Intro

A bank agreed to an interest rate swap with a company. Under the terms of the swap, the bank pays $4\mathrm{.}5\%$ per annum $($compounded semiannually$)$ every six months and receives sixmonth LIBOR in return, for $10$ years on a notional principal of $$200$ million. Today, when the swap has a remaining life of $2\mathrm{.}5$ years, the company defaults on the swap and will not make the promised floating payment, nor will it make any other payments in the future.

OIS rates are $3\mathrm{.}9\%$ for all maturities $($with continuous compounding$)$ and LIBOR rates are $5\mathrm{.}2\%$ for all maturities $($with semiannual compounding$).$ On the last payment date, the $6$month LIBOR forward rate was $4\mathrm{.}5\%.$

Attempt $\frac{1}{3}$ for $10$ pts$.$

Part $1$

What is the loss to the bank $($in absolute terms, $ million$)?$