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EGARCH model based on the exchange bond market volatility analysis

Author: XuWeiMin From: www.yourpaper.net Posted: 2009-03-30 16:57:58 Read:
First, the problem of the proposed

The bond market is an integral and important part of the economic operation, links monetary policy and fiscal policy, to communicate money market and capital market. At present, China's bond market structure split, the inter-bank bond market and the exchange bond market constitutes the main framework of the government bond market, the inter-bank market less participating institutions, the formation of oligopolies; Exchange of many market participants, the formation mechanism of competition. Exchange market, prices to be determined by buyers and sellers of competition mechanism, its transparent transaction process, the formation of the transaction price is fair, equitable. [1]
Volatility (Volatility) is a measure of the uncertainty of the assets, to measure the risk of asset. In general, the greater the volatility, the greater the risk. Engle (1982) first proposed autoregressive conditional heteroskedasticity model ARCH model to distinguish the variance and conditional variance and conditional variance as a function of the error in the past and change, new way to resolve the problem of heteroscedasticity. Bollerslev (1986) generalized autoregressive conditional heteroskedasticity GARCH model. Foreign scholars to apply this method to many other areas of the economy, shows the applicability of ARCH Models. Domestic scholars application ARCH Models empirical research on the securities market of Huang Houchuan, Chen Langnan (2003) [2] Wang Yanhui, Wang Kaitao (2004) Application EGARCH analysis assessment and analysis of the volatility of the stock market, Shenzhen stock market volatility. [3] national debt security is not natural, "327" national debt storm still smarting, the bond repurchase risk dragged down the number of securities companies and listed companies, the imbalance between supply and demand of the government bond market led to Treasuries further distortion of the price variation and interest rates, which will lead to a systemic risk for the government bond market. Fluctuations in the exchange bond, both for the country, or to institutional investors, including individual investors, are a cause for concern.

Second, the selection of indicators and data analysis

(A) the selection of indicators
The Shanghai Stock Exchange's bond trading accounted for 99% of the entire exchange market. In March 2006, the Shanghai Stock Exchange has a national debt stock of 43 government bonds pledged repo 9. SSE Government Bond Index (LEB) is the first bond index of the Shanghai Composite Index Series, it makes China's securities market stocks, bonds, index of funds "Trinity" a basic system. SSE Government Bond Index is based on a fixed-rate government bonds listed on the Shanghai Stock Exchange as samples the Weighted made in accordance with the bond issuance, the last trading day of each month, the remaining maturity of less than one year treasury bonds removed. Announced since January 2, 2003, the base date of December 31, 2002 basis points to 100 points code 000012. The purpose of the SSE Government Bond Index to reflect changes in China's bond market as a whole "indicator" of China's bond market price changes. SSE Government Bond Index is to provide investors with the precise scale of the investment, and lay a solid foundation for the innovation of financial products. Based on the above analysis, this article Select SSE Government Bond Index as an indicator of fluctuations in the exchange bond market measure.
(B) data analysis
SSE Government Bond Index dynamic announcement from 24 February 2003, the time interval of the data is from February 24, 2003 to 2005, a total of 696 data. Bond index yield (DLEB) by equation (1) get.
DLEB = InP t -InP t-1 (1)
SSE Government Bond Index historical trend shown in Figure 1, the trough is 99.1, April 30, 2004, the crest is December 10, 2005 109.73. Bond yields graphic shown in Figure 2, can be seen in a certain range in volatility. The data from the great wisdom of software, to use Eviews analysis processing.

Figure 1 Government Bond Index historical trend

Figure 2 bond index yield

Third, the empirical analysis

(A) The stationary test
ADF (Dickey and Fuller, 1981) and PP (Phillips and Perron, 1988) unit root test. SSE Government Bond Index yield sequence inspection found that the bond index series (LEB) is not a stationary series, the yield sequence (DLEB) is smooth sequence (see Table 1).

Table 1 unit root test

(B) normality test
Government bond yields and the characteristics of the time series variance not only with the time change, and sometimes change very heated. Its normality test, Skewness -1.80031 Kurtosis is 17.5419, deviated from normal levels. "Fluctuation cluster" (volatility clustering) characterized by Time observed showing, i.e. the variance is relatively small in a certain time period, while at another time is relatively large. Performance value distribution is leptokurtic (leptokurtosis and fat-tail) characteristics, mean near the tail area probability value is larger than the normal distribution, the probability of remaining area is smaller than the normal.
(C) ARCH effect test
Residuals t existence of ARCH or GARCH effects test, usually proposed by Engle (1982) Lagrange multiplier test method (Lagrange Multiplier test), referred to as the LM test, generally is t 2 get the fitting goodness R 2 autoregressive estimate AR (q). Then use Conclusion: ARCH or GARCH does not exist under the null hypothesis, the statistical amount TR 2 and subject to the degree of freedom of q x 2 distribution in the selected significant 2
distribution threshold level, when the value is greater than x TR 2 refuse the t there is no ARCH or GARCH null hypothesis that the presence of ARCH or GARCH effects. After fitting, the lag order and lag order constitute autoregressive time series significantly.
DLEB t = 1 DLEB t -1 2 DLEB t-3 t (2)
(D) EGARCH model
If a stationary random variable can be expressed as AR (p) in the form of order q of the variance of the random error term can be used error squared distributed lag model description, called ARCH model. For to avoid lag items too much of the ARCH model, can be added s t 2 lags, which formed GARCH model that generalized autoregressive conditional heteroscedasticity model.
EGARCH model index (Exponential) model proposed by Nelson in 1991, its purpose is the to portray conditional variance of the market of Chiang Kai-shek, the negative interference of the reaction of the non-symmetry. [4] model condition variance using the natural logarithm form means that the leverage effect is exponential. The conditional variance h t delay disturbance ti antisymmetric function:

ARCH items. Compared with GARCH and ARCH, the advantage of this model is that it can distinguish between the different effects of positive and negative information. The information is "feel good" negative information indicates "Lee bad. Although the positive information and the absolute value of the negative information, but the EGARCH model can distinguish between positive and negative information on the different effects of fluctuations. EGARCH model can be a good description of the asymmetry in the financial markets. Furthermore, since the variance is expressed in exponential form, and thus there is no constraint on the parameters in the model, which is a major advantage of the EGARCH model. The right of s the t 2 logarithmic equation, so regardless of the equation right is the positive or negative, as the the antilog s t 2 is always positive. 2 on the right-hand side is the conditional standard deviation s t information u t and its lagged term (the u t / s t ) represents the standard information. 3 the absolute value of the standard information is a mean U Save.
After analysis, EGARCH (1,1) is a good model of the fitting, i.e. of formula (2) and formula (4) regression analysis results are shown in Table 2, utilizing a bad influence is stronger than the influence of the positive information .

Fourth, the conclusions and recommendations

After the analysis, the Exchange bond index series are not stationary sequence, and the sequence of the yield smooth sequence distribution presents the characteristics of a fat tail, the rate of return in the range of memory in volatility. Worthy of note is the fitting from the EGARCH model Lee bad information is much greater than the impact of positive information.
Exchange bond market volatility can be attributed to three points: First, the volatility of the national debt, the exchange bond is not a once and for all, the risks remain; Second Treasury market segmentation, Granger causality test showed the inter-bank bond market passed with the exchange bond market price, microstructure transmission mechanisms play a decisive role; Finally, the behavior of investors, investor loss aversion, caused by the irrational behavior of irrational phenomena such as herding, and increase the volatility of the exchange bond market sex.
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