Very interesting to see what is going on in the UK regarding the mis-selling of swaps to small businesses.

This article in The Telegraph talks about the FSA’s potential sanctions against the four major banks and the growing discontent amongst those now facing significant financial loss.

Martin Wheatley told MPs the UK's largest banks had "questions to answer" over their sale of interest rate swap to SMEs (courtesy of The Telegraph)

“The FSA’s review followed an investigation by The Sunday Telegraph and The Daily Telegraph, which uncovered evidence of widespread mis-selling of complex interest rate derivatives by banks.”

This once again highlights the perils of placing 100% trust in your bank’s advice when it comes to hedging any type of financial risk.  Whether you are looking to mitigate exposure against interest rate shifts or currency fluctuations you should only enter into derivative transactions that you fully understand and that you can explain to your Board.

This echoes the warnings in Richard Eaddy’s recently-published report “7 things your bank won’t tell you about currency hedging”.  You can download this free report here

This unfortunate situation also clearly demonstrates the necessity of knowing the value of your swaps (or any derivative transaction), so that when the unexpected happens, you are fully aware of the implications on your position and are prepared to act accordingly.

If only they had been using Hedgebook…

Swap Curve

In the final article in this series, we will continue to build out our discount factor curve using longer datedpar swap ratesPar Swap rates are quoted rates that reflect the fixed coupon for a swap that would have a zero value at inception.

Let look at our zero curve that we have built so far using LIBOR rates.

zero curve

We are now going to build out this curve out to 30 years using par swap rates. These rates are as of Nov 10, 2011, and reflect USD par swap rates for semi-annual LIBOR swaps. The daycount convention is 30/360 ISDA.

par swap rates

Also keep in mind that these rates reflect the settlement conventions, so the one year rate is for an effective date of Nov 14, 2011 and termination of Nov 14, 2012. If we were to price a one year swap from the curve we have built so far, we can derive the 6mo discount factor, but we are currently missing the 1year factor. Since we know the swap should be worth par if we receive the principal at maturity, then the formula for a one year swap is:

1 year par swap rate resized 600

Notice that the T’s would be adjusted for holidays & weekends and are calculated using the appropriate discount factor. We can rearrange our formula to solve for df(1year).

swap bootstrapping

Using our example data:

discount factor par swap

We calculate the missing discount factor as: 0.99422634. But, this for a swap which settles on November 14th, and we are building our curve as of November 10th. So we need to multiple this by the discount factor for November 14th to present value the swap to November 10th. So the discount factor we use in our curve for Nov 14, 2012 is 0.9942107.

We continue by calculating discount factors for all the cashflow dates for our par swap rates. The next step is to calculate the discount factor for May 14, 2013. Our first step is to calculate a par swap rate for this date as it is not an input into our curve. We linear interpolate a rate between our 1 year and 2 year rates.

1.5 year par swap rate = 1 year + (2 year – 1 year)/365 x days

= .58% + (.60%-.58%)/365 x 181 = 0.589918%

We now can solve for the missing discount factor, continuing our bootstrapping through the curve.

zero curve construction

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

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.































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.


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:


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.

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

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.


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