(a)Firm XYZ is holding a long position in a $20 million interest rate swap that has a Remaining life of 15 months. Under the terms of the swap, six-month LIBOR is exchanged for 4% per annum every six months (both rates are compounded semi-annually). The interest rate for all maturities is currently 5% per annum with continuous compounding. The six-month LIBOR rate was 4.5% per annum three months ago. Compute the current value of the swap to firm XYZ. Show all workings

(b)In the context of risk-neutral valuation, describe the main challenge in the pricing of interest rate options. What is the solution which involves a zero-coupon bond with a $1 face value?