Hi all,
Came across a currency swap question, but I don’t understand the solution.
Consider a 1-year currency swap with semiannual payments. The two currencies are the USD and the EUR. The current exchange rate is $1.20/€.
The term structures of interest rates for USD and EUR at initiation of the swap are: Days LIBOR Euribor 180 days 6.2% 5.0% 360 days 7.5% 5.6%
The term structures of interest rates for USD and EUR on Day 60 of the swap are: Days LIBOR Euribor 120 days 6.8% 5.8% 300 days 7.9% 6.1%
Given that the exchange rate on Day 60 of the swap is 1.1/€, the value of the swap to the pay fixed and receive € fixed side of the swap is closest to:
a) $53,661.60 b) $1,309,836.30 c) $2,566,011.00
Solution:
USD
B60(120) = 0.9778 B60(300) = 0.9382 Sum = 1.916 PSFR(USD) = 0.0367
EUR
B60(120) = 0.9810 B60(300) = 0.9516 Sum = 1.9326 PSFR(EUR) = 0.0276
V = NAPC × (PSFR(PC) × Sum of PV factors of remaining coupon paymentst + PV factor for return of notional amount
V = $15m × ( 0.0367 × 1.916 + 0.9382) − ($1.1/€)(€12.5m) × ( 0.0276 × 1.9326 + 0.9516) = $15,127,758 − 13,817,921.7 = $1,309,836.30
I don’t understand how the solutions derive PSFR USD and EUR as 0.0367 and 0.0276. The figures I get for both are :
PSFR (USD) = (1-0.9382)/(0.9778+0.9382) = 0.03226
PSFR (EUR) = (1-0.9516)/(0.9810+0.9516) = 0.025
I’m guess its some sort of pro-rating of rates since its day 60 of the swap, but I can’t seem to get the figures the solution show.
Any help is appreciated. Thank you in advance.