Copula 模式在財務管理之應用

Abstract

本論文主要研究Copula模式在財務風險管理上的應用。在財務管理上，風險往往是無形的，因此將其具體化相當重要，而風險值(Value at Risk)就是個非常有用的風險測度，可以用來評估金融資產未來某特定時間的最大可能損失。當我們嘗試估計投資組合的風險值，則必然需考慮資產之間的關係，則Copula模型在此處便能被廣泛運用於描述資產之間的關聯性。首先，我們介紹二維的Copula模型以及風險值的概念，同時也會探討用來描述金融資產波動的時間序列模型。在實例上，我們假設某一投資組合包含兩個資產，且其資產波動性的模型假設皆為廣義自回歸條件異方差模型 GARCH(1,1)，並利用不同的Copula模型來估計此投資組合的風險值，由結果即可比較模型適合於否也將影響風險承受程度的判斷。

The thesis investigates the application of copula models in financial risk management. Value at Risk (VaR) is often used to measure the potential loss of financial assets. Estimation of VaR involves making assumptions about the joint behavior of multivariate returns or loss. Copula models are widely adopted because of their flexibility. In the thesis, we provide brief introduction of copula models and the concept of VaR. We also review time series models for describing the volatility of financial assets. Then for illustration, we choose different Copula models to estimate the VaR of a portfolio, which includes 2 assets, under the assumption that the volatility of log-return follows the GARCH(1,1) model.