We study the calibration of I2, a hybrid structural/reduced form credit model based on incomplete information. The I2 model incorporates the unpredictable nature of default and thereby accounts for positive short spreads and the abrupt drops in prices of credit sensitive securities. To use I2 as a tool to forecast default and price securities in a consistent way, we propose a procedure to calibrate I2 simultaneously to the physical measure and the equilibrium pricing measure implied by traded security prices. We incorporate complementary information held by different markets by pooling data from equity, bond and credit derivative markets.

The basis for this calibration is an analysis of the relationship between the physical measure and prices of credit sensitive securities. We characterize the set of pricing measures by extending a martingale representation result of Kusuoka (1999). The credit risk premium linking the pricing measure to the physical measure has two components. One accounts for investors' aversion towards diffusive price volatility. The other reflects aversion toward the default event itself.

The calibration is facilitated by the I2 reduced form security pricing formulae. The results include market implied estimates of the event risk premium, the physical probability of default and the fractional recovery rate of firm debt.