A $$100$ million interest rate swap has a remaining life of $10$ months. Under the terms of the

swap, six$-$month LIBOR is exchanged for $7\%$ per annum $($compounded semi annually$).$ The

average of the bid$-$offer rate being exchanged for six$-$month LIBOR in swaps of all maturities

is currently $5\%$ per annum with continuous compounding. The six$-$month LIBOR rate was

$4\mathrm{.}6\%$ per annum two months ago. What is the current value of the swap to the party paying

floating? What is its value to the party paying fixed? Derive the values both in terms of Bond

$(7$ points$)$ and in terms of FRAs $(7$ points$)$

$($hint $1$: pay attention to the timing and compounding frequencies! The swap has been

negotiated two months ago!$)$

$($hint $2$: In the FRAs valuing approach, the forward rate for the second forward contract is $5\%$

continuously compounded$)$