本文針對債券投資人所關切的信用風險，將 copula 函數加入既有測量信用風險值的 CreditMetric 模型，以考量資產間複雜的相依結構，據此提供債券投資人評估信用風險值 (credit VaR) 的參考依據。依據債券發行公司間的資產相依結構 (dependence structure) 以及 Standard & Poor’s 發佈的信用評等移轉矩陣 (credit transition matrix)，計算此投資組合於年終移轉至各個信用評等的預期價值與其對應的機率分佈圖，以估算此投資組合的信用風險值。不同於傳統常態分配的設定方法，本文利用 Archimedean copula family (以下簡稱 AC copula family) 來描述公司資產間複雜的相依程度。並依據 Genest and Rivest (1993) 所提出的無母數估計方法，估計美國上市公司所發行公司債投資組合的信用風險值。本文發現，整體來說公司間的資產相依結構並非如傳統常態分配所設定的模型一樣，而是具有厚尾 (fat tail) 的情況產生。並且針對投資者所關心的尾端風險，相較於Kendall’s tau等級相關係數則lower tail dependence更能描繪資產組合尾端的變化狀態，以幫助本文更精確且進一步的評估投資組合的信用風險值。

In this thesis, our aim was establish a framework as CreditMetrics for quantifying credit risk in portfolios of corporate bonds. We depended on assets dependence structures of corporate bonds and Standard & Poor’s credit transition matrices to compute all possible 64 year-end values and all possible 64 year-end joint likelihoods across 64 different states for a two-bond portfolio. The next step was to assessed the credit value-at-risk (Credit VaR).
In this thesis, we focued on the problem of modeling the multivariate distributions of several outcomes. To solve this problem we used a promising approach based on Archimedean copulas which is different from the conventional multivariate Normal assumption to focus explicitly on the dependence structure. We used the nonparametric methods of Genest and Rivest to assess the credit value-at-risk for American corporate bond portfolios. Our empirical distributions were heavier tailed than the normal distribution. If investors ignore this phenomenon, they will underestimate the VaR and make a downside loss.

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