Schmid, Bernd and Rudi Zagst, "A Three-Factor Defaultable Term Structure Model", Journal of Fixed Income, Vol. 10, No. 2, (Summer 2000), pp. 63-78.

Partial Introduction: Although credit risk has always been an important concern, only relatively recently have banks and other financial institutions become more aware of the weaknesses of their traditional credit risk exposure calculation techniques. New instruments like credit derivatives also require new models for credit risk pricing. Thus, it is not surprising that there have been many theoretical developments in credit risk research in the past several years.

There are two basic approaches for modeling default risks in bonds, structural models and reduced-form models. The structural approach dates to Merton[1974]. It assumes that the dynamics for the value of the assets of a firm across time can be described by a diffusion stochastic process and that the defaultable security can be regarded as a contingent claim on the value of the assets of the firm. Apart from the standard assumptions of continuous time co-arbitrage models, there are many shortcomings of this model. The liabilities of the firm are supposed to consist of only a single class of debt; the debt has a zero coupon; bankruptcy is costless; and interest rates are assumed to be constant over time. Thus, the assumptions of the Merton model are highly stylized versions of reality.

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