Applying Merton Jump Diffusion Model in Financial Distress Prediction

[[abstract]]過去實證結果顯示，金融資產價值或是資產價值報酬率的分配常有著胖尾(fat tail)的現象以及跳空(jump)的走勢，為了描述公司價值忽然地跌落或增加的現象，本文嘗試加入跳躍因子，將資產的動態過程假設為Merton (1976)所提出之跳躍擴散過程(jump diffusion process)，以捕捉資產價值不連續的現象，並且利用EM演算法進行參數估計，計算出Merton跳躍模型下之違約機率，建構出違約風險預測模型。 本文將所建構之違約風險預測模型之預測表現與傳統Merton模型以及Z-score模型相互比較後發現，Merton跳躍模型與傳統Merton模型之預測表現難分優劣，而Z-score模型之預測表現將優於Merton跳躍模型。[[abstract]]The empirical evidence shows that the existence of fat-tail or jump in many financial assets return or assets value distribution is a really common phenomenon In this paper we try to add a jump component in order to describe the sudden drop or increase in firm’s asset value so we consider the well-know jump diffusion process in setting the asset dynamic process for capturing the discontinuousness of asset value As for the parameters estimation we rely on the method called EM algorithm instead of maximum likelihood estimation Finally we calculate the risk neutral default probability under Merton jump model and constructed a default risk predictive model In this study we also compare the prediction performance to the commonly adopted model Merton model Z-score model and even the new version of Z-score model We find evidence that the Z-score models outperform our default predictive model And between the prediction performance of our model and of the traditional Merton model we cannot tell which one is better of