## Introducing floating legs

### For our example interest rate 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.

## Calculating Forward Rates

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

**Floating Coupon = Forward Rate x Time x Swap Notional Amount**

Where:

**Forward Rate** = The floating rate determined from our zero curve (swap curve)

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

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

In the next couple articles we will go through the process of building our zero curve that will be used for the swap pricing. In the meantime we will use the following curve to calculate our forward rates and discount our cashflows.

The numbers at each date reflect the **time value of money** principle and reflect what $1 in the future is worth today for each given date.

Let’s look at our first coupon period from Nov 14, 2011 to May 14, 2012. To calculate the forward rate which is expressed as a **simple interest rate** we use the following formula:

where:

Solving for R

In our example we divide the discount factor for May 14, 2012 by the discount factor for Nov 14, 2011 to calculate DF.

0.9966889 / 0.9999843 = 0.9967046

T is calculated using Actual/360. The number of days in our coupon period is 182. 182/360 = 0.505556

R = (1 – 0.9967046) / (0.9967046 x 0.505556) = 0.654%

Our first coupon amount therefore is:

**Floating Coupon = Forward Rate x Time x Swap Notional Amount**

$ 3,306.33 = 0.654% x 0.505556 x $1,000,000

Below is a table with our forward rate calculations & floating coupon amounts for the rest of our coupons.

The final step to calculate a fair value for our complete swap is to present value each floating coupon amount and fixed coupon amount using the discount factor for the coupon date.

**Present Value of Net Coupon is**

**(Floating Coupon Amount – Fixed Coupon Amount) x Discount Factor**

Our net fair value of this swap is $ 0.00 as of November 10, 2011.

So far in this tutorial we have gone through basic swap terminology, fixed leg coupon calculations, calculating forward rates for floating legs coupon calculations and discounted our cashflows to value a swap.

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

Next Article: Present value of money & bootstrapping a swap curve