Probability of default under Merton

[pascalb]

The Black-Scholes option pricing formula has d1=ln(S/K)+.... Yet, the Stulz reading and in the notes, has "BSM risk-neutral d2 is: d2=ln (S/K...) (p.8 of the notes). Should be not d1 and I understand replacing the risk-free for the mean drift. Trying to understand why we move from d1 to d2 by replacing the risk-free rate for the drift rate.

 

[David Harper CFA FRM]

@pascalb We don't, Merton's distance to default (DD) is still similar to BSM d2 (d1 and d2 look very similar ...) but with an actual drift rather than Rf rate, please see https://forum.bionicturtle.com/threads/merton-model-a-summary-of-the-issues.5646/