Valuation of Currency Swaps
- Just like IRS this swap can be valued using bonds approach and FRA approach
- Valuation using bonds
- Party 1 is receiving payments in Rupees while paying in AUDs. Hence we can say that he is long a rupee bond and short an AUD bond
- The value of the swap will be the difference in the PV of the bonds
- V_{swap }= B_{Rs} â€“ S_{0}B_{AUD}
- Where:
- S0 is the current spot exchange rate between Rs and AUDs
- Valuation as a portfolio of forward contracts
- In this case we determine the forward exchange rate at each point when the swap payments occur
- The foreign currency is converted using the forward exchange rate
- In the example above the 1 year, 2 year, 3 year, 4 year forward rate for USD-AUD exchange is used for converting AUD cash flows to USD every year
- This is then discounted back to the present value to give the value of the swap
Question:
The USD interest rate is 4% per annum and the AUD rate is 6% per annum. Assume that the term structure of interest rates is flat in the US and Australia. Assume current value of AUD to be $0.91. Company ABC, under the terms of a swap agreement, pays 7% per annum in AUD and receives 3% per annum in US$. The principal in the US is 10million USD and that in Australia is 11million AUD. Payments are exchanged each year and the swap will last for 3 more years. Determine the value of swap assuming continuous compounding in all interest rates.
Solution:
Valuation of currency swap in terms of bonds (millions):
Time |
Cash Flow ($) |
Present Value |
Cash Flow (AUD) |
Present Value |
1 |
0.3 |
0.2885 |
0.77 |
0.7264 |
2 |
0.3 |
0.2774 |
0.77 |
0.6853 |
3 |
0.3 |
0.2667 |
0.77 |
0.6465 |
3 |
10.0 |
8.8900 |
11 |
9.2358 |
Total |
9.7225 |
Total |
11.2940 |