Wednesday, 18 March 2020

LIBOR Fallback is not a curve change, it is a contract change!

In recent consultations, ISDA has proposed a new definitions for the LIBOR fallback. Similar definitions will probably be adopted by CCPs. The exact definitions have still to be clarified (LIBOR tenor or calculation period, calendar for 2 day shift, etc.), but the global idea is to replace a forward looking LIBOR by a backward looking composition on a different period. In previous notes and answers to the consultations, we have explain why the fallback cannot be applied exactly as described in the consultations, some new workaround will be required. Once those clear definitions are available and achievable, how do we include them in our pricing library?

The striking element of that change is not the change from one rate to another but the complete change of the LIBOR-linked derivatives term sheet. The term sheet is changed from a single rate known at the start of the period (or even 2 days before) to a combination of multiple rates known at (or around) the end of the period. This change of term sheet has a direct implication in terms of systems and valuation techniques. It is not possible to look at the fallback from a change of (forwarding) curve perspective. Yes a different curve will be needed, but this is only a very small issue. The main issue is that you have to dynamically change the instrument term sheet. By dynamically, we mean it is not a simple one-off re-booking of the trade in the systems. You may want to do the re-booking once the cessation has taken its full effects, by in the mean time you have to take the trade with its current description and do a what-if type analysis by changing the trade temporarily. The discontinuation date is still uncertain, so you need to do that transformation temporarily (in memory) and have the capacity to do it for several cessation dates, several spreads, several fallback definitions, etc.

This requirements is exactly why we developed the

almost 18 months ago.

We have seen some vendors proposing spread adjustment to RFR curves to price LIBOR swaps in the fallback. This is fine as a toy model to have an overview for vanilla swaps. But if you want a real in depth analysis, how does it work? How do you represent the 2 days shift effect, in particular when the 2 days cover a quarter-end, a year-end or a FOMC meeting? How do you include the difference between LIBOR tenor and calculation period? How do you include the jump on forward rate on the discontinuation date?

The decision to go the "transformer" route was not a random one for us. It was based on several prototypes in a production grade library and running detailed impacts on test portfolios with a market maker requirements in mind. Getting the general level correct by a shift is fine for a first global overview. The next step is to look at the details, at the pricing of short term instruments covering the transition expected date, at the impacts of date shifts, the exact curve shape at each intermediary date, etc. That can be done only by working on the instruments, not on the curves. Each instrument has its own idiosyncrasies that cannot be faked by a curve manipulation.

The inclusion of the jump on forward rate on the discontinuation date is particularly interesting for the moment. The current OIS/LIBOR spreads are very high with respect to the historical median. There is a real impact there. If you have a "fallback curve", how do you represent that? You could say that you would use a technique similar to the one you use for central bank meeting dates jumps. But unfortunately the impact is of a completely different nature. On the day before discontinuation, you have a forward looking LIBOR that covers 3 months. If you use a pseudo-discount factor approach to your LIBOR curve, you have a LIBOR curve for the next 3 months at the LIBOR level. For the 3 months RFR-based forward starting the next day, you need a RFR level (plus a fixed spread). But that RFR rate has an overlap of 3 months minus one day with the LIBOR. On that period, which rate do you use for the pseudo-discount factor curve? The LIBOR level or the RFR (+ spread) level? Today the UD-LIBOR-3M/OIS spread is around 75 bps while the historical median is about 25 bps. There is no way to get away from the contradiction between the levels with a curve approach. There is no reason to expect a convergence of LIBOR to RFR+spread as we appraoch the discontinuation date. And this is only for one single vanilla LIBOR payment, without even looking at the shift, period and composition issues. Even if the LIBOR had a fallback to a clean RFR term rate, this curve approach would not work at the transition.

We advice LIBOR-linked derivative users to implement the "trade transformer" approach in their internal libraries. Using curve based approach is running the risk of a nasty surprise when the actual cessation comes.


