# Pricing Cross Currency Swaps

## Fixed for Fixed Currency Swap

The fixed for fixed cross currency swap will be priced as a portfolio of forward foreign exchange contracts, where each exchange of payments is a forward foreign exchange contract. The assumption is that the forward exchange rates will be realized. The forward exchange rates will be calculated using the following equation:

where r and rf are compounded continuously

or

, if the interest rates were compounded on a discrete basis.

In our example below we will assume discrete compounding. We assume that the financial institution makes fixed USD payments and in return receives fixed YEN payments. Also we assume that the principal is exchanged at the beginning and end of the trade.

The payments in the swap will be as follows:

Stage 1: Principal Exchange

The principals/ notional amounts will be exchanged at the current exchange rate. The principal amounts in the two currencies are USD 10 million or 910 million yen calculated at the current exchange of 1USD = 91 yen. The financial institution will pay the yen notional and receive USD principal amount from the counterparty.

Stage 2: Interest flows

The currency swap that the financial institution has entered has the following terms regarding interest payments. It will receive 6% of the notional amount per annum in yen and pay 5% per annum in dollars on an annual basis.

Stage 3: Principal Exchange

At maturity, it will receive the yen notional and pay the USD notional amount.

The other terms of the contract will be as follows:

• The payments are to be made on the 1st day of the year starting 1/1/2011 and ending on the maturity date
• The maturity date is 1/1/2014
• The valuation or pricing date is 31/5/2010
• The day count convention used in calculating the interest rate payments for both legs is Actual/365.
• The LIBOR/ SWAP zero curve rates for USD and JPY (yen) are assumed to have been calculated as follows:

The results are given in the spread sheet below.

Just a few notes on the worksheet:

1. Forward exchange rate is calculated using the formula given above, i.e. . For example for period ended 1/1/2012, the forward exchange rate = (1/91)*(1.0122/1.0056)^1.59 = 0.01110.
2. Dollar value of yen cash flow is calculated using this forward exchange rate to convert the yen cash flow into dollar. For example for period ended 1/1/2012, the dollar value of yen cash flow is = fixed rate applicable to yen* yen notional amount*forward exchange rate = 6%*910,000,000*0.01110=USD606,213.
3. Net Cash Flow = Dollar Value of yen cash flow (receiving leg) – USD Cash Flow (paying leg) =606213-500000 =USD 106,213.
4. Present Value of Net Cash Flow is the Net cash flow discounted to the valuation date using the USD zero curve interpolated rates. For example for period ended 1/1/2012 the PV =106213/(1.0122)^1.59 =USD104,190

The price or value of the fixed for fixed currency swap is the sum of the present values of each future net cash flow payment.