Question

Suppose the term structure of interest rates is flat in the United States and Canada. The USD interest rate is 3% per annum and the CAD interest rate is 3.5% per annum. The current value of one CAD is 0.73 USD. In a swap agreement, a financial institution pays 6% per annum in CAD and receives 5.5% per annum in USD. The principals in the two currencies are $10 million USD and $14 million CAD. Payments are exchanged every 6 months, with one exchange having just taken place. The swap will last two more years. What is the value of the swap to the financial institution? Assume all interest rates are continuously compounded.

Answer 1

The swap involves exchanging the USD interest of 12 * .04 = 0.48 million for AUD interest of 20 * 0.08 = 1.6 million

The principal amounts are also exchanged at the end of the life of the swap.

All interest rates are continuously compounded.

The value of the USD bond is (r = 7% = 0.07):

= 0.48 * e-0.07*1 + (12+0.48) * e-0.07*2

= 0.48 * 0.93239 + 12.48 * 0.869358

= 11.29713504 million USD

The value of the AUD bond is (r = 9% = 0.09):

= 1.6 * e-0.09*1 + (20+1.6) * e-0.09*2

= 1.6 * 0.91393 + 21.6 * 0.83527

= 19.50412 million AUD

So, value of swap in million USD is

= 19.50412 * 0.62 - 11.29713504

= 0.79541936 million USD

=0.795 million USD