### 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 |