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引文資料
題名:
結合GARCH模型與極值理論的風險值模型
書刊名:
管理學報
作者:
林楚雄
/
高子荃
/
邱瓊儀
作者(外文):
Lin, Chu-hsiung
/
Kao, Tzu-chuan
/
Chiou, Chiung-yi
出版日期:
2005
卷期:
22:1
頁次:
頁133-154
主題關鍵詞:
風險值
;
GARCH模型
;
極值理論
;
VaR-x法
;
尾部指數
;
Value at risk
;
GARCH model
;
Extreme value theory
;
VaR-x method
;
Tail index
原始連結:
連回原系統網址
相關次數:
被引用次數:期刊(
3
) 博士論文(0) 專書(0) 專書論文(0)
排除自我引用:
3
共同引用:
6
點閱:72
本文主要延續McNeil與Frey (2000)所提出的結合GARCH模型與極值理論的風險值估計方法,並針對McNeil與Frey (2000)應用極值理論估計標凖化殘差項的極值分配法加以改進,以簡化風險值的估計過程並提升估計的凖確性。本文主要應用Huisman,Koedijk與Pownall (1998)及Huisman, Koedijk, Kool與Plam (2001)的VaR-x法來修正McNeil與Frey (2000)的極值估計方法。本文以六個股價指數作爲實證研究的對象,檢定本文結合GARCH模型與VaR-x估計法的凖確性。經失敗率及Kupiec (1995)之條件與非條件涵蓋比率檢定結果,顯示在高依賴水凖下,結合GARCH模型與極值理論相較於GARCH模型以及指數加權移動平均法的估計更爲凖確。此外,本文建立的模型較McNeil與Frey (2000)的模型、更具有容易以及凖確估計動態風險值的特性。本文的實證結果說明瞭同時掌握條件異質波動數以及厚尾分配的特性,在高依賴水凖下能提升風險值估計的凖確性。
以文找文
The purpose of this study is to construct a Value at Risk (VaR) model describing the tail of the conditional distribution of a heteroscedastic financial return series and simplify the estimation procedure of VaR. McNeil and Frey (2000) propose a method that can simultaneously tackle both extreme event and stochastic volatility for estimating VaR. They combine pseudo-maximum-likelihood fitting of GARCH models to estimate the current volatility and extreme value theory (EVT) for estimating the tail of the innovation distribution of GARCH model and show that their approach gives more accurate 1-day estimates than the others which ignore the heavy tails of the innovations or the stochastic nature of the volatility. However, Huisman, Koedijk, Kool and Palm (2001) indicate that using Hill index estimator (1975) to estimate the tail index of the innovation distribution would suffer from severe small-sample bias. As a result, the empirical applicability of the Hill index estimator is limited to cases in which a large sample is available, either in the form of high frequency data or in the form of a long sampling period, but in many practical cases this condition is not fulfilled. Moreover, even when a long sample is available, it may be interesting to split the sample and then analyze whether the tail structure of the sample has changed over time. In addition, an important part of the bias in the Hill index estimator, which itself does not provide a optimal number of tail observations, stems from the selection of the appropriate number of tail observations to include in the estimation process. In order to overcome above drawbacks, we propose an alternative approach based on the method proposed by Huisman, et al. (2001) to correct for the small-sample bias in Hill tail-index estimates of the innovation distribution. Our method does not condition its tail-index estimate on one specific number of tail observations. Instead, our method exploits information obtained from a set of Hill tail-index estimates each conditioned on a different number of tail observations. The result is a weighted average of a set of conventional Hill estimators, with weights obtained by simple least squares techniques. To improve on accuracy of VaR estimate, we use the Var-x developed by Huisman, Koedijk and Pownall (1998) to revise the conventional Hill estimator used by McNeil and Frey (2000). First, considering the stochastic volatility structure of conditional volatility of returns, we use GARCH-type model to obtain estimates of the conditional mean and volatility, and then statistical tests confirm that the error terms or innovations do form, at least approximately, iid series that exhibit heavy tails. Second, we use the mod/led Hill estimator developed by Huisman et al. (2001) to estimate tail-index of the innovation distribution obtained by GARCH model. Third, linking the features of tail index and the Student-t distribution, the extreme quantile of the innovation distribution will be obtained (i.e. VaR-x). Finally, taking the estimates of the conditional mean and volatility and the extreme quantile of the