ABC Inc. has a risk-neutral probability of default of 5% over every half-year period. The loss-given-default (LGD) is 75% of the face value of the debt in ABC Inc. If the risk-free interest rate for one year is 10% on a semiannual compounding basis, find the fair spread for a one-year maturity, semiannual pay CDS contract. Assume that the spread is paid at the beginning of each half-year, while default, if it occurs, occurs at the end of each semiannual period.
A) 228 bps
B) 357 bps
C) 428 bps
D) 551 bps

Question

Quizplus · Accepted Answer

The fair spread can be calculated using the formula:
Fair Spread = (Probability of Default * LGD) / (1 - Probability of Default) * Risk-free rate
Probability of Default = 5%
LGD = 75%
Risk-free rate = 10%
Therefore, Fair Spread = (5% * 75%) / (1 - 5%) * 10% = 357 bps, which is closest to option B.

ABC Inc Has a Risk-Neutral Probability of Default of 5% Over