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 firm 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 / (1 - Recovery rate)) * (1 + Zero-coupon rate in year 1) / (1 + Zero-coupon rate in year 2)Plugging in the given values, we get:Forward probability of default in year 2 = (2% / (1 - 40%)) * (1 + 6%) / (1 + 7%) = 5.08%Therefore, the forward probability of default in year 2 is approximately 5%.

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