Pricing Default Events : Surprise, Exogeneity and Contagion

In order to derive closed-form expressions of the prices of credit derivatives, the standard models for credit risk usually price the default intensities but not the default events themselves. The default indicator is replaced by an appropriate prediction and the prediction error, that is the default-event surprise, is neglected. Our paper develops an approach to get closed-form expressions for the prices of credit derivatives written on multiple names without neglecting default-event surprises. The approach differs from the standard one, since the default counts cause the factor process under the risk-neutral probability Q, even if this is not the case under the historical probability. This implies that the default intensities under Q do not exist. A numerical illustration shows the potential magnitude of the mispricing when the surprise on credit events is neglected. We also illustrate the effect of the propagation of defaults on the prices of credit derivatives.