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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?
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?
