# 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 â€“ 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
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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