Research On Risk Measures Based On Distortion Functions

Influenced by the factors of global economic integration, financial innovation and so on, huge changes in the financial market are taking place, and risks become more and more complicated. So the research and development of risk measurement models are our top priority. For a long time, VaR has been the first choice to estimate the risks. The main advantage is that it shows the minimum number of losses and loss probability in the worst damage. VaR is relatively simple to use with a wide variety of risks, but it has a major flaw: it doesn't take all the information of the initial loss distribution into consideration, ignoring the risk of extreme events of the tail, high-risk events.Although these extreme tail risks occur infrequently, it might create significant impact if the event occurs. Therefore, the small probability of extreme events of great value-the tail risks should call peoples' attention. If people want to make accurate judgment and prognosticate to these tail extreme events, we need to find a more suitable model which deals with these extreme cases. To solve these problems, different sets of measures started to appear. However, we still cannot reach a consensus that which one is more reasonable and what the standard is. Obviously, apart from seeking for the new risk measurement methods, we need to do another important task-measuring the risks accurately.In this paper, we study a special category of risk measures - Function Risk Measures, This type of risk measures in essence emphasizes the tail risk, which gives a greater weight to high-risk events through modifying the distribution, thus making investors recognize great risk loss subjectively and show risk aversion. Firstly, this article introduces the popular risk measure models, analyzes risk measures from distortion function, points out that the difference comparing with traditional methods, and studies their characteristics, making risk measure more accurate. Then, we compare different kinds of Function risk measures through selecting different distortion functions, hoping to find basis for the selection. Later, we analyze the parameters of distortion functions, making the measure value closer to the real value. Since the usual risk distribution is fat tail distribution, we have put forward two methods to modify distortion distribution function: parameter and non-parameter estimation methods, in order to fit preferably the tail of the distribution and get more precise estimate value of distortion distribution function, and conduct post hoc tests on estimated values correspond, which can therefore guide Function risk measure in actual situations. Finally, we make a summary and point out the defects and content which needs further research.