Figure 1: Historical time series of realized spread between USD-LIBOR-3M and SOFR compounded. The current crisis does not show yet fully on those figures as the SOFR compounded is backward looking. The full impact will be visible only in 3 months. For a forward looking view of the crisis impact, we refer to the previous post Forward looking the spread between forward looking and backward looking rates.

Figure 2: Distribution of realized spread between USD-LIBOR-3M and SOFR compounded with teh current median. The most recent realizations are in lighter colours. The most recent ones are mainly above the current median and we can expect that the median will increase in the coming months. More details are available in the previous post LIBOR Fallback: a median in a crisis.



We have done many other developments around the analysis of valuation and data in the context of the LIBOR fallback. This includes analysis of value transfer impacts, forward spreads, minimum and maximum spreads, discounting big bang, estimations based on forward curves with calibration using spread control (see Curve calibration and LIBOR-OIS spread).

Don't hesitate to reach out to discuss how those developments could be of interest in the context of the management of your portfolio.

Saturday, 14 March 2020

LIBOR Fallback: a median in a crisis

The ISDA proposed LIBOR fallback mechanism is based on a 5-year historical median estimate. If the LIBOR discontinuation take place as expected in January 2022, we already have a certain portion of the required historical data.

In this analysis, to keep the number of variables low, we look only at USD-LIBOR-3M and suppose that the announcement date is 1 September 2021 (3 month before January 2022). We interpret the "5 year of history" as meaning 5 years of LIBOR fixing for which we have the relevant SOFR fixings. This means we actually use 5 years and 3 months of overnight data (other interpretation of "5 years history" are possible). The LIBOR fixing are from 29 June 2016 to 29 June 2021.

We can plot the historical data from the known period (29 June 2016 to 13 March 2020); the histogram of the data is provided below. The figure also displays the median (as per ISDA proposal) and the median (for comparison). The median is 26.6 bps and the mean 29.2 bps.


There is still the period from 16 March 2020 to 29 June 2021 which is unknown. The proposal is to use the median. We have 876 data points out of the 1260 required. We can already put a hard bound on the lowest and highest possible median spread (conditional to our date hypothesis). The lowest median possible is 20.2 bps and the highest median possible is 36.5 bps. Those figures are represented below.


What about the mean? The mean depends on the exact value of each number, and there is no a priori bound on the individual spreads, so no a priori bound on the mean either. We can nevertheless create some "what-if" analysis. For that we use two extreme scenarios: one with all the remaining spreads at 0 bps and one with all the remaining spread at 100 bps. The graph of those values is proposed below.


The different daily spreads are not independent. There is significant overlap between the overnight rates used in consecutive daily spreads. The spreads tend to cluster, creating a trend in the median evolution. Where are we today (or more exactly were are we in the combination of LIBOR from 3 months ago and overnight up to today)? In the figure below, the have colour-coded the different occurrences. The lighter colours represent the more recent ones, each colour representing one of the 8 groups of 10 prints (a total of 80 recent print are in lighter colours).


The trend in the last months has been to be higher that the median. Note that the above figure do not include the LIBOR rates from the recent turbulent weeks; those will appear in the statistics only in a couple of months. Our best predication of those (see our recent post on Forward looking the spread between forward looking and backward looking rates) is that there will soon be very high spreads (above 100 bps).

This lead us to an embedded option in the fallback proposal. We mention our best estimate of the spreads in the coming months. Suppose that our estimation is perfect, are we sure that those spread will be included in the actual spread computation? The computation of the spread will be done on the announcement date (not on the cessation date). The announcement date will be decided by IBA and the panel banks, the procedure is thus giving a (free) option to the panel banks. Even disregarding the potential material nonpublic information embedded in the decision, there is a real option of non negligible value. Suppose that the option is exercised today and the announcement is made today (for an actual cessation in January 2022), what would be the impact? It is graphically depicted in the figure below. The direct impact would be an estimated margin of 24.5 bps, which is a decrease of 2 bps with respect to the first estimate in this post. Maybe more importantly it also removes the possibility of the spread going up to 36.5 bps which would be the case if all (market) spreads in the next 2 years or so were to be above 36.5 bps. The announcement option has a potential value of as much as 12 bps on all transactions with fixings post January 2022.


