# Swap rates versus Eurior/Libor - why does 1yr Euribor not = 1yr Swap?

Hi guys, I get the feeling I should really know the answer to this, but hope someone branier can shine light on the following. I need to create a cost of carry calculator at work - so bootstrapping aplenty. But I’ve noticed something I can’t quite figure out As of yesterday the 12m Euribor rate is 5.079. And the 1 year Swap rate (from FT.com) is 4.26. Why are these so different? Swap rate is the difference between Spot and Forward and Euribor is Spot - can I get to one number using the other? How might this work? I haven’t studied for months… perhaps this is the wake-up call I need ahead of re-sitting LII! Thanks, Andrew

It’s pretty messed isn’t it? The numbers are more different than we make them out to be. 1 yr Euribor is the rate banks borrow from one another for a year. Banks don’t want to lend to each other for a year because in a year there won’t be any banks (not sure about that part). The Euro Swap rate is the rate at which a swap is settled, not a rate at which actual money is lent. The 1 yr swap is settled quarterly based on 3 month money. If we are going into a depression we would expect that interest rates will go down so future swap payments should decrease from here. So the 1 yr swap rate being less than 3 month Euribor is a sign that we think we are going into a recession. If credit wasn’t an issue, you could arbitrage the world right now.

in addition: the “swap rate” only has meaning with reference to the term of the floating rate (1m, 3m, 6m etc.) The resulting swap curves all look different. I kmost of the time people talk about “the” swap rate, they mean the one wrt 6m floating rates payments. (I think this is so in Bloomberg, like EUSAx…) regards

Hi guys thanks for your replies - this makes sense. I’ve got a follow-up question though… So with the swap rates/ series of future spot rates known, if I plot these on a graph there’s a straight line between each year. How can I determine however the equivalent fixed rate for say 1 year and 37 days in or even the rate up to the 22nd year if I want to track the curve between the point and not the straight line? Sample data from 24/10 below fyi. I’ve seen exponential/logaritmic functions on the web e.g. in the following lehman (RIP) document but I can’t quite make sense of it. Any advice appreciated! Thanks, Andrew http://www.classiccmp.org/transputer/finengineer/[Lehman%20Brothers,%20Zhou]%20The%20Swap%20Curve.pdf (1st col is € Libor bid, 2nd col is € Libor ask) 1 year 4.17 4.22 4.28 4.31 2.65 2.71 2.71 2.74 0.89 0.95 2 year 3.84 3.89 4.30 4.34 2.59 2.67 2.71 2.74 0.91 0.97 3 year 3.93 3.98 4.37 4.41 2.70 2.78 3.06 3.09 0.99 1.05 4 year 4.01 4.06 4.44 4.49 2.82 2.90 3.37 3.40 1.08 1.14 5 year 4.06 4.11 4.50 4.55 2.92 3.00 3.59 3.62 1.17 1.23 6 year 4.11 4.16 4.55 4.60 3.02 3.10 3.73 3.76 1.23 1.29 7 year 4.16 4.21 4.58 4.63 3.11 3.19 3.87 3.90 1.30 1.36 8 year 4.21 4.26 4.61 4.66 3.19 3.27 3.95 3.98 1.36 1.42 9 year 4.26 4.31 4.63 4.68 3.26 3.34 4.05 4.08 1.41 1.47 10 year 4.31 4.36 4.64 4.69 3.33 3.41 4.09 4.12 1.46 1.52 12 year 4.39 4.44 4.63 4.70 3.44 3.54 4.12 4.15 1.52 1.60 15 year 4.44 4.49 4.59 4.68 3.54 3.64 4.12 4.15 1.62 1.70 20 year 4.35 4.40 4.39 4.52 3.50 3.60 4.07 4.10 1.76 1.84 25 year 4.19 4.24 4.18 4.31 3.37 3.47 4.02 4.05 1.83 1.91 30 year 4.07 4.12 4.00 4.13 3.27 3.37 4.02 4.05 1.85 1.93

Your question is how do you interpolate between the points? I would just use a spline but just because that’s easy. Whether or not there is any sense to that, I’m not sure.

Hi Joey, Well I spent some more time on this today, and I’ve interpolated using the cubic spline method (and linear for comparison). It has to be said that the former looks the most ‘right’… So, it’s occurred to me that what I’ve got is swap rates between AA-rated institutions. My (power) firm is BBB- rated… Can you suggest a resource out there that can help me figure out an approximate spread to apply to reflect this lower credit rating? Thanks, Andrew

I think you want the asset swap spread (Bloomberg of course). Check out this reference. http://www.yieldcurve.com/Mktresearch/files/BondSpreads_Feb06.pdf

Am I wrong, or is using a linear interpolation usually more precise (in term of market / forecasting power) than using the cubic spline method? I remember that when I first learned about bootstrapping, I though it didn’t make any sense to use a linear interpolation since a spline would be more precise. But when I read on the subject (on nuclearphynance), the posters there seemed to agree that since most of the analysts use linear interpolation it is often the best approach to use. Could someone confirm or deny this affirmation? For example, in an arbitrage context, this would mean that the added precision of the cubic spline method would be offset by the fact that mostly every instrument is priced and valued using a linear interpolation therefore the added precision could actually induce a difference between the forecasted and real values. Thanks. J.

Hmmm… Well, I agree that most everyone uses linear interpolation for price estimates, in part because brokerage tatements come that way. I guess it depends on what you are trying to do. I don’t have any evidence that splines are ebtter guess than linear interpolation, I just use them for this kind of thing as a knee jerk reaction.

Just a quick tip. Most of our clients are now building their curves using very few deposit rates and instead replacing them by futures for the short and middle term and swaps for the long term. Based on these points you should be able to build a curve looking more ‘normal’ with interpolation. The current curve with deposits and swaps usually has a ‘hump’ in the short term which gives several difficulties with interpolation and strange forward rates.

^ You have to be really careful about that and know what you are doing. In particular, futures are going to need convexity corrections (at least).