以KMV模型評價CDS價差之實證研究

Abstract

首先對於信用衍生性商品做出完整概括性的介紹，並比較相關產品的特色與差異，進而探討市場上常見用來評價信用違約交換的模型，加以比較優缺點以及實用性與精準度，即使無法精準的預估，但希望找出一種相對有效的評價方法。 分別比較了信用轉移矩陣、縮減式模型以及KMV模型，而信用轉移矩陣只 能區分AAA到C幾個大區間下的差異，但卻無法再細分各家公司的風險值並求 出應該有的權利金價格；縮減式模型則因為實務上無法找出各公司的殖利率曲線 ，即使是道瓊成分股也因各年期公司債的缺乏或是流動性因素使得殖利率曲線誤差過大，更別說是其他小型的企業了；因此我們最後選取了KMV模型，此模型 考慮了個別公司的權益市值、負債以及股價波動度…，包含了市場的交易因素，也考慮了波動造成的違約機率，雖然沒有將信用評等加入到評價模型中，但我們依舊推薦的理由是：信評公司在做評等改變時也大多依賴財務報表或是市場上的交易資訊，而KMV模型中都有涵蓋，即使沒有信用評等這個質化因子，還是可 以相當程度的反應在評價信用違約交換的價格上。 最後使用最被市場上所使用也最精準的KMV模型做為實證研究的主要模型 ，再抓取道瓊三十家成分股進行實證分析，比較出由模型中所計算出的價格與市場交易價格的價差關係，並畫圖比較相對關係，看出信用違約交換權利金在去年的金融風暴中有明顯的變化，十月前大部分公司都相當穩定，違約風險趨近於零 ，但在十月到十二月間因為市場大幅波動因素造成權利金都有不小的上揚，最後再進行多元回歸分析探討模型中主要因子對於前述價差的影響，同樣的也圖示出各參數對於信用違約交換價差的影響。

First, we introduce the overall concept about credit derivatives and compare the relative product character and difference. Then we discuss some models which the market often use to pricing credit default swap and compare these models’ advantage/disadvantage, usefulness and accuracy. Even we couldn’t predict very precisely, we want to find a relatively useful pricing method. We try to compare credit migration matrix, reduced-form model and KMV model, then we know that credit migration matrix can only separate credit rating from AAA to C. Reduced-form is useless because of lacking enough information like every firms’ yield curve. Even these firms like Dow Jones Components are still the same. So we choose KMV model as our empirical model for the dada, the model considerate about the market equity value, total debt, and equity volatility, including the market factors. Although it ignores the credit rating, we still recommend it. The reason is the rating agency give their rating is depending on the financial report or market information, so we can believe that the model is somehow reflect the real value in the CDS. Finally, we use the most people used and most accurate KMV model as our empirical model. We search for the Dow Jones Components and compare these CDS price and the model theoretical price. We found that the spread change a lot before and after the financial market crisis. We have done the regression by fixed effect panel data and show the pictures on the appendix.