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

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.

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.

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.

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.

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.

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.

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.

The Gringorten estimator revisited

Cook, Nicholas John,Harris, Raymond Ian Techno-Press 2013 Wind and Structures, An International Journal (WAS Vol.16 No.4

The Gringorten estimator has been extensively used in extreme value analysis of wind speed records to obtain unbiased estimates of design wind speeds. This paper reviews the derivation of the Gringorten estimator for the mean plotting position of extremes drawn from parents of the exponential type and demonstrates how it eliminates most of the bias caused by the classical Weibull estimator. It is shown that the coefficients in the Gringorten estimator are the asymptotic values for infinite sample sizes, whereas the estimator is most often used for small sample sizes. The principles used by Gringorten are used to derive a new Consistent Linear Unbiased Estimator (CLUE) for the mean plotting positions for the Fisher Tippett Type 1, Exponential and Weibull distributions and for the associated standard deviations. Analytical and Bootstrap methods are used to calibrate the bias error in each of the estimators and to show that the CLUE are accurate to better than 1%.