動態系統下違約機率模型之探討

Abstract

本文藉由重設Hull和White (2008) 所提出來的動態模型，探討在不同危險率結構的假設下，模擬資料和市場資料的誤差，得到較佳的危險率結構為隨著時間先上升再下降，並非傳統的常數函數，這與從慕迪累積違約機率表所得到的的結果相互呼應。另一方面，由於跳耀是動態模型的重要特徵，我們也比較了動態模型中有無跳躍的模擬資料，發現當動態模型中缺少跳躍時，會低估較高損失的機率。最後探討在不同危險率結構的假設下，其公司違約家數機率分布圖的性質。並且利用卡方分配來逼近公司違約家數機率分布圖。

This thesis revises the model proposed by Hull and White (2008). We discuss the errors between the simulation data and the market data under the different assumptions of the hazard rate. We find as time goes by, the structure of the hazard rate rises firstly and declines finally is better than the constant traditionally. The result is consistent with the outcome we obtain form the Moody’s cumulative default probability. On the other hand, the jump is the important characteristic of the dynamical model, so we compare the simulation data between the dynamical model with jump and the dynamical model without jump. We find the dynamical model without jump has the low-estimated probability which absorb higher loss. Finally, we discuss the properties of the probability distribution of the number of the defaults, and use the chi-square distribution to approximate it.