Extreme Quantile Estimation of Losses in KRW/USD Exchange Rate

Title & Authors
Extreme Quantile Estimation of Losses in KRW/USD Exchange Rate
Yun, Seok-Hoon;

Abstract
The application of extreme value theory to financial data is a fairly recent innovation. The classical annual maximum method is to fit the generalized extreme value distribution to the annual maxima of a data series. An alterative modern method, the so-called threshold method, is to fit the generalized Pareto distribution to the excesses over a high threshold from the data series. A more substantial variant is to take the point-process viewpoint of high-level exceedances. That is, the exceedance times and excess values of a high threshold are viewed as a two-dimensional point process whose limiting form is a non-homogeneous Poisson process. In this paper, we apply the two-dimensional non-homogeneous Poisson process model to daily losses, daily negative log-returns, in the data series of KBW/USD exchange rate, collected from January 4th, 1982 until December 31 st, 2008. The main question is how to estimate extreme quantiles of losses such as the 10-year or 50-year return level.
Keywords
Extreme value theory;two-dimensional point process;extreme quantile estimation;exchange rate;
Language
Korean
Cited by
1.
국제현물원유가의 일일 상승 및 하락율의 극단값 분석,윤석훈;

응용통계연구, 2010. vol.23. 5, pp.835-844
2.
코스피 지수 자료의 베이지안 극단값 분석,윤석훈;

응용통계연구, 2011. vol.24. 5, pp.833-845
1.
A Bayesian Extreme Value Analysis of KOSPI Data, Korean Journal of Applied Statistics, 2011, 24, 5, 833
References
1.
Fisher, R. A. and Tippett, L. H. C. (1928). Limiting forms of the frequency distribution of the largest or smallest member of a sample, Proceedings of the Cambridge Philosophical Society, 24, 180-190

2.
Gnedenko, B. V. (1943). Sur la distribution limite du terme maximum d’une serie aleatoire, Annals of Mathematics, 44, 423-453

3.
Leadbetter, M. R., Lindgren, G. and Rootrzen, H. (1983). Extremes and Related Properties of Random Sequences and Processes, Springer, New York

4.
Pickands, J. (1975). Statistical inference using extreme order statistics, Annals of Statistics, 3, 119-131

5.
Resnick, S. (1987). Extreme Values, Point Processes, and Regular Variation, Springer, New York

6.
Smith, R. L. (1989). Extreme value analysis of environmental time series: an application to trend detection in ground-level ozone (with discussion), Statistical Science, 4, 367-393