我們利用默頓模型的框架理論以及關聯擴散模型來分析公司的信用風險。 在到期日 T 時，如果公司的資產價值小於公司負債的帳面價值，稱作違 約。默頓模型原始的概念是在風險中立測度進行討論，利用其框架理論 於真實機率測度計算信用風險，接著也使用關聯擴散模型進行分析。根 據系統風險，我們想要了解兩模型在給定對數資產平均小於對數負債平 均下，違約機率有何變化。在參數估計上，使用最大概似估計法。發現 當公司相關性愈高時，給定對數資產平均小於對數負債平均的聯合違約 機率也愈高。

In this paper, we use the framework of Merton's model and the coupled diffusion model to analyze the companies' credit risk. The default is defined as the market value of the firm's assets less than the book value of the firm's liabilities at maturity time $T$. The original concept of the Merton's model is discussed in risk-neutral measure. We use the framework of Merton's model and the coupled diffusion model to calculate the default probabilities in the physical measure. Base on the systemic event, we want to know what change of the joint default probabilities conditional on the mean of log-inventories less than mean of log-liabilities. In the simulation study, we use the Maximum Likelihood technique to estimate the parameters. The higher correlation, the higher joint default probabilities conditional on the systemic event.

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