Application of Extreme Value Theory to Estimate of Value at Risk

• Main Authors: Wu Shen, Chung-Ling, 吳沈仲凌
• Other Authors: Liu, Hui-Mei
• Format: Others
• Language: zh-TW
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/72350392605650808968

碩士 === 國立臺北大學 === 統計學系 === 92 === ABSTRACT Application of Extreme Value Theory to Estimate of Value at Risk by Wu Shen, Chung-Ling July 2004 ADVISORS: Dr. Liu, Hui-Mei & Dr. Hong, Ming-Qin DEPARTMENT: GRADUATE SCHOOL OF STATISTICS MAJOR：STATISTICS DEGREE: MASTER There are many differnet definitions in risk, it accompanies when the investor faces the uncertainty of future return on investment. If the investor hopes to obtain higher return, they have to face higher risk. Therefore risk and return are two sides of investment in fact. Tranditionally, the mode of risk management is to distribute risk by asset divers if ication and to avoid risk by derivatives. But when it meets the bigger market fluctuation, the mentioned mode of risk management can''t effect original expectation because of the changes of parameter of statistic distributions. This reason helps forward the Estimate of Value at Risk maily on risk acceptance management become the focus of major discussion recently. Extreme Value Theory principally explores the tails of distribution, instead of the assumption of the whole. Therefore, Extreme Value Theory is available to find out the right model of distribution of tails return rate. Taiwan weighted share index and the exchange rate between NTD and USD are the objects of this study, that evaluates Value at Risk and forecasts the performance estimated by the different models. There are one stage approach VaR estimate model and two stage approach VaR estimate model which considers the time series effect. Concerning the calculation of Value at Risk, Normal, HS and POT methods are used in it. Besides, this study collocates GARCH model and two stage approach VaR estimate model to calculate Value at Risk, to eliminate the appearance of series correlation and volatility clustering. Result of Study is summarised as follows: 1. Two stage approach VaR estimate model eliminates the appearance of series correlation and volatility clustering, the performance of Value at Risk is more accurate than the model that doesn''t consider much time series. 2. There is the apprearance of high sken and fat tail in daily return rates of both Taiwan weighted share index and the exchange rate between NTD and USD. So it is more stable to use POT mehtod than the traditional Normal and HS method. 3.When dealing with great quantity of finance data, it should use two stage approach VaR estimate model to substitute for one stage approach VaR estimate model. Key word: Value at Risk、POT model、GARCH model、two stage approach VaR estimate model、failure rate.