Modeling the Extreme Risk of Financial Consecutive Losses in Generalized Pareto Distributions

以一般柏拉圖分配函數建立財務連續損失之極端風險模型

10.29705/EAR.201109.0007

陳尚武(Winfred Sun-Wu Chen)

DaR ； 極端值理論 ； 一般化柏拉圖分配 ； Drawdown ； Drawdown-at-risk ； Extreme value theory ； Generalized Pareto Distribution

東亞論壇

473期（2011 / 09 / 01）

73 - 80

英文

本研究探討如何有效建構極端風險值之數學模式。相較於傳統風險值分析（VaR），本研究導入極端值理論，運用一般化柏拉圖分配函數（GPT），推導出DaR是－可行的極端值實證及新的研究方向。

This study intends to explore the modeling of drawdowns variables. Although there are no previous evidences that financial drawdowns are normal, thin-tailed, or thick-tailed distributions, the extreme value theory (EVT) provides flexibilities to model the drawdowns. Throughout our study, we apply limit laws for maxima and uniformity of the convergence to present a comprehensive justification of generalized Pareto distribution (GPD) modeling on drawdowns variables, based on the peak over threshold (POT) framework of EVT. Our justifications provide a theoretical foundation for future studies on the estimation of various promising empirical Drawdown-at-risk (DaR) values.

1. Artzner, P., F. Delbaen, J.-M. Eber, D. Heath, and H. Ku. (2003), “Coherent Multi-period Risk Adjusted Values and Bellman's Principle”, Working Paper, ETH Zurich, Switzerland.
2. Riedel, F. (2003), “Dynamic Coherent Risk Measures”, Working Paper, Department of Economics, Stanford University Stanford University.
3. (1999).Internal Modeling and CADII.Risk Books.
4. Fisher, R. A. and L. H. C. Tippett (1928), “Limiting Forms of the Frequency Distribution of the Largest or Smallest Member of a Sample”, Proc. Cambridge Philos. Soc., 24, 180-190.
5. Adler, R.(ed.),Feldman, R.(ed.),Taqqu, M. S.(ed.)(1998).A Practical Guide to Heavy Tails: Statistical Techniques and Applications.Boston:Birkhauser.
6. Bali, T. G.(2003).An Extreme Value Approach to Estimating Volatility and Value at Risk.Journal of Business,76(1),83-108.
7. Clark, P. K.(1973).A Subordinate Stochastic Process Model with Finite Variance for Speculative Prices.Econometrica,41,135-155.
8. Embrechts, P.,Klüppelberg, C.,Mikosch, T.(1997).Modeling Extremal Events For Insurance And Finance.Berlin:Springer-Verlag.
9. Embrechts, P.,Resnick, S.,Samorodnitsky, G.(1998).Living on the Edge.Risk Magazine,11(1),96-100.
10. Haan, L. de(1984).Slow Variation and the Characterization of Domain of Attraction.Statistical Extremes and Applications
11. Jansen, D. W.,de Vries, C. G.(1991).On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspectives.Review of Economics and Statistics,73,18-24.
12. Johansen, A.,Sornette, D.(2001).Large Sock Market Price Drawdowns Are Outliers.Journal of Risk,4(2),69-110.
13. Mandelbrot, B. B.(1972).Possible Refinement of the Log-normal Hypothesis Concerning the Distribution of Energy Dissipation in Intermittent Turbulence.Statistical Models and Turbulence,New York:
14. Pickands, J.(1975).Statistical Inference Using Extreme Order Statistics.Annals of Statistics,3,119-131.
15. Vilasuso, J.,Katz, D.(2000).Estimation of the Likelihood of Extreme Returns in International Stock Markets.Journal of Applied Statistics,27,119-130.