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# Fractal Analysis And Risk Measurement On Shanghai Securities Markets

Posted on:2005-05-27Degree:MasterType:Thesis
Country:ChinaCandidate:Q YangFull Text:PDF
GTID:2156360122485457Subject:Applied Mathematics
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This paper has three chapters: in Chapter two, the method of rescaled range analysis is used to analyze the recent return of the shanghai stock market. We introduced a new unbiased rescaled range statistic R/S* that eliminates effects of short-term dependencies. Hurst exponents equal 0.661 and 0.643 respectively. The results of the analysis show that the shanghai stock market has nonlinear, persistence and nonperiodic cycles. In Chapter three, we introduce various kinds of Value-at-Risk models, point out their virtues and shortcomings, and compare theirfields of application. Moreover, this paper put forward two model--block maximamodel and peak-over-thresholds model--provide the gist of risk control anddecision-making by calculating the Value-at-Risk.VaR developed recently is a new standard to manage financial risk. VaR not only is an effective instrument but also is becoming a scientific system now. This paper profoundly studies the typical methods of VaR in the world at present, comprehensively summarizes the theory system of VaR, and gives overall compare and analysis about all kinds of VaR methods. The majority of the parametric methods of VaR approach use a normal distribution approximation. Using this approximation, the risk of the high quartiles (over 95%) is underestimated, especially for the fat-tailed series, which is common in financial data. In addition, all the VaR methods focus on the central observations or, in other words, on returns under normal market conditions. However, VaR is a risk measure that relates solely to the tails of the distribution. The extreme values which lies in the tail are some rarely happened events that have significant influence. Extreme Value Theory (EVT) is the statistical model to study the behavior of extreme values. Chapter three introduces the basic knowledge of EVT and the VaR method using EVT.In short, the study on the problem will be helpful for our financial institutions to measure and control financial risk, and ensure safe and stable of financial market.
Keywords/Search Tags:Rescaled Range Analysis, Hurst exponent, Value-at-Risk, tail index, extreme value theory
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