- 學位論文
擔保債權憑證之信用價差評價
Evaluating the Credit Spread of a Collateralized Debt Obligation
摘要
在1970年代，美國許多銀行因為承作長期固定利率住宅抵押房貸而面臨了經營方面的問題，美國政府為了幫助這些銀行，首先推出房屋抵押基礎證券，解決流動性不足的問題。後續美國政府再依據不同的目的及設計，衍生出資產基礎證券及擔保房貸憑證。除此之外，由於1990年以來的國際金融危機，導致銀行及投資人開始意識到信用風險的重要性。將流動性風險及信用風險這兩個問題結合，創造出擔保債權憑證這項金融衍生性商品。 我們對於擔保債權憑證的評價方式，先推導出整個投資組合累積至某一時點時的條件存活機率。接著使用縮減式模型配合隨機違約強度，考慮投資組合會受到市場的共同因子及個別公司特有因子的影響，同時考慮所有可能的情況，設定出危機率。進而推導出，在單一時點時，有多家公司同時存活時的存活機率，之後再將存活機率轉換為在單一時點的違約損失分配，我們利用間斷的方式，將整個研究期間區分為多個彼此之間不會互相重疊的區間，而將每一個區間的違約損失現值，及溢酬收益現值分別加總起來。最後，在無套利機會下，對擔保債權憑證分券的信用價差進行評價過程，繼而推導出擔保債權憑證公平合理的信用價差封閉解。本文除了推導出信用價差的封閉解之外，也推導出投資組合的聯合存活函數，希望其未來可以運用在多資產的信用連結票據及信用違約交換上。
並列摘要
In 1970, the banks face problems of business because their long fixed housing loans. The government of the Unite States then issues the Mortgage Backed Securities for helping those problems of liquidity. According to different purpose the securities, Asset Backed Securities and Collateralized Mortgage Obligations, are developed. Since 1990, the financial crisis made many international industries bankrupt due to care about the credit risk of a security. We intend to evaluate a Collateralized Debt Obligation using reduced-form model with stochastic default intensity. Moreover, the default correlation is considered in the model since default will be affected by common factors of macroeconomic, such as market index and income. Then, we derived a closed-form formula for the fair credit spread of Collateralized Debt Obligation. In the further studies, one can use our derived loss distribution to evaluate others derivative security which underlying asset is a portfolio, such as multi-asset credit link notes and multi-asset credit default swaps.