傳染性風險下的信用風險因子模型與多期連續的矩陣

Abstract

放款的利息收入雖是商業銀行主要之獲利來源, 但借貸行為卻同時使得銀行承受著違約風險。銀行應透過風險管理方法, 計算經濟資本以提列足夠準備來防範預期以及未預期損失。 另外, 若銀行忽略違約行為之間的相關性, 將有可能低估損失的嚴重性。因此, 為了在考量違約相關性下提列經濟資本, 本文由 Merton (1974) 模型出發, 以信用風險因子模型判定放款對象是否違約, 進而決定銀行面對的整體損失為何。 為簡化分析, 本文假設違約損失率 (loss given default) 為 100%。 再者, 為加強相關性, 本文亦將違約傳染性加入因子模型並比較有無傳染性效果時, 模型所計算出的損失孰輕孰重。 而在決定違約與否時, 須利用來自移轉矩陣上的無條件違約機率, 然信評機構所發布之移轉矩陣概遺漏諸多訊息, 依此, 本文以多期連續的移轉矩陣修正之並得到另一不同的無條件違約機率。 最後, 以臺灣的 537 家上市櫃公司作為資產組合, 經由蒙地卡羅模擬得到兩個因子模型的損失分配, 我們發現具有傳染性效果存在時, 預期損失和非預期損失較大且損失分配也較為右偏。

Despite interest income from loans is a major profit contributor for commercial banks, lending inevitably makes banks bear default risks. For the sake of avoiding expected and unexpected losses, risk management methods ough to be employed by banks to meet the ecomical capital requirement. Besides, loan loss severity may very well be underestimated\nif the correlation between default events is disregarded. Therefore, in order to calculate economical capital when taking default correlation into account, we start\nfrom Merton (1974) model, and identify if loans will be in default via facor models for portfolio credit risk and portfolio losses can then be detemined. To simplify our analysis in this paper, loss given default is assumed to be 100%. To intensify correlation, default contagion is, moreover, introduced to our factor model and we investigate\nwhich model results in larger losses as well.\n\nWhen determining default, we have to utilize rating transition matrices to obtain unconditional probability of default. Transition matrices published by credit rating agencies, however, have embedded drawback of insufficient information. We correct this flaw by means of another transition matrix based on continuous-time observations and produce different unconditional probability of default. Through Monte Carlo simulation, loss distributions are calibrated respectively from the two factor models under portfolio of 537 Taiwan listed and OTC companies. We find that expected and unexpected losses are larger and loss distribution is more right-skewed when infectious effects exsit.