Interval-Valued Risk Measure Models And Empirical Analysis

The financial risk measurement is the key and core of the financial risk management,and the prerequisite for the further implementation of the risk management strategy.In financial market,there are many methods to measure financial risk.VaR(Value at Risk)is one of the most popular methods and the risk management standard in the world.The proposal of the CVaR(Conditional Value at Risk)has improved the shortcomings of VaR.In recent years,many scholars have made a series of improvements and studies on the traditional VaR and CVaR computing models when the rate of return is the single value.However,there are other uncertainties in the actual financial market,such as fuzziness and inaccuracy,in addition to randomness.If the return rate is regarded as a random interval,it can describe not only the randomness of the market but also the inaccuracy caused by the ever-changing market.Based on the traditional risk measure models,this paper puts forward the interval-valued risk measure models.First we introduce the definition and the common estimation methods of the classical VaR and CVaR.The application of historical simulation and Bootstrap method in the calculation of VaR and CVaR are described in detail.Then,based on the above theory,we consider the return rate as a random interval.By employing appropriate intervals ordering method,we establish the interval-valued risk measure models for VaR and CVaR.In the empirical analysis part,we select Shanghai stock index and Shenzhen composite index,CSI 300,CSI 500 and 24 representative stocks in banking,real estate industry,entertainment and media industry,energy industry,agriculture,forestry,animal husbandry and fishery.According to the closing price,the highest price and the lowest price of the stocks.first we calculate the return rate and the interval-valued return rate.Then we use historical simulation method to calculate VaR,CVaR,interval-valued VaR and interval-valued CVaR respectively.Besides,Bootstrap method is used to improve the estimation accuracy of traditional historical simulation.Finally,the validity and accuracy of the three models are tested and compared by using Kupiec test.The results show that the accuracy of interval-valued risk measure models is the best.When the return rate is a form of accurate value,the historical simulation model based on Bootstrap sampling is more accurate than the historical simulation method based on the original samples.Finally,based on the depth analysis of the interval-valued risk measure model,we summarize the conclusion of the article and put forward research proposals and prospects in the following three aspects:the rule to order intervals,the test of interval-valued risk measure model and the use of variance-covariance method or Monte Carlo simulation method for interval-valued risk measure model.