| The research of the relationship between volume and price is attached great attention in both academic and practical world. Studies have shown that the statistical relationship between volume and price is significant and can be divided into two aspacts. One is the positive relationship between the absolute value of the changes of asset prices and the trading volumes. The other one is the positive relationship between the volatility of assets price and the trading volume. Meanwhile, the segmentation theories of the volume and price theories such as the mixed information distribution theory, the asymmetric information theory, the theory of disagreement analyses the markets’volume and price relationship by empirical analysis from economics, sociology, psychology perspectives, creating and verifying many new angles and methods to understand the market performances. As an important part of the technical analysis of financial markets, the volume and price theories have influence on the investors’understanding of market and the judgment of asset price in the future, affecting the market trading directly.The great importance of VaR(Value at Risk) for risk forecasting and controlling has been verified in the developing process of global finance market in the past several decades. With the integration of global economics and finance, as well as the fast development of financial derivative instrument, the risk exposed from or hidden in the capital market and the corresponding supervision and regulation methods have become the focus of people’s attention day by day. Under the circumstances, researchers came up with the concepts and measurement models of VaR and develop them to mature gradually."The Supplement Provision of Basel I on market risks" regarded assets’VaRs models as the standard model for risk measurement."The Basel Ⅱ"required banks to do the pressure test on the basis of building up risk control models, in order to calculate the VaR to monitor the risk lever of finance assets. The GARCH models are effective means to portray finance time series with time varying variance. On the basis of portraying the time series effectively, various sub-models with different characteristics can do the expanding targeted research on the regions such as the price and volume relationship and the Value at Risk. For instances, the use of classical GJR-GARCH and other asymmetry model can effectively reflect the leverage effect of financial markets. And we can selected best models to measure VaR model for specified targets and samples.After learning relevant papers, the article introduces the so-called "volume and price mixed information dummy variables", which can reflect information of different levels of yield rates and volume, into the classical GJR-GARCH models. Then judge the effectiveness of model fitting based on comparing the regression results of the experimental model and other classical model. After that, there comes up with some application such as the price and volume relationship analysis experiment and the risk measurement and control experiment. The detailed process is stated below.Firstly, the "Introduction" chapter gives the reasons why this thesis studies the relationship between volume and price and the VaR, explaining the background and the significance of the selected topic, as well as summarizing the relevant studies of the price and volume theory, value at risk theory and GARCH models.Secondly, the "Construction and application of the Volume and Price Mixed Information GJR-GARCH models" chapter provides a detailed review on the methods of various GARCH models and VaR measurement and tests, and elaborates the modeling steps such as the pre-test and post-test in the process of building up and assessing the GARCH models. Then explain the methods to make the volume and price mixed information variables, as well as the modeling ideas and basic form of the experimental model.Thirdly,"the data selection and pre-processing" chapter illustrates how to select the sample data and why selects the targeted dataset, and then mentioned the purpose and methods to pre-process the sample, recognizing the statistical characters and distribution of sample, making good preparations for further analysis.Finally, the "empirical results and analysis" section records the main empirical process and results of building up the experimental model, comparing the fitting results between the empirical and classical GARCH models, to evaluate the validness of the empirical model. If the experimental model is valid, on one hand, this thesis analysises the more specified structure of the asymmetric effectiveness, and analysis the volume and price relationship of Shanghai stock Index. On the other hand, it examines the risk measurement capability of experimental model by comparing with the same capacity of other classical models, using methods of statistical indexes and VaR tests..Then the thesis gets some meaningful conclusions as below. For reading convenience, separate the conclusions into two parts.The first part summarizes the conclusions of model fitting and application results.1. The volume and price mixed information GJR-GARCH model has a good effect on model fitting.Firstly, the results of the model’s ante and ex post tests such as parameters’ significant test, Box-Ljung Q test, ARCH-LM test, sign bias test and Pearson’s chi square Goodness-of-Fit test all have good performance. However, part of the parameters of the model can not pass the Nyblom’s parameters’stability test. But it is a common phenomenon of all the GARCH models built up in this research.Secondly, viewing from the constraints of the regression parameters, α, β, the parameters of the variance equation