The Quantile Regression Technology And Its Applications For Forecasting Of Value At Risk In Financial Market

The financial innovations and financial globalizations make the business activities of modern financial institutions face more market risks. In2007, the subprime mortgage crisis was triggered by the rapid development of the U.S. real estate market, which pushed five major Wall Street investment banks to be collapsed. The crisis was rapidly evolving into a global financial crisis. It has led to that the global economy has experienced the most severe recession since the1930s. In fact, except for the subprime mortgage crisis, the financial market is never calm. From the history of several financial crises, it has been seen that financial risks and financial development are accompanied. At the same time, the financial regulation experienced from freedom to preliminary control, from the preliminary control to strict comprehensive control and from the strict comprehensive control again towards the free development. Without a doubt, financial liberalization has greatly promoted the development of financial sectors and financial markets. However, when financial liberalization does not synchronize with strengthening financial supervision or institutional innovation lacks of corresponding system innovation, especially, regulatory innovation, there will undoubtedly increase the financial risk. With the emergence and innovation of financial derivatives, the variety of financial risks are rapidly growthing, which has brought many difficulties to the risk management. Thus, it is an urgent requirement to strengthen financial supervision. China’s financial market is reforming continuously and accelerating the opening. It not only brings us great opportunities, but also makes our financial institutions face more risks. Therefore, raising the level of market risk management and strengthening risk control are essential for the stability and development of Chinese financial markets.The measure of risk is the key of risk management and control. Along with the development of financial markets, it has attracted a high degree of attention about how to accurately measure the market risk. In many of the risk metrics model, VaR approach has been acquired the wide range of application and promotion, which is regarded as an important tool of risk measurement in all financial institutions and is considered to be the standard measure of international financial risk. Therefore, the vigorous development and application of VaR method have become significance for preventing financial risks and ensuring the effectiveness and rationality of risk management. Although the concept of VaR is simple, one has a variety of different viewpoints about how to compute its value. The core of the method is to estimate the statistical distribution or probability density function of the future earnings of financial position. This paper attempts to use the quantile regression method to calculate the VaR. This method is different from the traditional methods, which directly estimates models and needs not to consider the specific distribution pattern of models. In addition, the quantile method is a robust regression method and is particularly effective for studying the thick-tailed distribution of financial data. According to simulational and empirical analysis, the advantages and limitations of the quantile regression with other methods are compared in the calculation of VaR, so as to provide an alternative method for the measure of actual risk in the future.Generally speaking, this thesis consists of six chapters. The structure and contents are described as follows.The first chapter is the introduction of this article. It describes the background and significance of this study. After that, the background of the VaR method is briefly described and some views of this method that needs further to be improved are also pointed. Meanwhile, research summaries and literature reviews are given on the research progress and practical application of VaR in the domestic and foreign financial markets. Finally, the ideas, methods and innovation of this research are introduced, which details the quantile regression method for highlighting its strengths and advantages in the VaR estimation.The second chapter begins to expound the general framework of the financial risk management, which tries to find and specify the foundational and central position of the VaR in risk management. Firstly, a detailed explanation of financial market risks is presented, which mainly contains the affect, management and common measurement methods of financial market risk. Secondly, for describing the characteristics of financial markets, some basic statistics are given which involve the calculation of financial return and the properties of related statistics. In the end of this chapter, a brief introduction is presented on the development and current situation of China’s stock market. It takes an example of Shanghai and Shenzhen composite index to analyse their characteristics and properties of return distributions.A more comprehensive study and discussion on VaR theories and methods are given in Chapter three. This chapter explains the subject that VaR satisfies the requirement of the modern market risk measurement. Then, it details the VaR starting from its definition. For measuring risk, the difficulty for using the VaR is how to select the appropriate estimation method to calculate its value. Some estimation techniques of VaR are introduced by the order of theries and empirical research. Firstly, the basic principles and processes are explained for estimateing the value of VaR, which contains the parametric and non-parametric methods. Form two aspects of volatility and accuracy, it begins to explain how to make a backtest for VaR, in which an empirical analysis is performed. Later, the current popular VaR method based on volatility of modeling is mainly disscussed. Also, some common methods dealing with the financial data with heavy tail and asymmetric distribution are examined. At the end, several volatility methods are compared by employing the data of composite index in Shanghai stock exchange. The empirical results show that using these methods to calculate the VaR is relatively effective.The fourth chapter applies the technology of local polynomial with nonparametric quantile to compute the value of VaR. This chapter contains mainly two aspects. On one hand, the nonparametric model is introduced. The main advantage that nonparametric modeling can avoid the errors caused by specifying models is pointed out. Then, the local polynomial steps are given for the nonparametric model in which one problem related to variable selection is discussed. Subsequently, the method of local polynomial with nonparametric quantile is suggested to estimate nonparametric model. In the same time, the statistical properties and the variable selection method of this technology are also discussed. Furthermore, the finite sample properties of local polynomial with nonparametric quantile estimator are examined by Monte Carlo simulation. Simulation results prove that the proposed estimate is more robust than the local polynomial estimate. On the other hand, the nonparametric VaR modeling is considered, where the detailed procedure about how to use the local polynomial with nonparametric quantile method to calculate the VaR is emphatically described. Through empirical analysis, it is testified that this method is more accurate than some existing methods in calculating the VaR value.Considering the influence of trading volume, a direct calculation method of the VaR value is discussed in the fifth chapter. In the setting of Chinese stock market, a VaR forecasting model based on the varying coefficients modeling is recommended, whose variables include the additional indicator of trading volume. This chapter first gives the specific expression of varying coefficients model and describes some approximate methods of this model by local polynomials and polynomial splines. Then, a detailed explanation of the B-spline quantile method is presented and the specific steps that how to use this method to estimate the varying coefficient models are elaborated. During this process, the basic concepts, asymptotic properties and variable selection problems of B-spline are described respectively. At the same time, a Monte Carlo experiment is designed to test the effectiveness of B-spline quantile estimate. As expected, the experimental results show that the B-spline quantile estimates are robust and effective. Because the prices and trading volume of financial asset are the two most fundamental indicators of financial markets, whether the volume has an impact for risk needs to be inspected. Therefore, in the modeling of VaR, the index of asset turnover is added to the model, which deduces a varying coefficients VaR model. After that, an estimation procedures of this VaR model is given by the B-spline quantile method. Finally, the method is applied to the empirical research and the results demonstrate that the size of trading volume has a direct impact on VaR estimates.The sixth Chapter introduces the approach of weighted quantile Copula to compute the VaR value. Because the correlation structure between the assets does greatly influence the accuracy of the VaR value, the studies of correlation are very important in financial risk analysis. Copula function theory recently developed is viewed to be a new tool for studying the dependencies between variables. It proves that the Copula methos is more accurate and flexible than some traditional VaR methods. Firstly, the definition, basic properties, classification and expression with different parameters of Copula function are introduced. Secondly, some correlational indicators derived from Copula function are discussed deeply. Since those indicators can capture the non-linear relationship between variables, especially, the tailed relationship, they have more extensive adaptability than some common measure indicators. Then, the methods of Copula’s parameter estimation and model selection are recommended and investigated by Monte Carlo simulation. Whereafter, the technology of weighted quantile regression is proposed to estimate the unknown parameters in the Copula Function. Meanwhile, the quantile curves of several common Copula are deduced. Subsequently, the accuracy of the suggested methods is proved by applying a simulation study. At last, the method of weighted quantile Copula is applied for examining the correlation structure between Shangzheng and Shenzhen stock market and the VaR value of portfolio is obtainted.