風險值衡量：變幅DCC模型的應用

Abstract

本研究針對不同財務資料特性所提出之風險值模型進行評比，包括考慮厚尾性質的極值理論（extreme value theory；簡稱EVT）風險值模型，以及利用「時變」波動模型捕捉報酬具有條件異質變異特性的動態風險值模型。此外，將變幅（range）概念引入風險值估計中，利用Chou (2005)提出之CARR（Conditional Autoregressive Range）模型估計波動性，得到變幅基礎下的風險值模型，並以美國S&P 500股價指數與十年期財政部政府公債日資料做為研究對象，進行變幅與報酬基礎下的風險值模型在風險值預測能力之比較，實證結果顯示，變幅基礎下的風險值模型表現優於報酬基礎下的風險值模型。

最後，更將分析維度擴大至投資組合風險值的估計，探討不同相關係數估計模型對投資組合風險值估計的影響，結果顯示Chou, Liu和Wu (2005)提出之變幅基礎下的DCC（Dynamic Conditional Correlation）模型表現優於報酬基礎下的DCC模型，可獲得較準確的投資組合風險估計值，證實變幅可做為資產報酬風險評估之一良好指標。

This paper investigates the Value-at-Risk models that were proposed with different characteristics of financial data, including the extreme value theory (EVT) Value-at-Risk model and the dynamic models considering the heteroscedasticity problem. In addition, we adopt the concept of range to the Value-at-Risk estimation. We use the Conditional Autoregressive Range (CARR) model of Chou (2005) to measure the volatility, and get the range-based Value-at-Risk model. We use the daily data of the stock indices of S&P 500 and the 10-year Treasury bond yield for empirical analysis. The empirical results indicate that the range-based models have the better performance than the return-based models in the Value-at-Risk evaluation.

Finally, we expand the evaluation to larger dimentions for the portfolio situation, and examine the effect of different correlation estimating models on the Value-at-Risk measuring of a portfolio. We find that the range-based Dynamic Conditional Correlation (DCC) model gets more precise Value-at-Risk estimation than the return-based DCC model. In orter words, range data is a good tool for risk measuring of the asset return.