of the GJR-GARCH models are in line with the definition rules of ARCH and GARCH variables. And the sum of α and β is reduced to0.94, which is the minimum value of all the other GARCH models in comparison, showing that the experimental model can describe the leverage ratio in a more effective way to explain part of the information’s persistent influences presented by the short-term and persistent fluctuation.Thirdly, viewing from the information criterion statistics, the experimental model has a maximum number of variables among all the models in comparisons, while having a minimum value of AIC, BIC, SIC, which is another example that the model has a good the nature of fitting.2. The experimental model can be refined analysis of the effects of asymmetric in a more detailed wayViewing from the regression results of the volume and price mixed information GJR-GARCH model, the negative residuals appeared yesterday do not surely bring the leverage effect. The reason why the leverage parameter can pass the significant test is that part of yesterday’s price and volume performance increase the average volatility level of the yield rate today. Therefore, when we understand and apply the asymmetric effect models, we should notice that the asymmetric effect is valid in mean effect, and not every negative residual can promote the volatility level today.3. VaR measure capacity and risk forecasting capacity analysis based on volume and price mixed information GJR-GARCH model and other compared GARCH modelsFirstly, though the experimental model has a better performance in likelihood, information criterior and other statistical test than other contrast models, it doesn’t show unique advantage in risk forecasting. This phenomenon probably implies that the better fitting results of information criteria and statistics test do not guarantee the accuracy of risk measurement.Secondly, the value of violation rate of the experimental GARCH model is much smaller than other contrast models under student-t distribution, as well as being the comparatively small one at5percent significant level under norm distribution. On one hand, it implies that the bold VaR estimation of the experimental leads to comparatively stronger risk warning capacity. On the other hand, the value of VaR which is much smaller than1implies the experimental model over estimates the risk and has a high cost for risk management.Thirdly, the risk forecasting effectiveness is quite good for all the GARCH models used in the chapter at5%significant level under norm distribution, which is in line with the research result of Gong(2005). However, all the GARCH models can not achieve good risk forecasting result at5%significant lever under student-t distribution because of over estimating risks.The second parts of conclusions summarizes the conclusions of volume and price analysis of Shanghai stock index as blow.When a defined big or moderate decline appeared in the market yesterday, the implied price information seems to have a significant influence on the volatility of yield rate today in an average level. The evidence is that two third of the regression parameters deny the null hypothesis that parameter equals to zero at a1%significant level. And the other one third of the regression parameters accepted the null hypothesis at5%significant level.Different volume and price information asymmetry effect today will produce different effects. The t-1information of large decline with big turnover and moderate decline with big turnover is proved to make a maximum contribution to the asymmetric effect at t, and the value of the additional contribution to volatility is individually0.0085and0.0087. The t-1information of large decline with small turnover and large decline with moderate turnover is proved to have a relatively second largest contribution to the yield rate volatility at t, and the values of the additional contributions to volatility today are about0.007. The t-1information of small decline with large turnover, moderate decline with small turnover and moderate decline with moderate turnover are relatively small at an average rate of about0.5percent. At last, the t-1information of small decline with small turnover and small decline with moderate turnover doesn’t have a significant promotion to the additional volatility today.Above all, we can summarize two characteristics of how the volume and price performance affect the yield rate volatility today. The first one is that the higher the level of yield rate decline yesterday is, the bigger the contribution to the additional volatility rate it made. The other one is that among different levels of turnover at a same level of yield rate, the t-1information of big turnover brings much higher contribution to today’s additional volatility than other information. And the t-1information of small turnover with big or moderate decline would bring bigger yield rate volatility compared with the t-1information of moderate turnover, but the information of small decline with small turnover rate yesterday would be an exception. This thesis also use the classical price and volume theory to make economic explains of the volume and price phenomena mentioned above.Finally, we can find different distribution hypothesis and significant level can significantly affect the risk measurement and forecasting effectiveness of GARCH models. We can get a conclusion from empirical analysis that when making a judgment on the risk measuring capacity, we should take distribution and significant level into consideration, instead of judge the capacity by simply considering one specific significant level under one specific distribution. |
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