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극단값 변동성 추정치의 장기기억과 구조변화 -미국의 주요 주가지수의 경우-
권용재 ( Yong Jae Kwon ) 보험연구원 2010 보험금융연구 Vol.21 No.1
본 연구는 극단값 변동성 측정치(extreme value estimators)의 장기기억과 구조변화를 측정하였다. 장기기억은 변동성 측정치의 정형화된 사실 중 하나로서 다수의 연구들이 변동성 시계열이 장기기억의 특성을 가지고 있음을 보고한 바 있다. 그러나 Granger and Hyung (2004)과 Choi et al. (2006)의 연구는 기존의 연구들에서 측정된 변동성 시계열의 장기기억이 실은 구조변화에 의해 그 크기가 부풀려져 있을 수 있다고 주장한 바 있다. 본 연구는 이들의 연구를 극단값 변동성 측정치의 장기기억 연구에 적용하여 극단값 변동성 측정치의 장기기억의 수준이 부풀려져 있는지를 분석해 보았다. 분석해 본 결과 극단값 변동성 측정치의 비정기적인 구조변화가 장기기억의 정도를 증폭시키고 있음을 발견하였으나 이 효과를 감안하더라도 일정한 수준의 장기기억이 여전히 존재하고 있음을 또한 발견하였다. With numerous studies reporting long memory in financial volatilities, long memory became one of the stylized facts of volatility time series. Several researchers, however, including Granger and Hyung (2004) and Choi and Zivot (2007), argue that the long memory property of financial volatilities may be amplified by occasional structural breaks. This paper investigates the validity of the previous studies - whether long memory in extreme value estimators is overstated by structural breaks. I find an evidence that the degree of long memory in the extreme value estimators is inflated by structural breaks. I also find, however, that significant long memory is still discovered in the extreme value estimators even after the multiple breaks are controlled in the estimation.
An alternative method for estimation of annual extreme wind speeds
Yi Hui,Qingshan Yang,Zhengnong Li 한국풍공학회 2014 Wind and Structures, An International Journal (WAS Vol.19 No.2
This paper presents a method of estimation of extreme wind. Assuming the extreme wind follows the Gumbel distribution, it is modeled through fitting an exponential function to the numbers of storms over different thresholds. The comparison between the estimated results with the Improved Method of Independent Storms (IMIS) shows that the proposed method gives reliable estimation of extreme wind. The proposed method also shows its advantage on the insensitiveness of estimated results to the precision of the data. The volume of extreme storms used in the estimation leads to more than 5% differences in the estimated wind speed with 50-year return period. The annual rate of independent storms is not a significant factor to the estimation.
An alternative method for estimation of annual extreme wind speeds
Hui, Yi,Yang, Qingshan,Li, Zhengnong Techno-Press 2014 Wind and Structures, An International Journal (WAS Vol.19 No.2
This paper presents a method of estimation of extreme wind. Assuming the extreme wind follows the Gumbel distribution, it is modeled through fitting an exponential function to the numbers of storms over different thresholds. The comparison between the estimated results with the Improved Method of Independent Storms (IMIS) shows that the proposed method gives reliable estimation of extreme wind. The proposed method also shows its advantage on the insensitiveness of estimated results to the precision of the data. The volume of extreme storms used in the estimation leads to more than 5% differences in the estimated wind speed with 50-year return period. The annual rate of independent storms is not a significant factor to the estimation.
극한치이론을 이용한 VAR 추정치의 유용성과 한계:우리나라주식시장을중심으로
김규형,이준행 한국재무관리학회 2005 財務管理硏究 Vol.22 No.1
This study applies extreme value theory to get extreme value-VAR for Korean Stock market and showed the usefulness of the approach. Block maxima model and POT model were used as extreme value models and tested which model was more appropriate through back testing. It was shown that the block maxima model was unstable as the variation of the estimate was very large depending on the confidence level and the magnitude of the estimates depended largely on the block size. This shows that block maxima model was not appropriate for Korean Stock market. On the other hand POT model was relatively stable even though extreme value VAR depended on the selection of the critical value. Back test also showed VAR showed a better result than delta VAR above 97.5% confidence level. POT model performs better the higher the confidence level, which suggests that POT model is useful as a risk management tool especially for VAR estimates with a confidence level higher than 99%. This study picks up the right tail and left tail of the return distribution and estimates the EVT-VAR for each, which reflects the asymmetry of the return distribution of the Korean Stock market. 본 연구는 극한치 이론을 적용하여 국내 주식시장에 대한 VAR값을 구하고 이의 유용성을 살펴보았다. 극한치모형으로는 블록최대값모형과 POT 모형을 이용하였고 백테스트를 통하여 이들 모형의 적정성을 알아보았다. 극한치모형 중 블록최대값 모형은 신뢰수준의 변화에 따라 VAR 추정치의 변동이 매우 큰 것으로 나타났으며, 블록의 크기를 어떻게 선택하는가에 따라 모수의 추정치가 크게 달라져 VAR값의 안정성이 떨어지는 것으로 나타났다. 이는 국내 주식시장에 대해 VAR 측정시 블록최대값 모형을 사용하는 것은 적절치 않음을 시사하는 것이다. 반면 POT모형은 임계치의 선택에 따라서 VAR 값이 달라지기는 하나 상대적으로 안정적인 모습을 보이며, 또한 백테스트 결과 97.5% 이상의 신뢰수준에서 VAR값이 델타 VAR에 비하여 우수한 성과를 보이는 것으로 나타났다. 특히 POT모형은 신뢰수준이 높아질수록 그 우월성이 높은 것으로 나타나, 주로 99% 이상의 높은 신뢰수준의 VAR값을 이용하는 경우에 위험의 관리수단으로 유용한 모형임을 시사하고 있다. 또한 극한치모형은 수익률의 왼쪽 꼬리와 오른쪽 꼬리를 분리하여 추정하고 이를 VAR의 계산에 이용하기 때문에, 수익률분포가 비대칭적 특징을 보이는 우리나라 주식시장의 VAR 측정시 적절한 방법임을 확인할 수 있었다..
