Ebook A structural credit risk model with a reduced'form default trigger
This paper presents a credit risk model useful for both pricing credit sensitive instruments and risk management purposes. This hybrid model retains the interesting features of both reduced'form and structural models and both classes can be found as special cases of the proposed framework. Indeed, default is not necessarily triggered as soon as the assets cross some pre'specified threshold. Rather, default is related to the sensitivity of the firm to its debt ratio through a parametric intensity. Within this framework, similar capital structures may generate different default probabilities.
Many authors have tried to close the gap between structural and reduced'form models. An interesting approach is built upon incomplete accounting information. In Duffi e & Lando (2001), the value of the assets observed by the market is different from its real value, observed by the firmqs managers (the former equals the latter and a noise). Investors only periodically receive imperfect financial statements, creating a framework with stochastic default intensity. The result is an extension of Leland & Toft (1996). Giesecke (2001) presents a structural model in which the default barrier is a single unobservable random variable. Other models also relax the complete information assumption, notably, Çetin, Jarrow, Protter & Yildirim (2004), Giesecke (2004) and Giesecke and Goldberg (2004a, b). Jarrow & Protter (2004) argue that structural and reduced'form models are somewhat related and the link between the two relies on the amount of information available to the modeler.
Other contributions integrate both reduced'form and structural models. In Madan & Unal (2000), a model for the value of assets and liabilities is presented and default occurs when a single and random loss, occurring at a random time, is larger than the value of the equity. The resulting model is dealt with an intensity'based approach. Panjer & Chen (2003) show that discretized (where default only occurs at specific time points) versions of Merton (1974)qs structural model and reduced'form models can be written in one unifying framework.
The Chen et al. (2004, 2005) papers introduce a model where the credit state of the firm (interpreted as either the rating of the company or its distance to default) is a CIR'type of affi ne process with gamma'distributed jumps. A second process, dependent on interest rates and on the credit state of the firm, is required. Default either occurs as soon as the first process hits a barrier or when the second process jumps. Thus, default comes from either a predictable or an unpredictable process. Bakshi, Madan & Zhangqs (2006) model is a reduced'form model based on Vasicek'type state variables. One of the latter is the leverage of the firm. It should be noted that all models presented in these papers provide for non'zero short'term credit spreads, something that cannot be found in most structural models.
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