What are your options with regards to the fallback and how do you plan to exercise them? Don't hesitate to contact us to estimate them.



We have done many other developments around the analysis of spread data in the context of the LIBOR fallback. This includes analysis of value transfer impacts, forward spreads, minimum and maximum spreads, estimations based on forward curves with calibration using spread control (see Curve calibration and LIBOR-OIS spread).

Don't hesitate to reach out to discuss how those developments could be of interest in the context of the management of your portfolio.

Libor transition plans: Marc quoted in the press

Comments by Marc regarding the impact of the pandemic on some market infrastructure  transformation were reported in the press yesterday: Pandemic threatens Libor transition plans.

The comments were related to LIBOR transition and to uncleared margin rules.

Unfortunately, "A spokesperson for the UK’s Financial Conduct Authority – Libor’s regulator – did not respond to a request for comment."

A spokesperson for the UK’s Financial Conduct Authority – Libor’s regulator – did not respond to a request for comment.
A spokesperson for the UK’s Financial Conduct Authority – Libor’s regulator – did not respond to a request for comment.

Thursday, 12 March 2020

Forward looking the spread between forward looking and backward looking rates

Forward looking the spread between forward looking and backward looking rates or estimating the market misestimation 

The planned approach to adjustment spread in the new derivative LIBOR fallback arrangements are based on historical data. The spread historical data is based on one side the LIBOR forward looking rates and on the other side on the backward looking compounding setting in arrears.

This arrangement creates a spread which is a mixture of credit spread and market misestimation (see A Quant Perspective on IBOR Fallback consultation results, Section 5.2 for previous remarks on this). What is happening to that spread with the current crisis? By definition of the spread itself, we will be able to analyse this only in 3 months time, when all the overnight rates prints are known and we can compare the then backward looking overnight rate to the today forward looking LIBOR rate.

But it is possible to do a little bit better. We know the LIBOR rates over the last 3 months and we can project the overnight rates for the next 3 months. That does not really help us for the spread corresponding to today fixing, but it will help for the LIBOR fixing over the past three months. It is possible to get an estimate of the surprise (surprise cut in this case) that has already been realised.

The following graph is the result of that exercise for USD-LIBOR-3M and USD-SOFR. The LIBOR rates (dark blue line) are know up to today. The SOFR compounding rate in arrears based on the actual fixing (light gray line) are known up to the period corresponding to the fixing from 3 months ago. The projected in arrears for the 3 months up to today (dark grey) are based on known fixing up to today and projected fixing up to the end of the 3-month period. The spreads up to 3 months ago (yellow) are fully known and the spreads up to today are partly known (red) with the LIBOR side fully known and the SOFR side partly known.

We can see that the (projected) data already includes spike in the spread due to the surprise cut. The spike is above 100 bps. On the other side, for the fully forward looking LIBOR versus the fully forward looking SOFR (last red point on the graph), this is a spread without any unexpected element of monetary policy, has a spread larger than the average/median over the last years but is very far away from the spike. It does not mean that the credit crisis is suddenly seen as less severe over the last days, only that the market is not expecting unexpected policy changes.





We have done many other developments around the analysis of spread data in the context of the LIBOR fallback. This includes analysis of minimum and maximum spreads, estimations based on forward curves with calibration using spread control (see Curve calibration and LIBOR-OIS spread).

Don't hesitate to reach out to discuss how those developments could be of interest in the context of your portfolio management.

Sunday, 8 March 2020

Signing the LIBOR fallback protocol: a cautionary tale (2)

Following recent market moves, the graph accompanying the cautionary tale published in Risk.Net has been updated.

The full text is available on Risk.Net website (subscription required):


Updated without comment!