重隨機假設下動態違約相關性之描述及其資訊內涵：以指數型信用擔保債權憑證為例

On the Characterization and Information Contents of Dynamic Default Correlation under the Doubly Stochastic Assumption: The Case of iTraxx CDO Tranches

本文建立信用資產債權群組之動態違約相關性模型。其中，我們允許異質性信用風險事件之抵達由雙重（Autonomous）混合型卜瓦松跳躍過程（Mixed Poisson Jump Processes）所描述，且藉由跳躍幅度（Jump Sizes）反映信用事件之於信用資產池（Reference Pool）聯合存活機率（Joint Survival Probabilities）的危害程度。本文藉由提供驅動信用事件發生之頻率（Default Intensity）服從一雙參數伽瑪（Gamma）及帕雷圖分配（Pareto Distribution），以描述不同市場情境下信用事件發生之密集性。我們以市場指數型擔保債權憑證iTraxx Europe為例，驗證模型之市價擬合度，且藉由校準市價反推求得各分券之隱含相關性（Implied Correlation），進一步闡述隱含相關性於分券風險特徵及信用交易策略上所呈現的意涵。

In this paper we present a tractable model that dynamically characterizes the correlation structure for a portfolio of credit entities. Heterogeneous credit events are modeled as the arrivals of mixed Poisson jump processes and magnitudes of jumps represent the associated impacts of credit events on the joint survival probabilities of the credit portfolio. We assume that the default intensities of both sources of risk are driven by a combination of two-parameter Gamma and Pareto distributions as to capture the clustering effects of default events under different market scenarios. We conduct calibration of the model to iTraxx Europe as an example and verify the goodness of fit between the arket spreads and the model spreads of ours. We extract the implied jump-sizes that reveal information on the correlation structure, and further explore their impacts on the risk characteristics of CDO tranches.