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 prior post covering the two examples on caps and floors, we see that this value is
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:
|Period Start||Period End||ti+1||ZCti+1|
|Cash flow||Rate||Cash flow||PV of Fixed Leg||PV of Floating Leg|
As we can see the value of the IRS is equal to the value of the Cap minus the value of the Floor.