隱含關聯結構法－實證分析與避險應用

Abstract

近年來金融市場最重大的發展，就是創造了信用合約，使得信用風險得以透過交易來進行移轉，其中信用違約交換（Credit Default Swap, CDS）、信用指數（CDS Index）與信用指數批次證券（CDO Tranche on CDS Index）的推出與標準化，使得信用交易的流動性大為提升，也讓市場報價更具效率。目前在訂價信用衍生性商品時，都是選擇最貼近市場報價的Copula函數作為訂價的標準，但通常選定的函數無法完整描述聯合違約機率（Joint Default Probability）的關聯結構（Dependence Structure），所以透過市場報價計算各信用指數批次證券的複合相關係數（Compound Correlation）時，會有相關係數微笑（Correlation Smile）的現象，因此JP Morgan、Hull and White（2006）分別提出了基礎相關係數（Base Correlation）與隱含關聯結構法（Implied Copula Approach）來解決此問題。因此本篇研究係以Hull and White（2006）所提出的隱含關聯結構法為基礎，並透過對標準化合約市場報價的觀察，提供另一種計算信用衍生性商品Delta的方法。

One of the most prominent developments of the financial market in the recent years is the creation of credit contracts, which facilitates the transferring of credit risk through trading directly. Among the products evolving from this idea, the promotion and standardization of Credit Default Swap (CDS), CDS index, and CDO tranche on CDS index highly improve the liquidity of the credit market, and thus make the market quotes more efficient. Currently when a credit derivative is being priced, market makers usually choose the copula function that best fits the market quotes as a standard. However, the chosen function hardly ever achieves to completely describe the dependence structure of the joint default probability. Therefore, if we compute the compound correlations of different index tranches, the results will be showing a correlation smile. In accordance with this issue, JP Morgan, Hull and White (2006) had proposed the base correlation and the implied copula approach respectively to overcome this problem. By observing the relationship between market quotes of CDS index and CDO tranche on CDS index, this study is based on the implied copula approach to find an alternative way of calculating the delta of credit derivatives.