考慮信用風險之金融商品評價與分析

Under LIBOR Market Model Pricing Financial product with Default Risk

許健忠(Chien-Chung Hsu)

指導教授 ： 李存修

國立臺灣大學/管理學院/財務金融學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.10010

摘要

金融環境的改變，多樣化的衍生性商品推陳出新。而利率持續的低迷，更使得利率衍生的結構債商品在現今的社會更為重要。但是以往文獻評價利率結構型商品時，往往忽略發行機構本身可能的違約風險，故本文將信用風險導入模型當中，而在利率模型方面且選用近年來較為實用多因子的BGM市場模型。而且考量信用風險時，有別於以往使用David Li的方法建立違約曲線時，利用發行日當天的具有公司信用風險的債券價格，利用迭代的公式解出，預期當日公司未來的違約機率。此法往往會低估發行機構遠期的違約機率，當商品存續期間較長時所求得之含信用風險理論價格會失真。故本文導入Scho ̈nbucher(2003)所提出的有違約風險的LIBOR市場模型。利用有違約機率的lognormal Forward-LIBOR Model的概念，模擬未來每天的違約曲線的變動，改善David Li法只利用一天的資訊捕捉未來10年發行公司的違約機率。結果發現，若採用本文方法可發現發行公司遠期違約機率會明顯提高。故將此種違約機率帶入評價契約商品，藉由此法可以更合理的捕捉商品價格。

關鍵字

信用風險 ； 違約機率

並列摘要

Various derivative products have been issued in the market along with the development of financial environment. Interest rate-linked structured products are even more important as interest rate has been in low levels. However, past studies on pricing interest rate-linked structured products tend to ignore the default risk of the issuing institution itself. Hence, we will incorporate the credit risk into the pricing model. For the interest rate model, we choose the multifactor BGM market model which has been used broadly in practice. When taking the credit risk into consideration, David Li’s methodology tends to underestimate the long-term forward default probability of the issuing institution. The method of David Li creates the default curve by using the bond prices on the issuing date with corporate credit risk, and recursive formulas to find the default probability of the company in the future. When the duration of the structured product is long, the theoretical price of credit risk will be unreliable. Consequently, we implement the LIBOR market model presented by Scho ̈nbucher(2003) with default risk incorporated. We improved the default probability by using the concept of spot lognormal Forward-LOBOR Model to simulate the changes of the everyday default curve in the future, compared to David Li’s model which uses only one-day information to catch the default risk of the company of the following ten years. The results indicate that if we use the methodology presented in this paper, the long-term forward default probability will be obviously higher. It shows that we can price the Interest rate-linked structured products more reasonably by taking the default probability into account by utilizing the method introduced in this paper.

並列關鍵字

Credit risk ； default probability

參考文獻

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