• The Korean Journal of Applied Statistics
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• v.19 no.3
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• pp.481-504
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• 2006

VaR, a tail-related risk measure is now widely used as a tool for a measurement and a management of financial risks. For more accurate measurement of VaR, recently we are particularly concerned about the approach based on extreme value theory rather than the traditional method based on the assumption of normal distribution. However, many studies about the approaches using extreme value theory was done only for the univariate case. In this paper, we discuss portfolio risk measurements with modelling multivariate extreme value distributions by combining copulas and extreme value theory. We also discuss the estimation of ES together with VaR as portfolio risk measures. Finally, we investigate the relative superiority of EVT-copula approach than variance-covariance method through the back-testing of an empirical data.

• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.291-311
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• 2007

With a series of unexpected huge losses in the financial markets around the world recently, especially in the insurance market with extreme loss cases such as catastrophes, there is an increasing demand for risk management for extreme loss exposures due to high unpredictability of those risks. For extreme risk management, to make a maximum use of the information concerning the tail part of a loss distribution, EVT(Extreme Value Theory) modelling nay be the best to analyze extreme values. The Extreme Value Theory is widely used in practice and, especially in financal markets, EVT modelling is getting popular to analyBe the effects of extreme risks. This study is to review the significance of the Extreme Value Theory in risk management and, focusing on analyzing insurer's risk capital, extreme risk is measured using the real fire loss data and insurer's specific amount of risk capital is figured out to buffer the extreme risk.

• The Korean Journal of Applied Statistics
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• v.23 no.3
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• pp.471-485
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• 2010

VaR is used extensively as a tool for risk management by financial institutions. For convenience, the normal distribution is usually assumed for the measurement of VaR, but recently the method using extreme value theory is attracted for more accurate VaR estimation. So far, GEV and GPD models are used for probability models of EVT for the VaR estimation. In this paper, the PP model is suggested for improved VaR estimation as compared to the traditonal EV models such as GEV and GPD models. In view of the stochastic process, the PP model is regarded as a generalized model which include GEV and GPD models. In the empirical analysis, the PP model is shown to be superior to GEV and GPD models for the performance of VaR estimation.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.753-771
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• 2016

Value at Risk (VaR) is widely used as an important tool for risk management of financial institutions. In this paper we discuss estimation and back testing for VaR of the portfolio composed of KOSPI, Dow Jones, Shanghai, Nikkei indexes. The copula functions are adopted to construct the multivariate distributions of portfolio components from marginal distributions that combine extreme value theory and GARCH models. Volatility models with t distribution of the error terms using Gaussian, t, Clayton and Frank copula functions are shown to be more appropriate than the other models, in particular the model using the Frank copula is shown to be the best.

• Knowledge Management Research
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• v.22 no.2
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• pp.247-268
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• 2021

Investors mainly use PER and PBR among financial ratios for valuation and investment decision-making. I conduct an analysis of two basic financial ratios from a statistical perspective. Financial ratios contain key accounting numbers which reflect firm fundamentals and are useful for valuation or risk analysis such as enterprise credit evaluation and default prediction. The distribution of financial data tends to be extremely heavy-tailed, and PER and PBR show exceedingly high level of kurtosis and their extreme cases often contain significant information on financial risk. In this respect, Extreme Value Theory is required to fit its right tail more precisely. I introduce not only GPD but exGPD. GPD is conventionally preferred model in Extreme Value Theory and exGPD is log-transformed distribution of GPD. exGPD has recently proposed as an alternative of GPD(Lee and Kim, 2019). First, I conduct a simulation for comparing performances of the two distributions using the goodness of fit measures and the estimation of 90-99% percentiles. I also conduct an empirical analysis of Information Technology firms in Korea. Finally, exGPD shows better performance especially for PBR, suggesting that exGPD could be an alternative for GPD for the analysis of financial ratios.

