The current one-year and two-year zero-coupon rates are 6% and 7%, respectively. The one-year and two-year credit spreads are 1% and 2%, respectively. If the recovery rates on this class of bonds is 40% of face value, which of the following numbers most closely approximates the forward probability of default in year 2? Assume that interest rates and yields are in continuously-compounded and annualized terms. Assume also that if default occurs in any year, the recovered amount is received at the end of that year.
A) 1%
B) 2%
C) 5%
D) 9%

Question

Quizplus · Accepted Answer

The forward probability of default in year 2 is the probability that the bond will default in year 2 given that it has not defaulted in year 1. This can be calculated using the following formula:```Forward probability of default in year 2 = (Credit spread in year 2 - Credit spread in year 1) / (1 - Recovery rate)```Plugging in the given values, we get:```Forward probability of default in year 2 = (2% - 1%) / (1 - 40%) = 5%```Therefore, the answer is C) 5%.

The Current One-Year and Two-Year Zero-Coupon Rates Are 6% and 7