Monday 13 April 2020

LIBOR discontinuation: 2 years to go and calibration

The most talked about date in the LIBOR world, or disappearance thereof, is January 2022. That is 2 years to go!

You may think that there is a problem with my calendar or that I'm still in the mist of new year celebration and I have missed the fact that there is 3 months less than 2 years to go.

But I maintain it is 2 years to go, actually a couple of weeks less than 2 years. In finance there are many conventions to compute the meaning of a tenor. Why is January 2022 separated by 2 year from April 2020 in the LIBOR world? Take a 2 year swap in the most traded currency (USD) with the most traded LIBOR (USD-LIBOR-3M). If you traded a swap on 2-Apr-2020, the effective date was 6-Apr-2020, the last LIBOR coupon will start on 6-Jan-2022 with fixing 4-Jan-2022. The 2-year swaps traded a couple of days ago, on the 2-Apr-2020 were the first 2-year swaps impacted by the January 2022 discontinuation. This justifies the "2 years to go" part of the title.

What about calibration? In a recent post, we indicated that "LIBOR Fallback is not a curve change, it is a contract change!". Does it means that I have to change the contracts/instruments used in my curve calibration? The short answer is "Yes, you do!" If the contracts are changed, with some payments in the swap changed from a "LIBOR fixed in advance" to a "SOFR compounded in arrears with 2-day shift", those details have to be included in the curve calibration. As mentioned above, we have just past the 2-year (swap) mark for the discontinuation date. This is important as it means that on a 2-year swap, now 1/8 of it embed discontinuation. Moreover, if you use 18-month and 2-year swaps in your curve calibration, 1/2 of the 6-month period between those two nodes is impacted. Is the impact large? The only way to know if is to try with actual market figures.

For this we compare three cases: 1) Ignore the existence of discontinuation 2) Take into account the existence of discontinuation for calibration and pricing 3) Take discontinuation into account for pricing but not for calibration in a hybrid way. This last method is incoherent, but may be a natural first step where the change is introduced were it is the simplest.

First we look at the no-discontinuation/no-fallback case. We just use our standard curve calibration procedure. Here to make the things simple and look at one issue at a time we use curves described by zero-coupon rates with linear interpolation on the rate. Obviously for actual market making, you would be more careful on how you calibrate curve, probably using some piecewise constant forward rate and a coherent LIBOR/OIS spread as described in a previous post on "Curve calibration and LIBOR/OIS spread". Here we want to present the difference between the three methods above and the starting point is not our focus as long as we use the same method for all cases.

How does the curve look? The calibration is done as of Thursday 9-Apr and we display the USD-LIBOR-3M forward rates (not the zero-coupon rates) and the SOFR 3-month period forward rate on the same period as LIBOR. The x-axis is the LIBOR fixing date; there is one rate for each good business day. We observe a standard pattern with kinks. The LIBOR/OIS implied spread is represented with the small dots.

We now move to the discontinuation. For that, we need to introduce a couple of hypothesis: the discontinuation date and the adjustment spread. We have selected 1-Jan-2022 for the discontinuation and 25 bps for the spread. The difference is immediately obvious. First there is a clear jump on the graph, from a market implied spread based on the economical reality of LIBOR to a legal contract implied constant spread. After the discontinuation, the spread is constant. The jump in this calibration is more than 15 basis points. This is called in some places a "cliff-effect", it is a cliff-effect only in the graph, not economically. A given instrument has a given fixing date, e.g. the dreaded 4-Jan-2022 mentioned above, you know already that date, you know that it will be after the discontinuation (under our hypothesis of discontinuation on 1-Jan-2022), so there is no surprise, there is no cliff, this will be a SOFR + spread payment. You would be surprise if, like in the first graph, someone was telling you that the value is depend on the LIOBOR economical reality on that date! The cliff can only come from ignoring reality in your calibration/valuation.

Is there a big difference between the different cases? For that we focus only on the period from 1-Jun-2021 to 1-Jun-2022. The rates are displayed in the figure below.

Before that period, all the methods give the same results. The swaps up to 18-month tenors are not affected by the fallback. If we look at longer term, there will be an impact, but a lesser one. It is really around the discontinuation date that the difference is clear. In the graph we have added also the hybrid result with fallback on the pricing but not on the calibration. We see that around the discontinuation date, before it, the no-discontinuation approach is overestimating the rate and after it, it is underestimating it. The difference between the different cases is up to 10 basis points. The market rates are matched perfectly, so you don't see the difference on standard tenor swaps. But if you have to price a non-standard instrument, e.g. a FRA with a start date just before or just after the expected discontinuation date, you may mis-price it by as much as 10 basis points.

Conclusion: Calibrate wisely and make sure that the instruments you price and those you are calibrating to are taking the LIBOR fallback/discontinuation into account for the contract description.