13 August 2012

# Interest Rate Swap Tutorial, Part 2 of 5, Fixed Legs

Now that we know the basic terminology and structure of a vanilla interest rate swap we can now look at constructing our fixed leg of our swap by first building our date schedule, then calculating the fixed coupon amounts.

### Interest Rate Swap Fixed Legs

Now that we know the basic terminology and structure of a vanilla interest rate swap we can now look at constructing fixed legs of our swap by first building our date schedule, then calculating the fixed coupon amounts.

For our example swap we will be using the following inputs:

• Notional: \$1,000,000 USD
• Coupon Frequency: Semi-Annual
• Fixed Coupon Amount: 1.24%
• Floating Coupon Index: 6 month USD LIBOR
• Business Day Convention: Modified Following
• Fixed Coupon Daycount: 30/360
• Floating Coupon Daycount: Actual/360
• Effective Date: Nov 14, 2011
• Termination Date: Nov 14, 2016
• We will be valuing our swap as of November 10, 2011.

### Swap Coupon Schedule

First we need to create our schedule of swap coupon dates. We will start from our maturity date and step backwards in semi-annual increments. The first step is to generate our schedule of non-adjusted dates.

Then we adjust our dates using the modified following business day convention.

Note that all the weekend coupon dates have been brought forward to the next Monday.

### Swap Fixed Coupon Amounts

To calculate the amount for each fixed coupon we do the following calculation:

Fixed Coupon = Fixed Rate x Time x Swap Notional Amount

Where:

Fixed Rate = The fixed coupon amount set in the swap confirmation.

Time = Year portion that is calculated by the fixed coupons daycount method.

Swap Notional = The notional amount set in the swap confirmation.

Below is our date schedule with the Time portion calculated using the 30/360 daycount convention. More on daycounts can be found in this document titled Accrual and Daycount conventions.

Note the coupons which are not exactly a half-year due to the business day convention. If our business day convention was no-adjustment all the time periods would have been 0.5. This is a difference between swaps and bonds, as bonds will generally not adjust the coupon amounts for business day conventions, they will simply be 1/(# coupon periods per year) x coupon rate x principal.

The coupon amount for our first coupon will be 1.24% x 1,000,000 x 0.50 = \$6,200.00. Below are the coupon amounts for all of the coupons.

Now that we know our coupon amounts, to find the current fair value of the fixed leg we would present value each coupon and sum them to find the total present value of our fixed leg. To do this we calculate the discount factor for each coupon payment using a discount factor curve which represents our swap curve. We will build our discount factor curve later in this tutorial series.

Thanks to our sister company Resolution for providing us with this series of posts.

Next Article: Swap floating legs including calculating forward rates