## Online Finance – Pricing Interest Rate Options – Cap Floor Parity

### Cap-Floor Parity

The cap- floor parity says that being long a cap and short a floor with the same strike is equivalent to paying the fixed leg in the swap where the fixed rate is equal to the strike rate.

In other words, Cap – Floor = Swap.

From the above two examples on caps and floors we see that this value is

408.33-669.22 =-260.89.

Calculating an interest rate swap, with fixed rate equal to the strike of 12.5%, notional =100,000, payment frequency = annual and payment dates similar to that of the cap and floor above we see that the value of the swap is as follows:

 Swap Fixed Floating Period Start Period End ti+1 ZCti+1 % Fi % Rate % Cash flow Rate Cash flow PV of Fixed Leg PV of Floating Leg 01/01/10 01/01/11 0.59 12.150 12.150 12.50 7,363.01 12.15% 7,156.85 6,882.11 6,689.41 01/01/11 01/01/12 1.59 12.225 12.269 12.50 12,500.00 12.27% 12,269.24 10,406.76 10,214.64 01/01/12 01/01/13 2.59 12.349 12.583 12.50 12,500.00 12.58% 12,583.37 9,243.60 9,305.25 01/01/13 01/01/14 3.59 12.418 12.595 12.50 12,500.00 12.59% 12,594.82 8,209.61 8,271.89 Total 34,742.08 34,481.20 Price -260.89

As we can see the value of the IRS is equal to the value of the Cap minus the value of the Floor.