Can you explain to me in details step by step how to work this out --- Suppose t
ID: 2815143 • Letter: C
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.
Explanation / Answer
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 / (e0.028)
= 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 / e0.01 = 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
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