This is a good sample question from GARP: first, it is not too easy and not too hard; this IMO is about typical of the exam's difficulty and (ii) it does not favor formula memorization: the cited reference is de Servigny, but I do not think you will find the formula in the referenced reading. A formula is not needed, we can apply logic and yet another instance of a no-arbitrage idea - David

9. Suppose the rate on Company A’s one-year zero-coupon bond is 10.0% and the one-year T-bill rate is 8.0%. Assume the T-bill is riskless and the probability of default of Company A’s bond is 10%. What is the LGD of Company A’s bond?

a. 18.18%
b. 81.82%
c. 20.01% 
d. 79.99%

[my adds next, let’s beat this up!]

9b. [hard] Assume instead we are given that the LGD of Company's A's bond is 75% (using Basel II LGD for junior debt under foundation IRB approach). Assuming the credit spread remains 2% (10% - 8%), what is the implied probability of default (PD)?

9c. The answer assumes annual compounding. If we instead assume continuous compounding (i.e., risky bond returns 10% continuous and T-bill returns 8% continuous), what is the implied loss given default (LGD)?. Notice that compounding matters; semi-annual compounding would give a slightly different result.

9d. [hard] As Saunders writes, "Collateral requirements are a method of controlling default risk; they act as a direct substitute for risk premiums in setting required loan rates." Let collateral (recovery) = 1 - Loss given default (LGD) and solve for the credit spread as a function of the probability of default (PD) and the recovery (c).

9e. Which continuous probability distribution--that is reviewed in the assigned Rachev (Fat-tailed and Skewed Asset Return Distributions)--are we most likely to find in use to characterize the loss given default (LGD) or recovery function?

9f. How are recovery rates (1-LGD) estimated?

9g. What are the most important determinants of recovery/LGD?

My answers here in forum or here in wiki.

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