innovation distribution into a dynamics model of VaR, the estimate of VaR will be obtained. Our approach above has two features: one is to construct a VaR model describing the tail of the conditional distribution of a heteroscedastic financial return series; the other is to simpl5 the estimation procedure of VaR. To evaluate the performance of our method in terms of failure rates and Kupiec test, we apply the method to six historical series of log returns: the FTSE 100 index, the DAX index, the S&P 500 index, the NASDAQ index, the DOW index, and the Taiwan weighted stock index. The sample period is from January 1, 1991 to December 31, 2001. In addition, we also compare the relative performance of different VaR models which include EWMA model (equally weighted moving average approach), GARCH-normal model (assuming conditional normal distribution), GARCH-t model (assuming conditional t distribution), GJR-normal model (assuming conditional normal distribution and the condition volatility is asymmetry), GJR-t model (assuming conditional t distribution and the condition volatility is asymmetry), GARCH-Hill and GJR-Hill (incorporating EVT into GARCH-type model), and the GARCH-VaR-x and GJR-VaR-x proposed by this study. According to the analysis of the failure rates and Kupiec test, our empirical results present that the incorporated VaR-x into GARCH-type model does indeed give more precise estimates of the 99(superscript th) and 99.5(superscript th) percentile than the other models except for GARCH-Hill and GJR-Hill models. This finding indicates that considering the tail of the conditional distribution and heteroscedastic behavior simultaneously in VaR measures will obtain more accurate estimates at higher quantiles. However, our approach, employing the VaR-x to resolve the problems of selection of the appropriate number of the tail observations and small-sample bias of the Hill estimator simplifies the estimation procedure of VaR and achieve the same accuracy as GARCH-Hill and GJR-Hill models do. Thus our approach seems to be in favor of the measure of dynamic risk management.
以文找文
期刊論文
1.
Kearns, Phillip、Pagan, Adrian(1997)。Estimating the Density Tail Index for Financial Time Series。The Review of Economics and Statistics,79(2),171-175。
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De Haan, L.、Resnick, S. I.(1980)。A Simple Asymptotic Estimate for the Index of a Stable Distribution。Journal of the Royal Statistical Society,42,83-87。
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Dumouchel, W. H.(1983)。Estimating the Stable Index Alpha in Order to Measure Tail Thickness: A Critique。Annals of Statistics,11(4),1019-1031。
4.
Hall, P.(1990)。Using the Bootstrap to Estimate Mean Square Error and Select Smoothing Parameter in Nonparametric Problems。Journal of Multivariate Analysis,32,177-203。
5.
Koedijk, Kees G.、Kool, Clemens J. M.(1994)。Tail Estimates and the EMS Target Zone。Review of International Economics,2(2),153-165。
6.
Huisman, R.、Koedijk, K. G.、Pownall, R. A. J.(1998)。VaR-x: Fat Tails in Financial Risk Management。Journal of Risk,1(1),47-61。
7.
Longin, F. M.(1999)。Optimal Margin Level in Futures Markets: Extreme Price Movements。The Journal of Futures Market,19(2),127-152。
8.
Huisman, R.、Koedijk, K. G.、Kool, C. J. M.、Palm, F.(2001)。Tail-Index Estimates in Small Samples。Journal of Business & Economic Statistics,19(1),208-216。
9.
Jansen, D. W.、De Vries, C. G.(1991)。On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspectives。The Review of Economics and Statistics,73,18-24。
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Quintos, C.、Fan, Z.、Phillips, Peter C. B.(2001)。Structural Change Tests in Tail Behavior and the Asian Crisis。Review of Economic Studies,68(3),633-663。
11.
Jorion, P.(1998)。On Jump Processes in the Foreign Exchange and Stock Markets。The Review of Financial Studies,1(4),427-445。
12.
Billio, M.、Pelizzon, L.(2000)。Value-at-Risk: A Multivariate Switching Regime Approach。Journal of Empirical Finance,7(5),531-554。
13.
