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 | t_{i+1} | ZCt_{i+1 } % | F_{i } % | 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.
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