以混合雙指數copula模型定價合成型CDO

Abstract

CDO（擔保債務憑證）的估值在近期疫情和經濟不確定性背景下，仍然是金融領域的一個重要課題。傳統的copula模型，如單因子高斯copula，存在相關性偏斜和缺乏厚尾特徵等問題，導致校準和市場擬合上有顯著誤差。儘管已有各種具有厚尾特性的copula模型被提出，如Double t copula和NIG copula，但這些模型有些只能以近似方式求得分布，有些涉及過多的參數，導致計算時間增加和效率低下。各自都有部分缺陷。

本研究引入了高斯分佈和雙指數分佈混合（G-DE）copula模型，以解決過往copula模型的局限性。G-DE copula模型保留了厚尾特徵，並具有卷積特性，消除了數值近似的需求，並減少了參數估計的複雜性，從而提高了計算效率。更甚是透過混合高斯分布，使其大幅提升市場報價擬合度。我們的研究將G-DE模型與傳統copula模型進行比較，展示其在校準準確性、計算效率和整體性能方面的優勢。研究結果顯示，G-DE copula模型是CDO定價和風險管理的一個強有力的替代方案。

The valuation of Collateralized Debt Obligations (CDOs) remains a crucial financial topic, especially in the context of the recent pandemic and economic uncertainties. Traditional copula models, such as the one-factor Gaussian copula, suffer from issues like correlation skew and lack of heavy-tailed characteristics, leading to biases in calibration and market fit. Although various heavy-tailed copula models have been proposed, including the double t copula and NIG copula, they either require complex numerical approximations or involve excessive parameters, resulting in increased computational times and inefficiencies.

This study introduces the Mixtures of Gaussian distribution and Double Exponential distribution (G-DE) copula model, addressing the limitations of previous copula models. The G-DE copula model retains heavy-tailed characteristics while possessing convolution property, eliminating the need for numerical approximations and reducing the complexity of parameter estimation. This results in improved computational efficiency and better market quote fitting. Our research compares the G-DE model with traditional copula models, demonstrating its advantages in calibration accuracy, computational efficiency, and overall performance. The findings highlight the G-DE copula model as a robust alternative for CDO pricing and risk management.