Estimating Turn-of-Year Jumps in Overnight and Term Rate Curves
Summary
The document explains how a turn-of-year funding-rate jump can be estimated and represented in bootstrapped interest-rate curves. One approach compares an overnight curve built with the year-end forward level to a second curve where that level is interpolated from adjacent forwards. The difference between the resulting forecasts can be attributed to the jump and modeled explicitly.
The answer also explains how an overnight jump affects rates over longer tenors: a term rate averages overnight fixings, so a one-month rate dilutes a single jump across roughly twenty business-day observations. This helps explain why its jump may be around one-twentieth of the overnight move, while longer-tenor relationships depend on their averaging periods. The cited figures are examples from the referenced curve discussion, not a universal calibration rule. The answer notes that estimates can differ because of noise or because the jump is estimated directly from term rates; it does not provide a full derivation of the example calibration.
Key ideas
- Compare curves with and without the year-end forward level to estimate the overnight jump.
- The difference between their forecast fixings can be attributed to the jump.
- Term rates average overnight fixings, spreading a single overnight jump across the tenor.
- A one-month jump may be about one-twentieth of an overnight jump because it averages about twenty business days.
- Noise or direct estimation from term rates can explain deviations from the averaging approximation.
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# Yield curve: Turn of year effect jump calculation # 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 ## Answer by Luigi Ballabio (score 2, accepted) https://quant.stackexchange.com/a/35792 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.
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