Physical vs. Risk-neutral Measures in BSM Credit Model

Unlike in equity or fixed income derivative pricing, the concepts of hedging and portfolio replication are usually bypassed in credit modeling, especially when structural models are considered (although Vaillant 2001 discusses replicating credit derivatives using risky bonds, which mirrors replicating interest rate derivatives using risk-free bonds). To facilitate discussion we consider the BSM asset default boundary model. Usually we would ignore the nuances of probability measures and presume physical measure when writing down the asset dynamics. This produces the Distance to Default (DD) under the physical measure, which allows us to compute the Probability of Default (PD) under the physical measure. This is all very well, but when we want to calculate bond (or other security) prices using PD, we have to first convert the PD under P-measure into the PD under Q-measure. Bohn's Active Credit Portfolio Management pp. 177 explains this.