Question

Q.11 Consider a one year currency swap with quarterly payments. The domestic currency is the U.S dollar and the foreign currency is the Euro. The current exchange rate is $0.86 per euro.

1. Calculate the annualized fixed rates for dollars and euros. The current U.S term structure is the same as in problem 9, Part A.

Lo(90)= 0.0656

Lo(180)= 0.0640

Lo(270)= 0.0621

Lo((360)= 0.0599

The Euribor term structure is

Lo^euro(90)= 0.0682

Lo^euro(180)= 0.0673

Lo^euro(270)=0.0661

Lo^euro(360)=0.0668

2. Now move forward 30 days. The new exchange rate is $0.82 per euro and the new U.S term structure is the same as in problem 9 Part B;

L30(60)=0.0384

L30(150)=0.0379

L30(240)=0.0382

L30(330)=0.0406

The new Euribor term structure is

L30^euro(60)=0.0583

L30^euro(150)=0.0605

L30^euro(240)=0.0613

L30^euro(330)=0.0651

              Assume that notational principle is $1 or the corresponding amount in euros.

              Calculate the market values of the following swaps;

1. Pay Euro fixed and received $ fixed
2. Pay euro floating and receive $ fixed
3. Pay euro floating and receive $ floating
4. Pay euro fixed and receive $ floating

Answer 1

Lets first calculate $ and Euro discount factor.

For $:

Z 90 day = 1 / (1+(0.0656*90/360)) = 0.983865

Z 180 day = 1 / (1+(0.064*180/360) = 0.968992

Z 270 day = 1 / (1+(0.0621*270/360) = 0.955498

Z 360 days = 1 / (1+(0.0599*360/360) = 0.943485

The quarterly fixed rate on $ swap is:

= (1-0.943485)/0.983865+0.968992+0.955498+0.943485

= 1.47%

Annual Rate = 1.47%*360/90 = 5.88%

Similarly repeating for Euro

Z 90days = 0.983236

Z 180days = 0.967445

Z 270 days = 0.952767

Z 360 days = 0.937383

Quartery rate = 1.63%

Annual Rate = 6.52%