# exercise: currency swap

Discussion in 'P1.T3. Financial Markets & Products (30%)' started by fullofquestions, Sep 28, 2009.

1. ### fullofquestionsNew Member

Consider the following currency swap: Counterparty A swaps 3% on 25 million
USD for 7.5% on 20 million Sterling. There are now 18 months remaining in the
swap, the term structures of interest rates are flat in both countries with USD
rates currently at 4.25% and Sterling rates currently at 7.75%. The current
Sterling/USD exchange rate is 1.65. Calculate the value of the swap. Use
continuous compounding. Assume 6 months until the next annual coupon and
use current market rates to discount.
a. -1,237,500 USD
b. -4,893,963 USD
c. -7,422,044 USD (ANS)
d. -8,250,000 USD

First, it seems to me that this question takes a long time. Let me know if there is a faster way.

Fist question: could someone confirm the mechanics of the transaction?
T=+6months:
Counterparty A pays 3% on 25M USD discounted at 4.25% annually = - 750Ke(-.0425/2) = -734,230.6
Counterparty A receives 7.5% on 20M GBP discounted at 7.75% annually = 1.5Me(-.0775/2) = 1,442,986.8
T=+12months:
Counterparty A pays 3% on 25M USD discounted at 4.25% annually = - 750Ke(-.0425) = -718,792.8
Counterparty A receives 7.5% on 20M GBP discounted at 7.75% annually = 1.5Me(-.0775) = 1,388,140.5
T=+18months:
Counterparty A pays 3% on 25M USD discounted at 4.25% annually = - 750Ke(-.0425*1.5) = -703,679.9
Counterparty A receives 7.5% on 20M GBP discounted at 7.75% annually = 1.5Me(-.0775*1.5) = 1,335,378.9

Total:
Cpty A pays (2,156,703) USD
Cpty A receives 4,166,506.25 @ 1.65 USD per 1 GBP = 2,525,155

Adding these up is totally wrong. Any thoughts/tips?

2. ### rahul.goylMember

Hi David/FOQ
Even I am not getting this correct, below are my calculation. Would need your help. I think FOQ is missing out on the Notional to be added at the last node. I tried adding notional but still away from the Answer.

Fixed Disc Fac USD Floating Disc Fac GBP
375000 0.97897419 367115.3214 750000 0.961991177 721493.3827
750000 0.958390466 718792.8491 1500000 0.925427024 1388140.537
26125000 0.93823953 24511507.72 22250000 0.890252632 19808121.07
Pay 25597415.89 Rec 21917754.99
36164295.73
Ans : (-10566879.84)

Thanks
Rahul