• The Korean Journal of Financial Studies
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• v.10 no.1
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• pp.191-214
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• 2004

VaR에 의한 금융위험의 측정은 국제결제은행 바젤위원회의 내부모델 허용에 힘입어 금융산업에서 표준방식으로 확고한 입지를 차지하고 있다. 본 연구에서는 한국주식시장포트폴리오를 거래투자자산으로 보유한 경우의 VaR를 극단치이론에 입각하여 측정하고 이의 성과를 RiskMetrics의 성과와 비교하여 검토하였다. GPD의 모수적 추정에 의한 VaR의 사후검정결과는 표본내 사후검정이나 표본외 사후검정에서 어떤 신뢰수준에서도 기대되는 범위와 크게 벗어나지 않은 안정된 결과를 보였다. RiskMetrics의 EWMA방식도 역시 표본내와 표본외 사후검정 어느 경우에나 기대되는 범위에서 크게 벗어나지 않았지만 높은 신뢰수준에서는 그 성과가 GPD VaR에 비하여 상대적으로 불안정하였으며 위험의 과소평가 성향을 확인할 수 있었다. 비모수적 GEV추정에 입각한 VaR의 경우에는 위험을 과대평가하고 지나치게 보수적인 성향을 나타내었다. GPD의 모수적 접근에 의한 VaR 측정은 다양한 신뢰수준에서 정확한 검정결과를 보여주고 있으며, 시간적 흐름에 따르는 VaR의 행태도 지나친 변동성을 보이지 않아 외부규제 및 내부통제를 위한 금융위험의 측정지표로서 실용적인 가치가 있음을 확인할 수 있다.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1479-1494
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• 2015

Since the Markowitz's mean-variance framework for portfolio analysis, the topic of portfolio optimization has been an important topic in finance. Traditional approaches focus on maximizing the expected return of the portfolio while minimizing its variance, assuming that risky asset returns are normally distributed. The normality assumption however has widely been criticized as actual stock price distributions exhibit much heavier tails as well as asymmetry. To this extent, in this paper we employ the genetic algorithm to find the optimal portfolio under the Value-at-Risk (VaR) constraint, where the tail of risky assets are modeled with the generalized Pareto distribution (GPD), the standard distribution for exceedances in extreme value theory. An empirical study using Korean stock prices shows that the performance of the proposed method is efficient and better than alternative methods.

• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.833-845
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• 2011

This paper conducts a statistical analysis of extreme values for both daily log-returns and daily negative log-returns, which are computed using a collection of KOSPI data from January 3, 1998 to August 31, 2011. The Poisson-GPD model is used as a statistical analysis model for extreme values and the maximum likelihood method is applied for the estimation of parameters and extreme quantiles. To the Poisson-GPD model is also added the Bayesian method that assumes the usual noninformative prior distribution for the parameters, where the Markov chain Monte Carlo method is applied for the estimation of parameters and extreme quantiles. According to this analysis, both the maximum likelihood method and the Bayesian method form the same conclusion that the distribution of the log-returns has a shorter right tail than the normal distribution, but that the distribution of the negative log-returns has a heavier right tail than the normal distribution. An advantage of using the Bayesian method in extreme value analysis is that there is nothing to worry about the classical asymptotic properties of the maximum likelihood estimators even when the regularity conditions are not satisfied, and that in prediction it is effective to reflect the uncertainties from both the parameters and a future observation.

• The Korean Journal of Applied Statistics
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• v.26 no.3
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• pp.483-494
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• 2013

The importance of financial risk management has been highlighted after several recent incidences of global financial crisis. One of the issues in financial risk management is how to measure the risk; currently, the most widely used risk measure is the Value at Risk(VaR). We can consider to estimate VaR using extreme value theory if the financial data have heavy tails as the recent market trend. In this paper, we study estimations of VaR using Peaks over Threshold(POT), which is a common method of modeling fat-tailed data using extreme value theory. To use POT, we first estimate parameters of the Generalized Pareto Distribution(GPD). Here, we compare three different methods of estimating parameters of GPD by comparing the performance of the estimated VaR based on KOSPI 5 minute-data. In addition, we simulate data from normal inverse Gaussian distributions and examine two parameter estimation methods of GPD. We find that the recent methods of parameter estimation of GPD work better than the maximum likelihood estimation when the kurtosis of the return distribution of KOSPI is very high and the simulation experiment shows similar results.

