台灣上市公司發行債券信用風險量化之研究─以CreditMetricsTM與BSM模型為例

Abstract

由於信用風險控管日益重要，加上近年來信用風險量化模型已逐漸被銀行或其他金融機構用來作為衡量信用風險暴露與資本配置決策的參考工具，這也使得信用風險量化模型的精確性越來越受重視，從國際間風險控管規範的發展可見到一斑。 本研究嘗試以台灣公司債作為切入點，進行信用風險量化之研究，研究方法採用RiskMetrics的CreditRiskTM模型估計信用風險值，並進行部分修正得到調整後之信用風險值，另一方面利用Black-Schole and Merton所提出之選擇權模式估計違約選擇權價值，再比較此兩種信用風險量化指標之關係與變化趨勢。模型驗證部分採用前向測試與回溯測試。資產配置決策方面則將CreditRiskTM維持在某一信賴水準下所求得的信用風險值，作為BSM模型的違約選擇權價值，衡量兩種模型違約機率的相互關係。 本研究得到的實證結果如下： 一、各公司債信用風險值隨著衡量期間越長而越高，四、五年期債券信用風險值大多介於0至10之間，一旦超過五年期間，信用風險值會以很明顯的趨勢快速遞增。因此建議公司發行五年期債券為優先考量。 二、在回溯測試與前向測試上，調整前信用風險值相較於違約選擇權於債券的風險估計上無明顯優劣之分，但調整後信用風險值其預測能力明顯優於違約選擇權價值。 三、資產配置決策上，BSM模型不適用於估計公司股價報酬率波動性過高的違約選擇權價值。95%信賴水準之信用風險值，應用在BSM模型下其違約機率往往大於5%，且違約機率有隨著股價報酬率波動性而增加的現象。而在前向與回溯測試上，調整後信用風險值有較佳表現，因此總結為違約選擇權價值容易高估公司債的真實風險。 四、CreditMetricsTM評估個別債券因信評變動，使得投資者對其殖利率的改變所產生的債券價格變動風險，其出發點為個體觀點，而BSM模型則是從公司的資產報酬率波動性與股東對負債比等整體觀點來評估公司的信用風險。另一方面，同一家公司很可能發行各種不同到期日的債券，在評估個別公司債的信用風險時，應該從個體觀點出發，亦即是說，採用CreditMetricsTM相較於BSM模型，能夠得到更正確的評估結果。

Due to the increasing importance of the management on Credit Risk, and the gradual use of Credit Risk Quantification Model by banks or other financial company as a reference tool to measure the exposure to Credit Risk and to decide the capital allocation for these recent years, the exactness of the Credit Risk Quantification Model has been paid more and more attention to. We can see it from the development of international risk management standards. This research tries to study the credit risk quantification by digging into the range of Taiwan Company Bonds. The evaluating methods adopted RiskMetrics’s CreditMetricsTM to calculate the credit VaR and corrected it to get adjusted credit VaR, on the other hand, using Balck-Shole and Merton’s option model to calculate the default option value of the company bond and , at the same time, to compare the relationship and the variation trend of these two quantification indexes. As to the verification of the results, this research used the Back Testing and Forward Testing. In the decision of capital allocation, the credit value under some trust level was taken as the default option value in BSM model to evaluate the mutual relationship of the default probability of these two models. The evident conclusions of this research are as follows: 1. The longer the period used to evaluate the company bond is, the higher the credit risk value of it rises. Credit VaR of the bond with maturity of four and five years are in the range between zero and ten. Once the length of maturity exceeding five years, the credit risk will increase rapidly and obviously. Therefore, we suggest that the company should take the issue of bonds with maturity of five years as a first priority. 2. As for Back and Forward Testing, the performance of pre-adjusted credit VaR is the same as default option value, but adjusted credit VaR, when compared with default option value, the former usually performs better than the latter in the evaluation of the risk of the bond. 3. When talking about the decision of capital allocation, we find BSM model isn’t suitable for the estimate of the default option value if the company has the stock with extremely high volatility of reward rate. If the credit VaR under 95% trust level is applied to the BSM model, the default probability often exceeds 5% and we can see the possibility is increasing with the volatility of the rate of a company’s stock rewards. In both Back and Forward Testing, the credit VaR has better performance; that is, the default option value overestimates the true risk value of the bonds easily. 4. CreditMetricsTM starts from the “individual” view of the changed investors’ yield rate which influences the bond price, while the BSM model evaluates the company’s credit risk from the “overall” view of the asset to debt ratio and return volatility. On the other hand, most companies issue more than one bond, and that is, when estimating the credit risk of “individual” company bond, we should use CreditMetricsTM.