In the FRM Handbook, Jorion writes that if yields and default probabilities are “small” then we could simply the probability of default equation to : P = 1/(LGD)*(1-(1+Y)/(1+Y*)) to P = (Y*-Y)/LGD Where LGD is loss given default or (1 - recovery rate) and Y is the risk free rate and Y* is the yield for your risky bond. Probability of default questions and solving for implied yield given default probability in the textbook is typically solved with the more simpler equation. On the 2010 level 1 practice test they solve question #27 (Question to solve for implied yield given LGD, risk free yield and probility of default) with the longer equation. I am trying to see whether, there’s a certain case when you can apply the simpler version, or does GARP prefer us to use the longer version.