【正文】 布情況下CVaR和VaR兩種度量是等價的，可得出同樣的最優(yōu)解。此時，VaR僅為極小值點，可能不存在最優(yōu)解，而CVaR為極小值。其次，CVaR與VaR不同，它不是損失分布上單一的分位點，而是尾部損失的平均值，反映了損失超出VaR部分的相關信息，只有把大于VaR的所有尾部損失進行充分估計，才能用以計算CVaR。此外，由于CVaR的計算是建立在VaR基礎之上的，所以在得到CVaR值的同時，也可以獲得相應的VaR值，故而能夠針對風險實施雙重監(jiān)測，也便于相互校驗。 CVaR風險測度原理符號說明：x：是控制變量，y：代表不確定因素的隨機變量，：為置信水平對于每一個x，相應y的損失函數(shù)f（x,y）。如y 是一已知分布的隨機變量, 則f (x, y)就是依賴于y的隨機變量。在給定 (0 1)內, 投資組合風險的VaR值定義為:VaR (x): (x,) = min{。如給定置信水平c=95%，CVaR就是那5%的最大損失的平均值，故CVaR不會小于VaR。 CVaR的檢驗對于CVaR的檢驗，是相對于VaR值而言。第2章 CVaR法在市場風險度量中的運用在計算VaR值時，通常有兩種方法，在已知分布時采用參數(shù)估計方法來確定VaR值；未知時則用非參數(shù)方法。而大量實證研究表明，金融資產的收益存在著尖峰厚尾特征、波動集聚性、非對稱性，在對計算VaR值的各種方法優(yōu)缺點進行比較的基礎上，同時考慮對H股股指期貨收益波動的研究僅僅是對單資產的風險測量問題，故選擇參數(shù)方法中的單資產不同分布方法計算VaR值。 GARCH族模型若一個隨機變量有恒定的方差，則稱之為同方差，反之則為異方差。而條件異方差可以估計為一個自回歸過程，即 ARCH模型。在模型中具體包括：均值方程：：條件方差方程： GARCH(1,1)中。在GARCH(1,1)中，為保證其寬平穩(wěn)性。例如某一特定股票的收益率較正態(tài)分布給出的概率有更大的可能性遭受重大損失（或重大獲利），即產生了所謂的” 非正態(tài)誤差”。正態(tài)分布密度函數(shù)較常見，為自由度參數(shù)，d趨于無窮大時，分布收斂于正態(tài)分布。 模型求解本文數(shù)據(jù)選取2004年3月3日至2012年5月22日上海證券交易所上證180的交易數(shù)據(jù)。上證180日收益率定義為，其中，為上證180當日交易的收盤價格。由圖22可知，可知其偏斜度較小，表現(xiàn)為左偏，可知其表現(xiàn)為尖峰，則由圖21和22知該圖形是呈尖峰厚尾狀，這些數(shù)據(jù)并非服從正態(tài)分布。對這些數(shù)據(jù)作圖，如圖23。圖24 r的ADF平穩(wěn)性檢驗圖24是對收益率r進行平穩(wěn)性檢驗。圖25 r的正態(tài)分布檢驗圖26 r的t分布檢驗由圖25知，假設收益率服從正態(tài)分布，則由假設檢驗可知，%；由圖26知，假設收益率服從t分布，則由假設檢驗可知，%；所以比較可知，收益率在5%的顯著性水平下服從t分布。再進行方程估計，如下圖：圖28 序列r的方程估計由以上結果得出EGARCH模型的結果可以表示為：條件均值方程：條件方差方程為：。所有的數(shù)據(jù)可以參照附錄。本課題則是通過現(xiàn)在國際上較為通用的方法來進行風險的度量，即CVaR度量法。在附錄中可知，VaR風險度量法對這2000個數(shù)據(jù)進行模擬，%，而置信度為95%，可以得到VaR預測的結果的可靠性較低；%。目前，我國對于風險度量的方法的選取，主要還是依靠國外的經驗。本文對時下流行的證券VaR風險度量技術進行了較為全面的介紹，指出其理論缺陷和使用局限。誠然，目前CVaR尚未成為金融業(yè)的一項公認標準，除了在保險業(yè)有所研究和應用之外，鮮見于有關證券業(yè)的中外文獻。因此，相信在不久的將來，這項技術會被銀行業(yè)逐步認可并加以運用，在實踐中接受檢驗和不斷改進。四年的求學生涯，在師長、親友的大力支持下，走得辛苦卻也收獲滿囊。偉人、名人為我所崇拜，可是我更急切地要把我的敬意和贊美獻給一位平凡的人，我的導師。您治學嚴謹，學識淵博，思想深邃，視野雄闊，為我營造了一種良好的精神氛圍與學習氛圍，讓我感受頗多。從論文題目的選定到論文寫作的指導，經由您悉心的點撥，再經思考后的領悟，常常讓我有“山重水復疑無路,柳暗花明又一村”的感覺。從開始進入課題到論文的順利完成，有多少可敬的師長、同學、朋友給了我無言的幫助，在這里請接受我誠摯的謝意！同時也感謝學院為我提供良好的做畢業(yè)設計的環(huán)境。參考文獻[1] [D].西北工業(yè)大學碩士學位論文， 2004. [2] [M].上海：復旦大學出版社,2009,6. [3] Robert J. Powell amp。潘澤，維普[M].北京：機械工業(yè)出版社,2001.[8] Cebenoyan，；Strahan，Philip management，capital structure and lending at banks[J].Journal of Banking and Finance,2004,(1). [9] [M].杭州：浙江大學出版社,2009.[10][M].北京：北京大學出版社,2007.[11][D].南京:,6061.附錄A外文：ShortTerm Investment Risk Measurement Using VaR and CVaR Virgilijus Sakalauskas and Dalia Kriksciuniene Department of Informatics, Vilnius University, Muitines 8, 44280 Kaunas, Lithuania {, } Abstract. The article studies the shortterm investment risk in currency market. We present the econometric model for measuring the market risk using Value at Risk (VaR) and conditional VaR (CVaR). Our main goals are to examine the risk of hourly time intervals and propose to use seasonal deposition for calculation of the corresponding VaR and CVaR values. The suggested method is tested using empirical data with long position EUR/USD exchange hourly rate. Key words. CVaR 。 