8. Let T1 and T2 be the times to default (in year) for bonds 1 and 2 respectively. Assume that T1 and T2 are continuous random variables, and they jointly satisfy the Frank copula with =2. Recall that the bivariate Frank copula is given by C(u,v)=1log[1+e1(eu1)(ev1)]. You are given the following probabilities for T1 and T2, 2 (a) (5pts) A policy pays $1000 if at least one of the two bonds defaults by the end of the first year. If the continuously compounded interest rate is 10%, what is the fair value of this policy? (b) (5pts) Find the probability that both of them default during the second year. 8. Let T1 and T2 be the times to default (in year) for bonds 1 and 2 respectively. Assume that T1 and T2 are continuous random variables, and they jointly satisfy the Frank copula with =2. Recall that the bivariate Frank copula is given by C(u,v)=1log[1+e1(eu1)(ev1)]. You are given the following probabilities for T1 and T2, 2 (a) (5pts) A policy pays $1000 if at least one of the two bonds defaults by the end of the first year. If the continuously compounded interest rate is 10%, what is the fair value of this policy? (b) (5pts) Find the probability that both of them default during the second year