Some time ago a financial institution entered a swap where it agreed to receive 3.8% per annum

with semi-annual compounding and pay LIBOR every six months on $100 million. The swap has

exactly 13 months left, and the next exchange is in one month. The one-month LIBOR rate is 3.4%

per annum with semi-annual compounding, The six-month LIBOR rate that was determined five

months ago is 3.2% per annum with semi-annual compounding. Forward LIBOR rates for the 1-to-

7-month period and the 7-to-13-month period are 3.7% and 3.9% per annum respectively, with

continuous compounding. Risk-free zero rates for maturities 1 and 7 months are 3.1% and 3.5% per annum respectively, with continuous compounding. The forward rate for the 7 to 13-month period risk-free rate is 4.2% per annum with continuous compounding. Obtain the value

of the swap for the financial institution.

Show all of your work and remember: Is the compounding frequency (annual, semi-annual, quarterly, continuous,) given in a rate the same one I need? (Remember that in the formulas some rates have to be in continuous compounding and some in different compounding or do I need to transform the rates first to the appropriate one? Am I using the correct rate for example, should I be using a spot (zero) rate or a forward rate? In some cases, you may need to use a zero rate, but the rate given is a forward rate. If this happens you will need to first find the appropriate zero rate.