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    Title: 極端值方法在風險值估計的績效評估
    Other Titles: Performance Evaluation of Estimated Value-at-Risk under Extreme Value Theory
    Authors: 劉惠美;黃向義
    Liu, Hui-Mei;Huang, Hsiang-Yi
    Contributors: 政大統計系
    Keywords: 最大區塊法模型風險值;極端值理論;穿越門檻值模型;風險值
    Block maximum model;Extreme value theorem;Peak-over-threshold model;Value-at-Risk
    Date: 2009-12
    Issue Date: 2013-12-12 18:09:02 (UTC+8)
    Abstract: 大部分的財務報酬率資料均為厚尾的分配，但一般傳統風險值的計算模型皆假設其為常態分配，以至於無法精確詳盡的描繪出資料尾端的分配，造成低估風險值的現象。極值理論(Extreme Value Theory)主要是探討分配的尾端特性，或可計算出較精確的風險值。本文以極值理論之全參數法、半參數法及最大區塊法評估極端值理論在風險值估計的效果。本文共模擬四種分配的資料，分別為具有厚尾現象的標準化後的t分配其自由度分別為3、5、15，以及標準常態分配。由於主是要探討極端事件的問題，所以考慮採用1-α之值接近於1（如：0.9、0.95、0.99…），再使用不同的極值理論方法來估計風險值。模擬結果顯示用全參數法效果最好，而最大區塊法會有明顯低估的現象，半參數法則表現普通。本文亦已台幣對美元匯率的報酬率與台灣加權股價指數做實證研究，結果顯示：台幣對美元匯率的報酬率資料符合理論中的高峰厚尾分配，極適合用極端值模型來估計風險值。在台灣加權股價指數的實證部分，當信賴係數為0.9999時，極值理論模型所估得的風險值多數會超過0.07。但由於台股加權指數有7%漲跌幅的限制，這部分的問題仍有待進一步的探討。
    Due to the simplicity and easy-to-use, it is often assumed that financial data return is normally or log-normally distributed in which the tail probability is exponential decay. However, risk managers are primarily concern the risk of extreme rare events which could lead to catastrophic losses. Due to the ability of catching the extreme tail behavior of a distribution, the extreme value theory (EVT) has been extensively discussed in the field of risk management. The full parametric peak-over threshold (POT), semi-POT and block maximum models are the main methods used in EVT. To evaluate the effect of EVT methods, through simulation, we study the Value-at-Risk (or extreme quantile) estimation results for four different distributions. Our Monte Carlo simulation results show that the full-POT method performs best. Finally, an empirical study is done for the New Taiwan Dollar exchange data through backtesting.
    Relation: 智慧科技與應用統計學報, 7(2), 1-23
    Data Type: article
    Appears in Collections:[Department of Statistics] Periodical Articles

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