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Discussions About Value At Risk And Risk Measures

Posted on:2009-11-18Degree:MasterType:Thesis
Country:ChinaCandidate:R XieFull Text:PDF
GTID:2189360245995242Subject:Probability theory and mathematical statistics
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A great reform has taken place since the collapse of the Bretton Woods System. Following the rapid development in the global financial market, the intension of fluctuation and the complication of market risk in this world have been raised to a higher level. Crucial financial disasters occurred frequently these years, such as the failure of business of Barings Bank, and Societe Generale affair happened recently, as a consequence, risk management had been one of the utmost concerns on the financial market. Academic and financial institutions pay much attention to the risk measure on both the theoretical and methodical reseach. VaR was proposed for the first time by Sterd.Guerddy, the general manager of the global institution of the J.P.Morgan in 1980's, who conceived that "risk of value" is more important than "risk of profit"(Jorion[1]). Then VaR entered into people's eyesight, and became one of the main methods of risk measures in the international financial market for its directness and understandabiliry.But the traditonal methods of VaR can not describe cases of heavy tail of return series and ones of of volativity, resulting the precise loss of risk estimation of extreme events. Extreme Value Thoery is a method which could measure the loss at the condition of extreme market.It is capable to excess sample, and describe precisely quantil on the tail of distribution. ARMA-GARCH model can describe the dynamic characteristic of volativity. The arti-cal introduce GEV, GPD and ARMA-GARCH model to get dynamic VaR, according to the research of McNeil[4]. Using closing prices data of China Shanghai Composit Index from 11/20/1995 to 4/17/2008, we compute VaR with three different methods(ARMA-GARCH, GEV-GARCH, GPD-GARCH).VaR has the model risk, and Artzner[9] pointed out that it does not satisfy the sub- additive property. Jiang[12] did some futher reseach in applying the g-expectation into the risk measures, introducing the g-expectation and proving that it is the sufficient and necessary condition of the coherent risk measures. In chapter 2, we review the notions of coherent risk measure, g-expectation,and their relationship as well. In a continuous complete market, by measuring the risk of a financial position using a certain sequence of g-expectation satisfying the coherence axiom, we find a different case of risk pricing in profit of this coherent risk measure with using the equivalent martingale measure in the frame of classical linear expectation.
Keywords/Search Tags:Value at Risk, Extreme Value Theory, Coherent Risk Measures, BSDE, g-expectation
PDF Full Text Request
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