Simulation Study And Empirical Analysis Of Nonparametric Estimation Of VaR And ES

In recent twenty years, due to the effect of economic globalization, the modern financial theory and information technology and other factors, the global financial markets were developed rapidly. This led to open financial markets deepening, the free flow of capital in the global scope greatly accelerated. The risk characteristics of different types of capital in the global financial market reconfigured and recombined, greatly changed the mode of operation and the risk performance of the global financial market, the financial markets are showing volatility hitherto unknown. At the same time, the financial institutions in order to avoid the financial risk, improve market competitiveness and to avoid regulation has been launched some financial innovation activities. In the relaxation of regulation and under technological progress stimulation this phenomenon is very active. In the financial background of economic globalization and financial liberalization, financial risk management has become a topic of concern. And how to quantify these financial risk, namely how to measure the financial risks, has become an important problem in need of solution.Currently, the main tools in use or have been proposed to measure risk are the standard deviation, absolute deviation, value at risk (VaR), conditional value at risk (CVaR), the worst conditional expectation (WCE) and expected shortfall (ES) etc. Among them, value at risk (VaR) played a very important role in the field of financial risk management. In1996, the Basel Committee laid stress on the importance of value at risk (VaR) on the market. Therefore, the world’s financial analysts have used it to design financial institutions risk measure. However, since1999, Artzner et al first proposed the concept of coherent measure of risk, the risk measure VaR was questioned, because someone from the theoretical and empirical analysis proved that does not satisfy the sub-additivity property, so then it is not a coherent risk measure. In order to construct a risk measure that is coherent, easy to estimate and calculate, Acerbi et.al. proposed the concept of Expected Shortfall(ES), and proved it is a coherent risk measure, and can be convenient for calculation.The value at risk is preferred by the financial institutions and managerial staff, but is has a fatal disadvantage, that is not satisfy sub-additivity. While the expected shortfall possesses the desired sub-additivity property, that makes it become an increasingly popular risk measure in financial risk management.In different conditions of window width, window width is greater, the kernel estimator is smaller. We consider two nonparametric expected shortfall estimators:one is a sample average of excessive losses larger than a VaR; another is a kernel estimator by smoothing the first estimator(Scaillet,2004Mathematical Finance). We are looking forward to bring about a more precise estimator by smoothing. The analysis exposes that the kernel smoothing does not produce more precise estimation of the expected shortfall (ES). This outcome is differed from the estimation of value at risk (VaR), smoothing can reduce both the variance and the mean square error of estimation. Hence, the ES estimator based on the sample average of excessive losses is better than the kernel one.The paper is divided into four chapters:Chapter1, we introduces the development background of the financial risk measurement, along with the significance of risk managementChapter2, the theoretical model and nonparametric estimation of VaR and ES are given, and also given the standard error of VaR and ES.Chapter3, reports the numerical simulation results. Using the five kinds of common time series model, report results from a simulation study which evaluates the kernel estimator and sample estimator. The outcome revealed that the kernel estimator does not more accurate than the sample estimator.Chapter4, is an empirical study on two financial series. Using the kernel estimator of ES to study the Shanghai stock index and Shenzhen composite index, the results show the volatility of Shenzhen composite index is higher than the volatility of Shanghai stock index.