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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:

SwapFixedFloating
Period StartPeriod Endti+1ZCti+1
%
Fi
%
Rate
%
Cash flowRateCash flowPV of Fixed LegPV of Floating Leg
01/01/1001/01/110.5912.15012.15012.507,363.0112.15%7,156.856,882.116,689.41
01/01/1101/01/121.5912.22512.26912.5012,500.0012.27%12,269.2410,406.7610,214.64
01/01/1201/01/132.5912.34912.58312.5012,500.0012.58%12,583.379,243.609,305.25
01/01/1301/01/143.5912.41812.59512.5012,500.0012.59%12,594.828,209.618,271.89
Total34,742.0834,481.20
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.