Learning objectives: Calculate the value of a plain vanilla interest rate swap from a sequence of FRAs. Explain the mechanics of a currency swap and compute its cash flows. Explain how a currency swap can be used to transform an asset or liability and calculate the resulting cash flows. Calculate the value of a currency swap based on two simultaneous bond positions. Calculate the value of a currency swap based on a sequence of forward exchange rates. Identify and describe other types of swaps, including commodity, volatility, credit default, and exotic swaps
Questions:
23.8.1. Some time ago, a bank entered into a receive-fixed, pay-floating interest rate swap where it agreed to receive semi-annual payments at a rate of 6.0% per annum and pay the SOFR six-month rate on a notional of $500.0 million. The swap now has a remaining life of 1.30 years. Therefore, payments will be exchanged in 0.30, 080, and 1.30 years.
The continuously compounded risk-free rates (based on SOFR) are 4.30%, 4.60%, and 5.15% for, respectively, 0.30, 0.80, and 1.30 years. Because the risk-free rate observed in the last 0.20 years was 3.90%, and it contains 40% of the days that determine the next exchange), the floating rate for the exchange in 0.30 years is 40%*3.90% + 60%*4.30% = 4.140%. The floating rate for exchange at 0.8 years is the forward rate for the period between 0.30 and 0.80 years. This is 4.78% with continuous compounding (aka, c.c.). Similarly, the floating rate for the exchange at 1.30 years is the forward rate for the period between 0.80 years and 1.20 years. This is 6.030% with continuous compounding. The semi-annual equivalents of these rates are 4.1831%, 4.8376%, and 6.1218%.
Which of the following is nearest to the value of the swap to the bank?
a. -12.3 million
b. +7.0 million
c. + 22.8 million
d. +45.0 million
23.8.2. About swaps, each of the following is true EXCEPT which is false?
a. At any given time during the life of a bilateral OTC swap, at least one of the counterparties incurs both market and credit risk
b. A difference between the typical interest rate swap and currency swap is whether the principal (aka, notional principal) is exchanged
c. Both overnight indexed swaps (OIS) and volatility swaps need to determine a realized (aka, actual) financial variable at the end of a period or tenor
d. A commercial bank funded by short-term floating-rate deposits that extends long-term fixed-rate loans can hedge market risk by entering a swap where it is the floating-rate payer and fixed-rate receiver
23.8.3. Consider a currency swap where interest on euros at the rate of 7.0% is paid, and interest on U.S. dollars at 8.0% is received. The euro principal is 100.0 million euros, and the USD principal is 110 million dollars. Interest is exchanged once per year, and three years remain, ie.., three more exchanges, including the final swap of principal. The current exchange rate is EURUSD $1.20. The risk-free rates in dollars and euros are 5.0% and 4.0%, respectively. All rates are given with annual compounding. In US dollars, which of the following is nearest to the value of this pay euros-receive dollars currency swap?
a. -11.0 million
b. +3.3 million
c. +12.9 million
d. +25.5 million
Answers here:
Questions:
23.8.1. Some time ago, a bank entered into a receive-fixed, pay-floating interest rate swap where it agreed to receive semi-annual payments at a rate of 6.0% per annum and pay the SOFR six-month rate on a notional of $500.0 million. The swap now has a remaining life of 1.30 years. Therefore, payments will be exchanged in 0.30, 080, and 1.30 years.
The continuously compounded risk-free rates (based on SOFR) are 4.30%, 4.60%, and 5.15% for, respectively, 0.30, 0.80, and 1.30 years. Because the risk-free rate observed in the last 0.20 years was 3.90%, and it contains 40% of the days that determine the next exchange), the floating rate for the exchange in 0.30 years is 40%*3.90% + 60%*4.30% = 4.140%. The floating rate for exchange at 0.8 years is the forward rate for the period between 0.30 and 0.80 years. This is 4.78% with continuous compounding (aka, c.c.). Similarly, the floating rate for the exchange at 1.30 years is the forward rate for the period between 0.80 years and 1.20 years. This is 6.030% with continuous compounding. The semi-annual equivalents of these rates are 4.1831%, 4.8376%, and 6.1218%.
Which of the following is nearest to the value of the swap to the bank?
a. -12.3 million
b. +7.0 million
c. + 22.8 million
d. +45.0 million
23.8.2. About swaps, each of the following is true EXCEPT which is false?
a. At any given time during the life of a bilateral OTC swap, at least one of the counterparties incurs both market and credit risk
b. A difference between the typical interest rate swap and currency swap is whether the principal (aka, notional principal) is exchanged
c. Both overnight indexed swaps (OIS) and volatility swaps need to determine a realized (aka, actual) financial variable at the end of a period or tenor
d. A commercial bank funded by short-term floating-rate deposits that extends long-term fixed-rate loans can hedge market risk by entering a swap where it is the floating-rate payer and fixed-rate receiver
23.8.3. Consider a currency swap where interest on euros at the rate of 7.0% is paid, and interest on U.S. dollars at 8.0% is received. The euro principal is 100.0 million euros, and the USD principal is 110 million dollars. Interest is exchanged once per year, and three years remain, ie.., three more exchanges, including the final swap of principal. The current exchange rate is EURUSD $1.20. The risk-free rates in dollars and euros are 5.0% and 4.0%, respectively. All rates are given with annual compounding. In US dollars, which of the following is nearest to the value of this pay euros-receive dollars currency swap?
a. -11.0 million
b. +3.3 million
c. +12.9 million
d. +25.5 million
Answers here:
