短期利率條件分配之尾部差異性檢定與風險值

Testing for the Difference in the Tails and VaR of Taiwan's Short-Term Interest Rate

利率風險的管理需充分掌握機率分配的尾部行為。為達到此目的，本文先使用極值模型來描述台灣商業本票利率變動分配的尾部，並探討其厚尾現象；其次，我們正式檢定分配的雙尾特徵是否相同，以了解雙尾極端值的發生是否類似；再次，比較這些模型於計算利率商品風險值之實際表現；最後，考慮短期利率結構性改變的影響，驗證實證結果的穩健性。為解釋利率變動的序列相關與條件異質性，我們先使用ARMA與GARCH模型來過濾資料，再應用極值模型，以符合極值理論的獨立性要求。實證結果顯示，台灣商業本票的利率變動分配與常態分配比較，具有厚尾與不對稱現象，表示根據常態分配假設所得之風險值會有低估之虞；而尾部參數檢定的結果指出，雙尾的特徵差異具有統計的顯著性，且右尾較左尾為厚，並有更強的證據支持利率變動分配的左尾曾發生結構性改變，然而右尾並無充分的結構改變證據；回溯測試的結果指出，結構性改變以前，右尾以極值模型的預測表現最優，左尾則以GARCH模型為最佳。結構改變以後，則以Cond. GEV模型為右尾最佳的預測模型，而極值模型及GARCH在左尾的表現均差，均無法正確估計結構性變動後之VaR。此一結果顯示，結構性改變不僅會影響利率變動分配的行為，亦會影響模型的風險值預測能力，因此為一不可忽略的因素。

To effectively manage interest rate risk, it is crucial to estimate the tail behavior of distribution of interest rate accurately. This article investigates the tail behavior of Taiwan Commercial Paper rates by applying extreme value theory (EVT) to the tail of the distribution of interest rate changes. The formal statistical tests are conducted to test the differences between the characteristic parameters of the left and the right tails in order to have an insight into the occurrence of extremes in the tails. The structural change of interest rate changes are also considered to verify the robustness of empirical results. The interest rate changes are firstly filtered by ARMA and GARCH models to account for the serial correlation and heteroscedasticity. Then EVT are used to model the tails of the residuals and the performances of the models are evaluated accordingly. The empirical results show that distribution of interest rate changes is fat-tailed and asymmetric, indicating the normality assumption will lead to underestimation of VaR. In addition, we find that the right tail is statistically fatter than the left one. According to the results of structural change tests, the evidences of structural change in 1998 in left tails are stronger whereas those of right tails are weaker. The backtesting results show that, before structural change, EVT models are the best VaR model of right tail whereas GARCH outperforms EVT models in left tail. After structural change, Cond. GEV is the superior model for right tail, but for left tail, none is proved to be reliable models as all models overestimate VaRs. The results indicate that structural change, which is the unavoidable factor to be accounted for, will affect not only the tail behavior of distribution of interest rate changes but also VaR forecasting power of models.