Solution for QID #1118: For a maturity of T = 1 year, let the default probability of | StudyHelpMe

For a maturity of T = 1 year, let the default probability of a rm be p = 0:1. De ne an indicator variable d = 1 if default occurs and d = 0 if default does not occur. (a) What is E(d)? (b) What is V ar(d)? 7. Given two rms with default probabilities p1 = 0:1, p2 = 0:2. The correlation of joint default (d1; d2) = 0:5 where d1; d2 are indicator variables for default of each rm. What is the probability of both rms defaulting? 8. If Pr[d1 d2] = 0:08 and p1 = 0:1, p2 = 0:2, what is Pr(d1jd2) and Pr(d2jd1)? Note the not so obvious outcome that a very small probability of joint default may actually underlie a high probability of conditional default. 9. Given two rms, if the probability of neither defaulting is 80% and the probability of each defaulting is p1 = 0:1 and p2 = 0:2, what is the probability of both defaulting? 10. If Pr(d1 d2) = 0:01 and p1 = 0:1; p2 = 0:2, what is the probability of exactly one default?