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1、A New Exploring on Definition and Measuring of Financial Risk -Based on Wavelet AnalysisHan HaiboSchool of Statistics,Lanzhou Commercial College, 730020Abstract There are tow important concept in traditional field of financial risk defining and measuring. That is the degree of loss or volatility of
2、return and the occurred probability of them. However we ignore one fact. Usually we think that two assets have same risk if their variance of return were same. On the other hand, does this mean that an asset has more risk whose frequency of return volatility is higher? We should research this proble
3、m practically. Traditional measuring method of financial risk focus on the timely changing characteristics of variance or the calculating of volatility amplitude. This method cant estimate the frequency of volatility. This paper tries to analyze the timely changing characteristics of frequency using
4、 wavelet analysis and give a new concept of financial risk.Key words Financial risk, Wavelet analysis, Timely changing characteristics, Measurement1. IntroductionAt present，there is no uniform definition of risk in academia , because scholars who study risk from different angles, has different inter
5、pretations on the concept,. We can conclude some representative viewpoint as follows:(1) Risk is the uncertainty of the event possible result in the future. ( A. H. Mowbray ,1995)(2)Risk is the uncertainty of loss. (F. G. Crane, 1984)(3)Risk is the damage degree of possible loss. (Hu Yida, 2001)(4)R
6、isk is the size of loss and the possibility of taking place. (Zhu Shuzhen, 2002)(5)Risk is the interacted result of factor which composed of risk. (Yi Danhui, 2000)(6)Define risk as volatility with standard statistics method. (P. Jorion, 1997)(7) Define risk as stochastic characteristics of uncertai
7、nty2. Exploring of financial riskFrom the concept of risk above we can find that each definition and measurement of risk is inseparable from the two key concepts, the volatility of return and the probability of it taking place. Because these two core concept were foundations, risk measurement also c
8、annot be inseparable from variance which describe separate degree of data, as well as its probability distribution function. At present most method of risk measurement is based on these two key factors. The method is more and more complex and the result is more and more precise. But its result only
9、describes the volatility amplitude, whatever how precise is the results and how complex are the models. (such as ARCH model, SV model, etc.) Therefore, we think the risk is the uncertainty degree, the variance large the possible of loss is bigger, vice versa.However we ignore one fact. Usually we th
10、ink that two assets have same risk if their variance of return were same. On the other hand, does this mean that an asset has more risk whose frequency of return volatility is higher? We should research this problem practically.To a rational investor, return of assets was not influenced even it chan
11、ged frequently if he was a long term investor. However frequent changes of return should change the expectation of investor, and change his decision of investment. On the other hand, frequent changes of return will increase the difficulty which select the time of exchange to a short term investor. F
12、rom this analysis we believe that frequent changes of return will change investment behavior. So frequency of volatility is also the resource of risk.Author: Associate professor Han Haibo. Economics master of Wuhan University. Main study field is analysis of financial data. Tel:13919235333 E-mail:Tr
13、aditional method of financial risk focus on the timely changing characteristics of variance and the calculation of volatility amplitude. This method cant estimate the frequency of volatility. So we need establish a new method to discover and measure the timely changing character of volatility freque
14、ncy. Because of its amelioration of tradition Fourier transformation, wavelet analysis method is the best one what we need. 3. Brief introduction of wavelet analysisThe fundamental idea behind wavelets is to analyze according to scale. Indeed, some researchers in the wavelet field feel that, by usin
15、g wavelets, one is adopting a whole new mindset or perspective in processing data. Wavelets are functions that satisfy certain mathematical requirements and are used in representing data or other functions. This idea is not new. Approximation using superposition of functions has existed since the ea
16、rly 1800s, when Joseph Fourier discovered that he could superpose sins and cosines to represent other functions. However, in wavelet analysis, the scale that one uses in looking at data plays a special role. Wavelet algorithms process data at different scales or resolutions. If we look at a signal with a large window, we would notice gross features. Similarly, if we look at a signal with a small window, we wou
