# derivatives question doubt

can someone help me with this question. Am not undestanding the calculation of value of the \$ fixed side and value of € fixed side (in €) .Thanks.

1. A bank entered into a 1-year currency swap with quarterly payments 200 days ago by agreeing to swap \$1,000,000 for €800,000. The bank agreed to pay an annual fixed rate of 5% on the €800,000 and receive a fixed rate of 4.2% on the \$1,000,000. Current LIBOR and Euribor rates and present value factors are shown in the following table. Rate Present Value Factor 70-day LIBOR 4.0% 0.9923 90-day LIBOR 4.4% 0.9891 160-day LIBOR 4.8% 0.9791 180-day LIBOR 5.2% 0.9747

70-day Euribor 5.2% 0.9900 90-day Euribor 5.6% 0.9862 160-day Euribor 6.1% 0.9736 180-day Euribor 6.3% 0.9695 The current spot exchange rate is €0.75 per \$1.00. The value of the swap to the bank today is closest to: A. –\$64,888. B. –\$42,049. C. \$42,049.

Solution given

coupon on \$ fixed side = \$1,000,000 × (0.042 / 4) = 10,500 value of the fixed side = (0.9923 × \$10,500) + (0.9791 × \$1,010,500) = 999,800 coupon on € fixed side = €800,000 × (0.05 / 4) = €10,000 value of € fixed side (in €) = (0.9900 × €10,000) + (0.9736 × €810,000) = €798,516 value of € fixed side (in ) = € value of swap to bank = \$999,800 – \$1,064,688 = –\$64,888

You have to convert €798,516 to \$ at €0.75 = \$1.00; they didn’t show that.

value of the \$ fixed side = (0.9923 × \$10,500) + (0.9791 × \$1,010,500) = \$999,800

value of € fixed side (in €) = (0.9900 × €10,000) + (0.9736 × €810,000) = €798,516

As it was a 1-year (360-day), quarterly-pay swap, there are 2 payments left: a principal and interest payment in 160 (= 360 − 200) days, and an interest payment in 70 (= 160 − 90) days.

For the USD leg, the principal is USD1,000,000 and the interest is USD10,500. For the EUR leg, the principal is EUR800,000 and the interest is EUR10,000.

The 70-day present-value factor (PVF) for USD is 0.9923 and the 160-day PVF is 0.9791. The 70-day and 160-day PVFs for EUR are 0.9900 and 0.9736, respectively.

Therefore,

• PV(USD) = PV(70-day USD payment) + PV(160-day USD payment) = (0.9923 × USD10,500) + (0.9791 × USD1,010,500) = USD999,800
• PV(EUR) = PV(70-day EUR payment) + PV(160-day EUR payment) = (0.9900 × EUR10,000) + (0.9736 × EUR810,000) = EUR798,516

EUR798,516 × USD1.0/EUR0.75 = USD1,064,688

Value of the swap = PV(what you will receive) − PV(what you will pay) = USD999,800 − USD1,064,688 = USD−64,888

Got it!! Thanks a lot.

My pleasure.