It does not need to assume the distribution of rewards. Mathematical optimization method is used for the direct calculation of VaR. This method has been greatly developed since it was proposed. It is a very important method of the quantile regression. This article also discusses the further improvements and applications of this method.Kuester (2006) proposed the AR-GARCH model based on the IG model of CAViaR proposed by Engle and Manganelli (2004). Julia (2012) proposed the AR-TGARCH model based on Kuester(2006). AR-TGARCH model is improved to establish threshold I-AR-TGARCH model, threshold II-AR-TGARCH model, constant-AR-TGARCH model, constant-threshold I-AR-TGARCH model and constant-threshold II-AR-TGARCH model considering threshold function of Richard (2012),Chenlei(2012) and Cathy (2012) in this article. These models are used to analyse the data of Taiwan weighted index, Shanghai composite index, Shenzhen component index and the small board index. We compare the advantages and disadvantages of each model through DQ test, RQ values and the LR statistic. The results show that the four indices are affected by lag risks and Shenzhen component index and the small board index are affected least. Through DQ test, RQ values and the LR statistic, IG and AR-TGARCH model are the worst, AR-TGARCH model is better than IG model. Threshold I-AR-TGARCH model, threshold II-AR-TGARCH model, constant-AR-TGARCH model, constant-threshold II-AR-TGARCH model and constant-threshold II-AR-TGARCH model proposed in this article are better than IG model and AR-TGARCH model. Through the DQ test, RQ values and LR test statistics, threshold II-AR-TGARCH model, constant-threshold I-AR-TGARCH model and constant-threshold II-AR-TGARCH model are better than other models. Constant-threshold II-AR-TGARCH model is the best model in all the models, threshold II-AR-TGARCH model is followed, constant-threshold I-AR-TGARCH model is at the last. Constant-threshold models are better than threshold models. Through the Granger causality test, the Shanghai composite index is mutual Granger causality with Shenzhen component index. Both indices have conductivity. The small board index is affected by the Shanghai composite index and Shenzhen component index, but the Shanghai composite index and Shenzhen component index are not affected by the small board index. The Shanghai composite index has conductivity on the Taiwan weighted index, but not vice versa.Overnight-AS model and Overnight-SAV model are proposed in this article to measure the overnight risk of exchange rate based on AS mode and SAV model of CAViaR by adding the dollar index. Then these models are used to measure the risks of Yen exchange rate, HK exchange rate and RMB exchange rate and then we compare the pros and cons of each model through DQ test, RQ values and the LR statistic. The results show that the overnight risks of these three exchange rates are affected by lag risks and RMB exchange rate is suffered the biggest risk. Overnight-AS model and Overnight-SAV model proposed in this article are better than AS model and SAV model. Overnight-AS model is better than Overnight-SAV model especially for5%of Yen exchange rate. Fluctuations in the dollar index will increase the overnight rates risks of these three markets. The impact of the RMB exchange rate by the dollar index is less than HK exchange rate and Yen exchange rate. The impact of the weaker dollar on overnight risk is greater than the impact of the stronger dollar. These provide new ideas and methods for the management of exchange rate overnight risk.It is the first attempt to study the real estate risk of different urban areas and the city is divided into the city center, the emerging urban and remote town, the real estate is divided into the commercial real estate, office buildings and residential real estate. We improve the SAV model and AS model of CAViaR models to analyze the real estate risk of Wuhan city, also the two models are compared. The results show that the improved AS model is better than the improved SAV model, the risk of the city’s real estate is affected by the lag risk and remote town is affected the greatest. The impact of the commercial real estate risk on the city center is greatest. We should prevent commercial real estate in excess. The emerging urban risk is affected by the largest office buildings risk. We should control the supply of office space to prevent excessive. The impact of residential real estate on the remote town is greatest. We must strive to control the supply of land and a sharp rise in the number of residential real estate.