# Yield curve: Turn of year effect jump calculation

I'm trying to get the values for the turn of year jumps that can be found at section 4.8 of

Everything You Always Wanted to Know About Multiple Interest Rate Curve Bootstrapping But Were Afraid To Ask

and I don't see how the 8.5 bps for the eonia at 2014 are calculated.

In this section it says:

...we are allowed to estimate the coefficient using instruments with a given underlying rate tenor (e.g. those on Euribor3M used for C3M ), and to apply it to any other curve Cx taking into account the proper weights...

Does this mean is it taking the value from another tenor rates?

In this section also says:

The Con yield curve displays both the 2013 (10.2 bps) ON and the 2014 (8.5 bps) turn of year jumps. The C1m yield curve displays the 2014 turn 1M of year jump between 1st Dec. 2013 (+1.8 bps) and 2nd Jan. 2014 (−1.6 bps) with size roughly equal to 1/20 of the ON jumps

This makes me more confused as it talks about a size for 1M jump of roughly 1/20 of ON jump and:

• I don't see where the 1/20 applies (it later talks about jump for 3M is 1/3 of 1M jump which is 0.6bps and 0.5bps and makes sense to me)
• As it says is roughly equal makes me think this value has been calculated in a different way and then compared to what should be

## 1 Answer

I don't have a full answer to your question, but I re-did some of the calculations in one of the chapters of the QuantLib Python Cookbook. The part on EONIA bootstrapping is available for free; look around the page for a "Read free sample" button.

In short: if you bootstrap an EONIA curve without taking the jump into account, one of your forward levels will be off. In order to estimate the jump, you can create another curve that replaces that forward level with one which is interpolated between those around it and is thus not affected by the jump. If you forecast end-of-year rates off the two curves, the difference between the two fixings can be attributed to the jump, which can thus be estimated and then modeled explicitly. Details are in the chapter I linked.

As for the other points in the question: the idea is that the jumps for the various tenors are all due to the jump in the overnight rate. The rates over longer tenors can be seen as an average of the overnight rates (plus a spread, of course). The 1/20 ratio is due to a month having more or less 20 business days, causing the 1-month rate to be the average of about 20 fixings, only one of them including the jump. The "roughly equal" might mean that there's noise in the calculation of the average, or (as you say) that the estimate of the jump can be done in a different way, that is, directly on 1-month rates.

• Thanks Luigi. I think I get the idea on how to calculate the jumps size from Ametrano but I don't see how to get those 8.5 bps for the second jump :( About the book, I already have it (the complete version actually) and I think is a really good job. Your book plus python quantlib is one of the most didactic things I've seen in quantitative finance ever. Congrats :) Aug 27 '17 at 14:35
• Thanks for the kind words! The second jump is missing from my calculations too. I'll let you know if I manage to add it at some point. Aug 27 '17 at 14:49