Improving Efficiency of the Moment Estimator of the Extreme Value Index
Yun, Seokhoon The Korean Statistical Society 2001 Journal of the Korean Statistical Society Vol.30 No.3
In this paper we introduce a method of improving efficiency of the moment estimator of Dekkers, Einmahl and de Haan(1989) for the extreme value index $\beta$. a new estimator of $\beta$ is proposed by adding the third moment ot the original moment estimator which is composed of the first two moments of the log-transformed sample data. We establish asymptotic normality of the new estimator and examine and adaptive procedure for the new estimator. The resulting adaptive estimator proves to be asymptotically better than the moment estimator particularly for $\beta$<0.
On Efficient Estimation of the Extreme Value Index with Good Finite-Sample Performance
Yun, Seokhoon The Korean Statistical Society 1999 Journal of the Korean Statistical Society Vol.28 No.1
Falk(1994) showed that the asymptotic efficiency of the Pickands estimator of the extreme value index $\beta$ can considerably be improved by a simple convex combination. In this paper we propose an alternative estimator of $\beta$ which is as asymptotically efficient as the optimal convex combination of the Pickands estimators but has a better finite-sample performance. We prove consistency and asymptotic normality of the proposed estimator. Monte Carlo simulations are conducted to compare the finite-sample performances of the proposed estimator and the optimal convex combination estimator.
GENERALIZING THE REFINED PICKANDS ESTIMATOR OF THE EXTREME VALUE INDEX
Yun, Seok-Hoon The Korean Statistical Society 2004 Journal of the Korean Statistical Society Vol.33 No.3
In this paper we generalize and improve the refined Pickands estimator of Drees (1995) for the extreme value index. The finite-sample performance of the refined Pickands estimator is not good particularly when the sample size n is small. For each fixed k = 1,2,..., a new estimator is defined by a convex combination of k different generalized Pickands estimators and its asymptotic normality is established. Optimal weights defining the estimator are also determined to minimize the asymptotic variance of the estimator. Finally, letting k depend upon n, we see that the resulting estimator has a better finite-sample behavior as well as a better asymptotic efficiency than the refined Pickands estimator.
Generalizing the Refined Pickands Estimator of the Extreme Value Index
Seokhoon Yun 한국통계학회 2004 Journal of the Korean Statistical Society Vol.33 No.3
In this paper we generalize and improve the rened Pickands estimator of Drees (1995) for the extreme value index. The nite-sample performance of the rened Pickands estimator is not good particularly when the sample size n is small. For each xed k = 1; 2; : : : ; a new estimator is dened by a convex combination of k dierent generalized Pickands estimators and its asymptotic normality is established. Optimal weights dening the estimator are also determined to minimize the asymptotic variance of the estimator. Finally, letting k depend upon n, we see that the resulting estimator has a better nite-sample behavior as well as a better asymptotic eciency than the rened Pickands estimator.
Minimax Choice and Convex Combinations of Generalized Pickands Estimator of the Extreme Value Index
Yun, Seokhoon The Korean Statistical Society 2002 Journal of the Korean Statistical Society Vol.31 No.3
As an extension of the well-known Pickands (1975) estimate. for the extreme value index, Yun (2002) introduced a generalized Pickands estimator. This paper searches for a minimax estimator in the sense of minimizing the maximum asymptotic relative efficiency of the Pickands estimator with respect to the generalized one. To reduce the asymptotic variance of the resulting estimator, convex combinations of the minimax estimator are also considered and their asymptotic normality is established. Finally, the optimal combination is determined and proves to be superior to the generalized Pickands estimator.
VaR(Value-at-Risk) 모형을 이용한 화재보험 손해 위험도 측정
권순일,김무환 한국리스크관리학회 2019 리스크 管理硏究 Vol.30 No.1
This study applies VaR, which is a representative risk measurement indicator, to the given data and verifies which model is most suitable with insurance damage amount. We derive VaR for each of the models employed, perform backtesting, and compare the results. To do this, we sum up the given data on the daily basis and then analyze it and at the same time try to analyze it by the raw data. According to the results of the analysis, we did not find the clustering of volatility in aggregated daily data and it was proved that VaR estimates by extreme value theory (EVT) and historical simulation (HS) models are relatively preferred to the other models. On the other hand, in the case of the original data, the clustering of the volatility is found and the VaR is estimated after filtering by the GARCH model. As a result of the backtesting, the VaR estimate by the GARCH-EVT model proved to be the best model.