Simulation Study And Empirical Analysis On Local Liner Estimation Of CVaR And CES

With the accelerating process of economic globalization, people gradually realize that the opportunities is greater, the risk is higher. As a result, more and more people begin to pay more attention to this problem--how to measure and control the risk? At home and abroad, many scholars began to research this field. In1994, the Morgan investment bank, puts forward the earliest VaR technology in the "Risk metrics", because it has many advantages, VaR gradually accepted by everyone, so far, the VaR method as an international financial risk control indicators, become a more essential tool in the enterprise risk management.VaR value at risk is an important financial risk measure index, recently there are many study about dynamic VaR and VaR (CVaR). This paper introduces the research of VaR as well as the improvement of CVaR on VaR, then introduces three kinds of methods:rule of window width, Silverman rule of thumb, Extremely smooth principle and cross validation method. Proposed using a new non-parametric estimation-local linear estimation, and use it to estimate the conditional value at risk(CVaR) and expected loss(ES), then compare with the N-W estimation. Comparison of different methods of different error between the estimated value and the true value, we found a local linear estimation is superior to N-W kernel estimator.In the simulation study, selected the window width by using the Silverman rule of thumb, with R software programming, generating a random samples to estimate the value of CVaR and CES, using the list shows the confidence level of different P values and in the case of X, the changes of CVaR and CES.Finally, in the empirical study, use the Shanghai Composite Index and the Shanghai and Shenzhen300index data (sample period from March29,2010to January20,2011) as the research object, with the ADF test the sequence, we found that the sequence of Shanghai Composite Index and the Shanghai&Shenzhen300index sequence have no unit root after the first order difference, so the series are integrated of order one sequence.Finally, the stock market data of CVaR and CES value was calculated by the method of local linear estimation.Both the Shanghai&Shenzhen300index, and Shanghai Composite index, estimates of risk wave function is obtained by using nonparametric local linear, it shows a U shape, the so-called "volatility smile" phenomenon, this can be considered a variation risk measure, has the characteristics with R fluctuation, easy and intuitive analysis.For the general investors of lacking related knowledge of probability and statistics, the use of risk metrics-concept of standard deviation, analysis is not intuitive, and is also not easy to explain and identity.Whether it is CVaR or CES, the estimated value of the graph shows a U shape, corresponds exactly to the so-called "volatility smile". When the risk propensity reduce, the hysteresis loss of Shanghai composite index value will gradually tend to experience average value. These results have certain reference value to evaluate the risk of stock market.