Interest Rate Swap Tutorial, Part 4 of 5, Swap Curve Construction

Zero Curve

In the previous articles we described basic swap terminology, created coupon schedules and calculated fixed and floating coupon amounts. We also present valued our cashflows and calculated forward rates from our Zero Curve. A zero curve is a series of discount factors which represent the value today of one dollar received in the future.

In this article we are going to build up the short end of our discount factor curve using LIBOR rates. 

Here are the rates we are going to use. They represent USD Libor as of November 10, 2011.

ON

0.1410%

T/N

0.1410%

1W

0.1910%

2W

0.2090%

1M

0.2490%

2M

0.3450%

3M

0.4570%

4M

0.5230%

5M

0.5860%

6M

0.6540%

7M

0.7080%

8M

0.7540%

9M

0.8080%

10M

0.8570%

11M

0.9130%

Our first step will be to calculate the start & end dates for each of our LIBOR. Our TN settles in one day, and the other rates all settle in two days. We also will need to calculate the exact number of days in each period. Keep in mind that November 12th was a Saturday so our TN rate ends on the Monday, November 14th.

libor curve

Our formula for converting rates (simple interest) to discount factors is

simple interest discount factor

Where R is our LIBOR rates and T is our time calculated by the appropriate daycount convention, which in this case is Actual/360.

So our first discount factor reflecting the overnight rate is:

overnight rate

which equals: 0.999996083348673.

Bootstrapping

For our subsequent rates, they settle in the future. So when we calculate their discount factors, we will need to discount again from their settle date. See the image below to see the time frame each rate represents.

zero curve bootstrapping

Because we need the previous discount factors to calculate the next discount factor in our curve, the process is known asbootstrapping.

To calculate the discount factor for TN:

TN rate LIBOR

Which equals; 0.999988250138061 x 0.999996083348673 = 0.999984333532754

We continue the process for each time period, to build up the short end of our curve.

libor discount factors

We have shown how to convert LIBOR rates into a discount factor curve, while taking into consideration the settle dates of the LIBOR rates.

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

Next Article: Building the long end of the curve using Par Swap Rates.

Is your beloved spreadsheet costing you a fortune?

Why is it that we love our spreadsheets so much?

They are labour intensive, they’re often very complex and we all know about the risk of errors, yet we continue to nurture and protect our increasingly unwieldy spreadsheets like they are family.

In spite of the seriousness of the potential risks, including lost revenue and profits, mispricing and poor decision making, fraud due to malicious tampering, and difficulties in demonstrating fiduciary and regulatory compliance; New Zealand businesses have been reluctant to end their love affair with the trusty spreadsheet.

(I like this cartoon from Jocelyn Paine’s blog)

Don’t get us wrong, we can relate to the attachment to spreadsheets, but there is a time and a place for everything and we don’t think spreadsheets are the place for managing complex financial derivatives…

If you would like to entertain yourself reading about other people’s misfortune at the hands of their trusty spreadsheets you may enjoy reading this article from CIO magazine about “Eight of the worst spreadsheet blunders of all time”

If you are still convinced that spreadsheets are right for you, or just can’t bear to part with them, this article provides some good tips on how to minimise your risk (courtesy of www.louisepryor.com).

But if you think it’s time to move your organisation’s financial risk management into the 21st century, we would love to show you Hedgebook.