Browse By

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.

One thought on “Online Finance – Pricing Interest Rate Options – Cap Floor Parity”

  1. Pingback: Derivatives Posts Index | Learning Corporate Finance
  2. Trackback: Derivatives Posts Index | Learning Corporate Finance

Comments are closed.

Comodo SSL