1. 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

1. 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?