Hull, John C.、White, Alan D.(1998)。Value at risk when daily changes in market variables are not normally distributed。Journal of Derivatives,5(3),9-19。
14.
Hill, B. M.(1975)。A Simple General Approach to Inference about the Tail of a Distribution。The Annals of Statistics,3(5),1163-1174。
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Duffie, D.、Pan, J.(1997)。An Overview of Value at Risk。The Journal of Derivatives,4(3),7-49。
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Longin, Francois M.(2000)。From Value at Risk to Stress Testing: The Extreme Value Approach。Journal of Banking & Finance,24(7),1097-1130。
17.
Pickands, J. III(1975)。Statistical Inference Using Extreme Order Statistics。Annals of Statistics,3(1),119-131。
18.
Glosten, L. R.、Jagannathan, R.、Runkle, D. E.(19931200)。Relationship between the Expected Value and the Volatility of the Nominal Excess Return on Stocks。Journal of Finance,48(5),1779-1801。
19.
Alexander, C. O.、Leigh, C. T.(1997)。On the Covariance Matrices Used in Value at Risk Models。Journal of Derivatives,4(3),50-62。
20.
林楚雄、陳宜玫(20020800)。臺灣股票市場風險值估測模型之實證研究。管理學報,19(4),737-758。
延伸查詢
21.
Bollerslev, Tim(1986)。Generalized Autoregressive Conditional Heteroskedasticity。Journal of Econometrics,31(3),307-327。
22.
Bollerslev, Tim(1987)。A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return。The Review of Economics and Statistics,69(3),542-547。
23.
Kupiec, Paul H.(1995)。Techniques for Verifying the Accuracy of Risk Measurement Models。Journal of Derivatives,3(2),73-84。
24.
McNeil, A. J.、Frey, R.(2000)。Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach。Journal of Empirical Finance,7(3/4)=56,271-300。
25.
Mittnik, S.、Paolella, M. S.(2000)。Conditional Density and Value-at-Risk Prediction of Asian Currency Exchange Rates。Journal of Forecasting,19(4),313-333。
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Booth, G.、Akgiray, V.(1986)。Stock Price Processes with Discontinuous Time Paths: An Empirical Examination。Financial Review,21,163-184。
27.
Barone-Adesi, G.、Giannopoulos, K.、Bourgoin, F.(1998)。Don't Look Back。Risk,11(8),100-103。
28.
黎明淵、林修葳、饒秀華(1999)。藉由馬可夫轉換模型解決風險值計測過程高峰、厚尾與偏態問題-國內主要股市指數實證結果。中國財務學刊,7(3),61-94。
延伸查詢
29.
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30.
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研究報告
1.
Pictet, O.、Dacorogna, M.、Müller, U.(1996)。Hill, Bootstrap and Jackknife Estimators for Heavy Tails。Olsen & Associates。
2.
Danielsson, J.、De Vries, C. G.(1997)。Value-at-Risk and Extreme Returns。沒有紀錄。
3.
Dacorogna, M.、Müller, U.、Pictet, O.、De Vries, C.(1995)。The Distribution of Extremal Foregin Exchange Rate Returns in Extremely Larage Data Sets。0。
4.
Cherief, Guermat、Harris, Richard D. F.(2000)。Robust Variance Estimation and Value-at-risk?。0。
圖書
1.
Gouriêroux, C.(1997)。ARCH Models and Financial Applications。New York, NY:Springer Verlag。
2.
Jorion, P.(2000)。Value at Risk。McGraw-Hill。
3.
Reiss, R. D.、Thomas, M.(1997)。Statistical Analysis of Extreme Value。Statistical Analysis of Extreme Value。Basel, Switzerland。
其他
1.
Embrechts, P.(1999)。Extreme Value Theory: Potential and Limitations as an Integrated Risk Management Tool,沒有紀錄。
2.
Danielsson, J.,De Vries, C. G.(1997)。Beyond the Sample: Extreme Quantile and Probability Estimation,Rotterdam, Netherlands。
圖書論文
1.
Danielsson, J.、De Vries, C. G.(2000)。Value-at-Risk and Extreme Returns。Extremes and Integrated Risk Management。Risk Book。
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