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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
      • Vswap = BRs – S0BAUD
    • 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






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