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P1.T3.723. Swaps: valuation with OIS and LIBOR, comparative advantage, and currency swap valuation

Nicole Seaman

Director of FRM Operations
Staff member
Learning objectives: 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 FRAs. Describe the credit risk exposure in a swap position. Identify and describe other types of swaps, including commodity, volatility, and exotic swaps


723.1. A $100.0 million interest rate swap has a remaining life of 15 months. Under the terms of the swap, six-month LIBOR is exchanged for 3.60% per annum (compounded semiannually). Six-month LIBOR forward rates for all maturities are 3.00% (with semiannual compounding). Two months, the six-month LIBOR rate was 2.90% (this assumption is shown in purple cell below). OIS rates for all maturities are 2.80% with continuous compounding.

Which is nearest to the current value of the swap to the counterparty who is paying the floating rate? (Inspired by Hull's EOC Problem 7.2, 10th Edition)

a. -$295,850
b. +$931,000
c. +$1.80 million
d. +$2.14 million

723.2. Suppose the five-year fixed-rate borrowing costs to General Electric (GE) and Qantas Airways (QA) in U.S. dollars (USD) and Australian dollars (AUD) are given as shown in the table below:

Although GE has a comparative advantage in the USD market, QA has a comparative advantage in the AUD market. However, GE wants (or is willing) to borrow Australian dollars and QA wants (or is willing) to borrow US dollars:

The AUDUSD exchange rate is AUDUSD $0.80 (ie, $0.80 USD per 1.0 AUD) and both want to borrow AUD 20.0 million. The currency swap's financial intermediary will charge 20 basis points (0.20%) and can hedge its currency risk (put another way, the financial intermediary is willing to assume the currency risk). If GE and QA want to share equally the gains enabled by the swap, which of the following currency swap best achieves this?

a. GE pays USD 5.60% and QA pays AUD 5.40%
b. GE pays AUD 5.60% and QA pays USD 5.40%
c. GE pays AUD 5.70% and QA pays USD 5.50%
d. GE pays AUD 6.10% and QA pays USD 5.90%

723.3. Suppose that the term structure of risk-free interest rates is flat in both Japan and the United States. The Japanese interest rate is 2.0% per annum and the U.S. interest rate is 3.0% per annum (both with continuous compounding). A financial institution has entered into a currency swap in which it receives 15.0% per annum in yen (¥) and pays 10.0% per annum in dollars ($) once a year. The principals in the two currencies are $10.0 million and ¥1,000.0 million yen. The swap will last only for another two years (i.e., there are only two remaining cash exchanges, although the final principal must be exchanged) and the current exchange rate is ¥110 yen per dollar.

Which is nearest to the current value of the swap to the financial institution, in U.S. dollars?

a. $51,400
b. $725,000
c. $11.33 million
d. $5.65 million

Answers here: