回收率是不是算错了

问题如下：

The head of the fixed-income department of a bank asks a risk analyst to review an outstanding bond issued by Company GRN, a livestock producer. The bond currently trades at a spread of 250 bps over the risk-free interest rate and has a recovery rate of 75%. Senior management of the bank has expressed concern about the slowdown in business activities in the livestock industry, which is expected to last for the next 3 years. The analyst applies the constant hazard rate process in estimating default probability and assumes that, under a stressed market scenario, the bond would trade at a spread of 480 bps over the risk-free interest rate curve, and its recovery rate would decrease to 40%. Assuming the stress scenario prevails, what would be the correct estimate of the probability that Company GRN would not default on its bond over the next 3 years?

选项：

A.

69.8%

B.

78.7%

C.

86.6%

D.

74.1%

解释：

B is correct. First, calculate the hazard rate under stressed condition:

Using the constant hazard rate process, the probability of surviving up to end of year 3 (t = 3) = exp(-λt) = exp(-0.08*3) = 0.7866 = 78.66%.

A is incorrect. 69.77% is the result obtained by incorrectly using the recovery rate and not the LGD in the hazard rate formula.

C is incorrect. 86.59% is the result obtained by incorrectly taking the hazard rate per year to be equal to 4.8% (ignoring the recovery rate). Thus, probability of surviving up to end of year 3 = exp(-λt) = exp(-0.048*3) = 0.8659 = 86.59%.

D is incorrect. 89.14% is the result obtained by incorrectly using the original spread (250 bps) and recovery rate of 75% to calculate the hazard rate per year = 250 / (10,000/0.25) = 0.10, which provides probability of surviving up to end of year 3 = exp(-λt) = exp(-0.10*3) = 0.7401 = 74.1%.