1 IntroductionTrading in the stock and currency markets has many mon features, yet these markets have major differences as well. Currency market has higher volatility, which causes higher risks of trade. There are many reasons which cause substantial volatility of the currency market. * The transactions, related to the pairs of currencies exchanged, have much more trading partners, paring to the stock trading. * Currency exchange attracts much more instant, even unqualified traders, while stocks’ trading requires at least basic minimal financial knowledge. * The rearrangement of stock portfolio is related to quite big taxes, paring to relatively liberate tax policy in currency trading. The traditional way of risk estimation in the stock markets is based on periodic risk evaluations on daily basis or even by taking longer periods. This practice is in most cases based on empirical experience and is convenient for application in trading stocks. Yet even most simple analysis of currency markets indicates, that this kind of risk evaluation could be not sufficient, as during the period of 24 hours it changes several times: for particular hours it can differ even up to four times, as it is further shown in this article. The paper aims at the estimation of the market risk for the shortterm investments in currency market by suggesting the modified RiskMetrics model, based on risk evaluation according to hourly profit alterations of the financial second part of the article describes and evaluates the theoretical settings for risk analysis in the currency markets by applying traditional models. The econometric description and substantiation of the suggested model is presented in part 3. The fourth part presents experimental verification of the method using FOREX historical data of EUR/USD hourly exchange rate fluctuations.2 Theoretical Assumptions and NotationsOne of the most widely used factors for market risk measurement is Value at Risk (VaR), which is extensively discussed in scientific literature starting already from the 1990. Historically, the concept of the ValueatRisk is related to the covariance calculation method that was first adopted by the Bank as a branch standard, called RiskMetrics model [15]. The VaR measure means the biggest loss of investment R during the time interval, at the fixed rate of probability p of unfavorable event: where p in most cases is selected as or (or 1% or 5%). The loss of investment R is understood as negative difference of the buying price and the selling price：In the article profitability is denoted as . The VaR measurement is very popular for its relative simplicity of interpretation, as risk can be evaluated by single value the loss rate at the occurrence of the unfavorable lowprobability event. This brought the VaR measure acceptance almost as