本文應用極值理論實的參數與非參數模型實證分析台灣短期利率的極端行為，探討貨幣市場開放政策與金融風暴等不利事件對利率極端行為的影響。對於這些短期利率行為如:厚尾、不對稱、左、右尾厚尾程度不一…等特性的了解，有助於掌握短期利率的極端行為，俾於正確估計利率風險。另外，本文也探討過濾(filtered)及未過濾(unfiltered) VaR (Value at risk)模型的預測表現，以建議合適的利率風險估計模型。實證結果顯示，首先，與常態分配相較，短期利率變動分配之尾部更厚，代表常態分配假設的VaR將低估實際風險；第二，短期利率變動的非條件分配屬於厚尾的ARCH 或Student’t分配型式；第三，利率變動分配的右尾比左尾更厚，代表極端利率上漲發生的機率與變動幅度將高於極端利率下跌的機率與幅度；第四，利率變動分配的尾部在1999年以後更為肥厚，造成厚尾程度發生結構改變的主要因素為央行的利率政策，而非貨幣市場開放政策；第五，基於左、右兩尾存在的兩個結構改變點，長時間的利率資料不能視為來自同一分配的樣本資料；第六，應用極值理論於財務資料時，為提高VaR估計結果的正確性，資料間的相依性與異質變異性需加以考慮；最後，2001年以前，極值理論模型能正確的估計短期利率的VaR；2001以後，歷史模擬法及GARCH法則比極值模型有更佳的預測表現；極值模型中以Hill估計式及動差比估計式的風險預測能力較好，其預測結果亦較為穩健。

The current study empirically analyzes the extreme behavior and the impact of deregulation policies as well as financial turmoil on the extreme behavior of changes of Taiwan short term interest rate. A better knowledge of short-term interest rate properties, such as heavy tails, asymmetry, and uneven tail fatness between right and left tails, provide an insight to the extreme behavior of short-term interest rate as well as a more accurate estimation of interest risk. The predicting performances of filtered and unfiltered VaR (Value at risk) models are also examined to suggest the proper models for management of interest rate risk. By applying Extreme Value theory (EVT), tail behavior is analyzed and tested and the VaR based on parametric and non-parametric EVT models are calculated.The empirical findings show that, first, the distribution of change of rate are heavy-tailed indicating that the actual risk would be underestimated based on normality assumption. Second, the unconditional distribution is consistent with the heavier-tailed distributions such as ARCH process or Student’t. Third, the right tail of distribution of change of rate are significantly heavier than the left one pointing out that the probabilities and magnitudes of rise in rate could be higher than those of drop in rate. Fourth, the amount of tail-fatness in tail of distribution of change of rate increase after 1999 and the vital factors to cause structural break in tail index are the interest rate policies taken by central bank of Taiwan instead of the deregulation policies in money market. Fifth, based on the two break points found in tail index of right and left tail, long sample of CP rates should not be treated as samples from a single distribution. Sixth, the dependent and heteroscedastic properties of data series should be considered in applying EVT to improve accuracy of VaR forecasts. Finally, EVT models predict VaR accurately before 2001 and the benchmark model, HS and GARCH, generally are superior to EVT models after 2001. Among EVT models, MRE and CHE are relative consistent and reliable in VaR prediction.

1. Introduction 1
2. Literature review 5
2.1 VaR and fat tail 5
2.2 Extreme value theory 5
2.3 Structural Break of Tail index 10
3. Methodology 13
3.1 VaR models 13
3.2 Extreme value theory 15
3.3 Threshold choice 21
3.4 Tests on tail behavior 22
4. Empirical Results 28
4.1 Preliminary data analysis 28
4.2 Full Sample Estimation 32
4.3 Tests of Structural Break 40
4.4 Backtesting Results of VaR 45
5. Conclusion 55
References 57

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