Default compensator, incomplete information, and the term structure of credit spreads

We provide a framework for the analysis of term structures of credit spreads on corporate bonds in the presence of informational asymmetries. While bond investors observe default incidents, we suppose that they have incomplete information on the firm's assets and/or the threshold asset level at which informed equity investors liquidate the firm. As a natural tool for the characterization of conditional default probabilities, prices of default-contingent claims, and credit spreads, we construct the compensator of default in terms of investors' threshold prior and the conditional running minimum asset distribution. With perfect asset observation, a new phenomenon appears: the default compensator is singular. Here an arrival intensity for default does not exist even though the default is completely unpredictable. In a setting where the assets of the firm follow a geometric Brownian motion, we show that the term structure of credit spreads is decreasing or hump-shaped, depending on the level of the current asset value. Spreads for maturities going to zero are only positive if the assets are at an historic low and the firm is quite risky. With imperfect asset observation, an arrival intensity for default does exist. This intensity is characterized through the compensator. In the geometric Brownian motion setting, the spread term structure is always decreasing with strictly positive spreads.