關聯結構分析在外匯投資組合風險值估計上之實證分析

The Empirical Analysis on Exchange Rates Portfolio Value-at-Risk Estimation Incorporating Copula Methods

劉正揚(Zheng-Yang Liu)

指導教授 ： 林志娟

淡江大學/商管學院/統計學系碩士班/碩士(2016年)

https://doi.org/10.6846/TKU.2016.00636

摘要

風險值已成為金融機制中不可或缺的一部份，本研究以常被使用的歷史模擬法、變異數-共變異數法和極值理論估計風險值，其中在變異數-共變異數法中分別以樣本共變異數矩陣、指數加權移動平均和關聯結構模型法三種方式進行估計；極值理論則是對於金融資產厚尾的特性加強討論。在關聯結構模型中採用對稱關聯結構中的常態關聯結構和T關聯結構模型來描述，得到投資組合資產間相關性的結構，據此進一步估計風險值。
本研究模型評估，以巴賽爾協定所制定的回溯測試及 Kupiec(1995)和Christoffersen(1998)提出的方法衡量風險值模型的合適性；另外使用誤差平方根和絕對平均百分誤差比來比較不同風險值模型下的資金運用效率性。
在實證分析中，選取人民幣、歐元、日幣、南非幣、台幣兌換美元五種匯率作為投資組合，在給予固定目標期間和信賴水準下計算各模型風險值，最終以資金運用效率性而言，指數加權移動平均為最適合的風險值模型。

關鍵字

指數加權移動平均 ； 關聯結構模型 ； 極值理論 ； 回溯測試

並列摘要

Value-at-Risk(VaR) has become a vital issue of financial regulations. While a large numbers of VaR methods are proposed, we use historically simulation, variance-covariance method, and extreme value theorem in this study. Three different estimation methods are adopted in the variance-covariance method. They are sample covariance matrix, exponentially weighted moving average and copula method, respectively. Extreme value theorem is used to consider the fat-tailed behaviors in financial data. Copula function is used to describe the correlation structure among assets, and used to estimate the VaR.
Backtesing and Christoffersen(1998) tests are adapted to validate the accuracy of the seven estimation approaches. Besides, there are two criteria used to assess the capital efficiency of seven methods, which are root mean square error and mean absolute percentage error.
In empirical analysis with fixed horizon and confidence level to calculate the VaR, five different exchange rate portfolios are studied. Conclusively, exponentially weighted moving average method outperforms the aforementioned seven approaches in terms of the capital efficiency.

並列關鍵字

Exponentially Weighted Moving Average ； Copula ； Extreme Value Theorem ； Backtesting

參考文獻

林志娟、張慶暉、羅惠瓊、吳旻珊，(2008)，“資產風險值估計方法之探討與比較”，永豐金融季刊，第42期，131-164頁。

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Christoffersen, P. and Diebold, F. (2000), “How Relevant is Volatility Forecasting for Financial Risk Management”, Review of Economics and Statistic, Vol. 28, 12-22.

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