Risk Disaggregation And Credit Risk Valuation In The Merton Like Way

Recent literature focuses on the systematic and specific components of credit risk (Dichev [1998], Wilson [1998], Jarrow, Lando & Yu [2001]). It is currently assumed, at least implicitly, that financial data are all subject to one latent systematic factor (Jarrow, Lando & Yu [2001], Lucas, Klaassen, Spreij & Straetmans [2001]). In this paper, we formalize those insights by distinguishing between one systematic risk component and one idiosyncratic risk component in credit risk valuation. Such a risk disaggregation allows us to state an analytical formula for valuing European type calls. Given that corporate debt could be priced through a call on the firm assets value and with a strike corresponding to the debt’s value at maturity, we then apply this distinction to the risky debt valuation framework stated by Merton (1974). A closed form formula of a bond’s price is first deduced, leading then to an analytical expression of the related credit spread. We consequently give an explicit formulation for the market risk, namely the undiversifiable part, and the idiosyncratic risk, namely the diversifiable part, of the default risk characterizing any corporate bond. This methodology allows us to highlight some valuation errors concerning default risk valuation when identifying only one source of risk. In accordance with Wilson (1998), the results show that credit risk valuation techniques have to take into account the two main sources of risk affecting financial assets in the market. The correlation between defaults being captured through the market component of every corporate bond or every debt security.