Question

Can you explain to me in details step by step how to work this out

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Suppose that the 1-month USD LIBOR rate (continuously compounded, CC) is 2.1%, the 7-month USD LIBOR rate (CC) is 2.6%, and the 12-month USD LIBOR rate (CC) is 2.8%, all per annum.

In a currency swap, a financial institution pays a fixed rate of 3% per annum on a notional principal of USD 100 million and receives a fixed rate of 2% per annum on a notional principal of EUR 80 million in return, with payments being exchanged once per year and all rates compounded annually. The swap has a remaining life of twelve months. The EUR LIBOR curve (CC) is flat at 1%. The spot exchange rate is 1 USD = 0.84 EUR. Compute the value of the swap (in EUR) to the financial institution.

Answer 1

Remaining period = 12 months

Ie, the final interest rate and notional payment exhange is left

Cash Outflows in USD = (0.03*100) + 100

   = 103 USD

Present value of cash outflows = 103 / (e^0.028)

   = 100.156 USD

{use 12 month LIBOR as discount rate , USD 12 month LIBOR = 2.8% CC }

Cash inflows = (0.02*80) + 80

   = 81.6 EUR

PV of Cash Inflows = 81.6 / e^0.01 = 80.788 EUR

{ EUR LIBOR for 12 month = 1% }

Value of Swap = PV of Cash Inflows - PV of Cash Outflows

= 80.788 EUR - 100.156 USD

= 80.788 EUR - (100.156 * 0.84) EUR

= 80.788 EUR - 84.131 EUR

= - 3.343 EUR