• Journal of Korean Philosophical Society
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• v.116
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• pp.389-410
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• 2010

Augustin wurde sozusagen von der Rhetorik zum Christentum bekehrt. Der einstmalige Rhetorikprofessor (bis 386) distanziert sich von seiner $fr{\ddot{u}}heren$ Kunst. Aber er $kn{\ddot{u}}pft$ als Bischof im vierten Buch seiner weniger bekannten Schrift "De doctrina Christiana" (DDC; abgef. 427) wieder an die antike Rhetorik, speziell an Cicero, an. So wird die augustinische $Sp{\ddot{a}}tschrift$ $f{\ddot{u}}r$ eine antike Rhetorik in christlicher Verwendung gehalten. Es stellt nun die Frage, was Augustin zur $R{\ddot{u}}ckkehr$ zu seiner $fr{\ddot{u}}heren$ Kunst bewegte. Neuere Forschungen sehen in Augustins Werk eine Grundlage der mittelalterlichen Predigttheorie oder einen $blo{\ss}en$ Versuch, die Rhetorik vom Makel des Sophistischen zu befreien. Gewiss ist seine Einstellung zur "leeren Beredsamkeit" der Sophistik eindeutig, aber dies war eine Haltung, die letztlich von allen seinen christlichen Zeitgenossen geteilt wurde und folglich eines geringen Beweises bedurfte. Die Aufmerksamkeit, die Augustins $sp{\ddot{a}}terem$ Einfluss und seiner Ablehnung der Zweiten Sophistik geschenkt wird, kann den Blick $tr{\ddot{u}}ben$ $f{\ddot{u}}r$ seine Rolle bei der $L{\ddot{o}}sung$ eines christlichen Dilemmas aus dem vierten Jahrhundert. Augustin sah die Gefahren einer entgegengesetzten rhetorischen $H{\ddot{a}}resie$. Die $S{\ddot{u}}nde$ des Sophisten besteht darin, dass er die Notwendigkeit des Inhalts verneint und glaubt, nur die forma alleine sei $w{\ddot{u}}nschenswert$. Der gegenteilige Fehler, dem Geschichtsschreiber der Rhetorik niemals einen Namen gegeben haben, beruht auf dem Glauben, dass derjenige, der im Besitz der Wahrheit ist, auch ipso facto in der Lage ist, die Wahrheit anderen zu ${\ddot{u}}bermitteln$. Es handelt sich um eine $ausschlie{\ss}liche$ $Abh{\ddot{a}}ngigkeit$ von der materia. Augustin erkannte eine Gefahr und benutzte DDC dazu, eine Verbindung von Inhalt und Form in der christlichen Predigt voranzutreiben. Nur wenn man daher das Buch als einen Teil der $gro{\ss}en$ Debatte des vierten Jahrhunderts ansieht, tritt seine historische Bedeutung klar hervor. Der Leser ist beeindruckt davon, dass der Autor darauf insistiert, es sei eine Torheit, dem Feind ein $n{\ddot{u}}tzliches$ Instrument zu ${\ddot{u}}berlassen$. Augustin $erkl{\ddot{a}}rt$, dass die Kunst der Beredsamkeit rege in Gebrauch genommen und nicht kurzerhand abgelehnt werden solle, weil sie mit dem Makel des Heidentums behaftet sei. Kurz gesagt, geplant ist das vierte Buch von DDC als eine ratio eloquentiae Christianae.