信用衍生性商品在市場上交易漸趨熱絡，創新速度更是一日千里，市場上琳琅滿目的信用衍生性商品，投資人要如何審慎客觀評估風險後再檢視自身能承擔的風險後投資，諸如此類的議題在近幾年備受關注。尤其在2007金融海嘯之後，所有信用衍生性產品也無一倖免，信用評等公司對信用衍生性產品的評價，也備受挑戰，因此，辨識風險以及驅避風險在後金融海嘯時期，已是一刻不容緩之待解決問題。固定比例債務債券(Constant Proportion Debt Obligations; CPDO)亦是金融海嘯前一年所發明的創新信用衍生性商品，由於其高收益特性以及強調極低投資風險，吸引了許多投資人爭相購買，但金融海嘯時期，也是付之一炬。為了使投資人更了解此商品的風險，本研究運用在跳躍擴散模型假設下，存在封閉解的雙出場障礙式選擇權複製此商品的風險因子，並且為了描述此商品具有動態調整槓桿的時間相依(Time Dependent)性質，加入了蒙地卡羅模擬法，捕捉任意時點上，投資人面臨的風險，將風險因子拆解選擇權後，也更能讓投資人能以投資選擇權的知識運用到此商品來操作。最後，為了使投資人趨避諸如金融海嘯時期的風險，本研究也用選擇權的Delta 避險策略，替商品虛擬一現貨市場，並模擬出其避險之績效。 / The increasing trading volumes and innovative structures of credit derivatives have attracted great academic attention in the quantification and analysis of their complex risk characteristics. The pricing and hedging issues of complex credit structuers after the 2009 financial crisis are especially vital, and they present great challegens to both the academic community and industry practitioners. Constant Proportion Debt Obligations (CPDOs) are one of the new credit-innovations that claim to provide risk-adverse investors with fixed-income cash flows and minimal risk-bearing, yet the cash-outs events of such products during the crisis unfolded risk characteristics that had been unseen to investors. This research focuses on the pricing risk quantification, and dynamic hedging issues of CPDOs under a Levy jump diffusion setting. Based on decomposing the product's risk structure, we derive explicit closed-form solutions in the form of time-dependent double digital knock-out barrier options. This enables us to explore, in terms of the associated hedging greeks, the embeded risk characteristics of CPDOs and propose feasible delta-netral strategies that are feasible to hedge such products. Numerical simulations are subsequently performed to provide benchmark measures for the proposed hedging strategies.

本文的主旨在評價二次擔保債權憑證。在條件獨立機率的假設下，我們使用factor copula的方法去刻劃違約事件間的相關係數，並提供了一個有效率的迴圈演算法去建構損失分配。本方法同時考慮違約數目及違約位置，同時亦可解決重疊性的問題。本文所建構的是Hull and White(2004)的延申模型。我們也對各參數作敏感度分析，以求得其對分券價差的影響。文中亦主張一些風險衝量指標，以量化重疊性的程度等風險議題。 / In this paper we address the pricing issues of CDO of CDOs. Underlying the conditional indepdence assumption we use the factor copula approach to characterize the correlation of defaults events. We provide an efficient recursive algorithm that constructs the loss distribution. Our algorithm accounts for the number of defaults, the location of defaults among inner CDOs, and in addition the degree of overlapping between inner CDOs. Our algorithm is a natural extension of the probability bucketing method of Hull and White (2004). We analyze the sensitivity of different parameters on the tranche spreads of a CDO-squared, and in order to characterize the risk-reward profiles of CDO-squared tranches, we introduces appropriate risk measures that quantify the degree of overlapping among the inner CDOs. Hull and White (2004) presents a recursive scheme known as probability bucketing approach to construct conditional loss distribution of CDO. However, this approach is insufficient to capture the complexities of CDO². In the case of the modeling of CDO, we are concerned for the probabilities of different number of defaults upon a time horizon t, e.g., the probabilities of 3 defaults happened within a year. With the mentioned probabilities, we can then calculate the expected loss within the time horizon, which enables us to figure out the spreads of CDO. However, in the modeling of CDO², an appropriate valuation should be able to overcome two more difficulties: (1) the overlapping structure of the underlying CDOs, and (2) the location where defaults happened, in order to get the fair spreads of CDO².