## Online Finance – Pricing an Interest Rate Swap – Calculating the MTM of the Swap

### Step 13: Determine the cash flows

The cash flows for the receiving and paying legs are as follows:

 Fixed Leg Payment Floating Leg Payment Period End Rate Cash flow Rate Cash flow 01/01/2011 12.00% 7,200.00 12.65% 7,590.00 01/01/2012 12.00% 12,000 12.77% 12,772.30 01/01/2013 12.00% 12,000 13.09% 13,085.98 01/01/2014 12.00% 12,000 13.09% 13,093.33

The fixed leg payments are straight forward, simply the fixed rate * notional amount, i.e. 12% * 100,000 = 12,000. For the first duration because of the fractional period, the cash flow will be adjusted as follows: fixed rate * tenor*notional amount = 12% *0.6*100,000 = 7,200.

The floating leg payments are based on Interbank Rate + spread where spread is given as 50 basis points. Interbank Rate will be the forward rate derived. Therefore the Floating Rate above is the Forward Rate + Spread and the Cash flow is (Forward Rate+ Spread)*Notional Amount. For the second payment due this is (12.272% + 0.50%) * 100,000 = 12,772.30. As in the case with fixed rate payments, the first payment has to be adjusted because it is only for a fractional period. The cash flow will equal (12.15% + 0.50%) * 0.60 * 100,000 = 7,590.

### Step 14: Discount the cash flows

The next step is to discount the cash flows using the interpolated zero coupon rates. The resulting present values for the sample IRS are given below:

 Period End PV of Fixed Leg PV of Floating Leg 01/01/2011 6,721.29 7,085.36 01/01/2012 9,977.67 10,619.81 01/01/2013 8,862.27 9,664.28 01/01/2014 7,871.04 8,588.18 Total 33,432.2680 35,957.6383

For example for the period end 01/01/2010, the discount cash flows for the fixed leg are calculated as follows:

PV of Fixed Leg = 12000 ÷ (1+12.226%)1.6 = 9,977.67

### Step 15: Calculating the price of the IRS

The price of the interest rate swap is the Net PV of cash flows, i.e. the Total Present Value of the Receiving Leg less the Total Present Value of the Paying Leg.

In our example this is the total PV of Floating Leg- total PV of Fixed Leg = 35,957.64-33,432.27 =2,525.37.

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