擔保債權憑證之評價-考量動態模型、傳染效應與隨機回復率

Synthetic CDO Pricing with Contagion Effect and Stochastic Recovery to the Dynamic Model

劉益成(I-Chen-Liu)

指導教授 ： 鍾麗英

國立臺北大學/商學院/統計學系/碩士(2010年)

摘要

擔保債權憑證(Collateralized Debt Obligation, CDO)是近年來快速發展的衍生性金融商品。在合約中依據資產的違約風險分成數個分券，每個分券承擔該區間的資產損失金額。此商品對於銀行而言，達到風險分散及增加流動性的效果；對於投資人而言，可依其風險偏好及預期報酬選擇特定分券投資。以往評價擔保債權憑證多以因子模型為主，雖然因子模型能解決高維度計算的困難，但因子模型無法描述損失分配的期間結構，只能處理單一時點的擔保債權憑證，無法評價與時間高度相關的信用衍生性商品，如遠期生效擔保債權憑證、擔保債權憑證選擇權等。因此，有許多學者開始研究動態的違約模型，描述損失分配的期間結構，並以此評價與時間高度相關的信用衍生性商品。
自2007年發生次級房貸風暴後，全球經濟陷入恐慌，造成許多流動性不佳公司倒閉，公司倒閉原因可能是因為經濟環境不佳或者是受到其他公司違約事件影響。本文以Hull and White(2008)中提出的動態模型為基礎，結合隨機回復率與傳染效應，探討動態模型加入這兩種效應對擔保債權憑證評價的影響，並利用市場資料比較三種模型的評價結果。實證結果指出，次級房貸發生之後，傳染效應與隨機回復率模型的配適結果比一般動態模型佳。最後進行傳染家數的敏感性分析，探討傳染家數的設定是否穩健。

關鍵字

合成型擔保債權憑證 ； 傳染效應 ； 回復率 ； 動態模型

並列摘要

Collateralized debt obligation (CDO) develops very fast in recent years. Gaussian copula model becomes the standard pricing model because of its simplicity and efficiency, but this model can’t describe the structure of default distribution, conducing failure in pricing of securities with timing features, examples include forward CDOs and CDO option. Hence, there’s some research in dynamic model for non-standard CDO tranches.
In 2007, the global economic suffered from the subprime mortgage crisis, the credit markets emerged adverse consequences. The simple dynamic model proposed by Hull & White (2008) is not sufficient to establish default environment, therefore we consider contagion effect and random recovery in simple dynamic model. In contagion dynamic model, we separate the assets to two groups, one is infecting group the other is infected group. We also consider sensitivity test in the numbers of infecting group.
Finally, we utilize models to price iTraxx and CDX.IG. In our result, contagion effect and random recovery model improve the fitting in the product of CDX.IG.

並列關鍵字

CDO ； contagion effect ； stochastic recovery ； dynamic model

參考文獻

Andersen, L., and J. Sidenius. “Extensions to the Gaussian Copula: Random Recovery and Random Factor Loadings.” Journal of Credit Risk, Vol.1, No.1 (2004): PP. 29-70.

Andersen Leif(2006), “Portfolio Losses in Factor Models: Term Structures and Intertemporal Loss Dependence”, Bank of America.

Andrei, V. Lopatin, “A simple dynamic model for pricing and heterogenous CDOs.” Working paper, 2008.

Balakrishna, B.S. “Levy Density Based Intensity Modeling of the Correlation Smile.” Working paper, Munich University, 2008.

Chourdakis, K. “The Cyclical Behavior of Default and Recovery Rates.” Working paper, 2008.