We have two B$-$rated bonds, with one$-$year default probability at $3\mathrm{.}5\%.$ Suppose that the

interest rate is $4\mathrm{.}1\%,$ and their default times satisfy the Gaussian copula with $\backslash$rho $=0\mathrm{.}6,$

calculate the following expected present values, i$.$e$.$ fair prices.

$($a$)$ What is the fair price of a first$-$to$-$default swap which pays $$1,000,000$ if at least one of

them defaults by the end of the first year?

$($b$)$ How about a second$-$to$-$default swap which pays $$1,000,000$ if both default in the first

year