### LIBOR transition: How to lose money, automatically!

LIBOR transition is involving large value transfers between market participants. In the past, I offered to my faithful readers the possibility to make money on LIBOR fallback (see the series starting here). The money making machine required to take some "spread positions" and trust that the LIBOR cessation process would complete in a time frame of a couple of years. The LIBOR cessation completed on 5 March 2021 with the announcement regarding the forthcoming cessation. The term "position" above is in between inverted commas because the point was that it was not really a spread position from a market risk perspective, only from a name perspective. It turns out that there is a little bit of market position in the trade as described in Fallback transformers: gaps and overlaps and the following muRisQ's blogs. The position I proposed In November 2019 has made more than 10 bps in rates.

Now that you have made some money with hard work, I propose a mechanism to lose money automatically!

To change a little bit the settings, I'm moving from the direct LIBOR transition to the indirect impacts on the ICE Swap Rates (ISR). ICE Swap Rates were representing the level of the IBOR-indexed swap rates. Now the mechanism has been extended to SONIA-indexed swaps in GBP. The other currencies don't have (yet?) SOFR, ESTR, TONA or SARON indexed swap rates.

The LIBOR-indexed swap rates will disappear with the disappearance of LIBOR. There is a legal framework for LIBOR fallback put in place by ISDA and incorporated in ISDA definition since January 2021. The story could stop there: fallback for LIBOR imply a fallback for LIBOR-indexed swaps. From a quant perspective this is true, but from a lawyer perspective it is not the case. ISR-indexed products, e.g. CMS of cash-settle swaptions, rely on a single number published on a screen. The LIBOR fallback rely also on a single spread number, but its impact on the swap rate depends on a full discounting curve (and its calibration and interpolation arbitrary choices). Quant will certainly agree on the general mechanism and agree that there are many possible acceptable solutions that fit into the mechanism; they will all be ** approximately correct**. But this is not good for lawyers; they want a precise mechanism based on a fixed rule and a single input. The existing payoff is based on one number (ISR) the fallback should be based on one number. In this way one obtains a mechanism that is

**. Precise because the rules are clear, but wrong because there is no way within the constraints to obtain a mechanism coherent with the already decided LIBOR fallback.**

*precisely wrong*Different working groups proposed lawyer acceptable formulation of a ISR fallback. Those formulations are based on approximation, trying to obtain something within the legalese constraints. The WGSRFRR proposed one approximation that I commented in ICE Swap rate fallback - long expected - approximations. There is also a proposal by the USD ARRC. Nothing has been proposed to my knowledge for CHF or JPY.

The proposals lead to an ISDA consultation on which I commented in ISDA consultation on ICE Swap Rate fallback. My negative answer to the consultation is based on two main issues: wrong and no validation. The "*wrong*" part will be discuss further in the main part of this blog. The "*no validation*" part is the fact that an approximate formula is proposed, but there is no in-depth analysis of how "*approximated*" it is but also there is not even a discussion about the unsaid constraints that lead to the formula and the potential existence of a better formula within those constraints. There is a review of the formulas by The Brattle Group, but the very light review can be summarized by "*something is necessary*" (and nowhere "*what is proposed is sufficient*").

After this long introductory rant, let's go to what you are all waiting for: losing money!

This involved you receiving (yes, receiving, no premium paid) a long vanilla option. The option is purely bilateral and pre-UMR, so no CCP rules with "*at its sole discretion*" in it, no IM and associated MVA, and no exotic feature. And still you lose money!

The option you have received is a plain vanilla European GBP swaption (yes for option purposes, GBP swaption can still be European, even after the Brexit) with automatic exercise at the ICE Swap Rate (LIBOR version) level and delivering a bilateral plain vanilla LIBOR swap; the exercise date is after 1 January 2022. You may say that those options are not the most common, and I would agree with you. But once you have an example of strange behavior, you can adapt the scenario to the actual products that you have in your books.

By mistake, you have sign with the counterparty the bilateral agreement to apply the WGSRFRR recommended fallback. The automatic exercise is now done on the fallback LIBOR-linked ISR rate which is given by the formula reproduced in Figure 4 at the end of the blog. I need to explain why I said "*by mistake*" in the previous sentence.

Now let's look at the pay-off value of such a long option. To make the example concrete, we take an option on an underlying with tenor 1 year. The option is exercised at some time in the future and obviously we don't know what the rates will be in the future. Two things will be important to understand if we make or lose money: the exercise fallback ISR rate the the value of the underlying swap delivered.

The fallback ISR is based on approximation, so the exercise rate will not be exactly the exercised swap rate. Let's look at the difference between those two rate in Figure 1.

**Figure 1. Difference between proposed fallback ICE Swap Rate and actual fallback-LIBOR swap rate. GBP LIBOR-3M with tenor 1Y.**

The curve used (only one curve, LIBOR has disappeared by that date and only the SONIA curve exists) is described by its "level" (zero-coupon rate at time 0) and its "slope" (difference of zero-coupon rate between time 1 and time 0). Depending on the values, the difference is between -1.5 and +1.5 bps. This is of the same order of magnitude than other figures reported for this approximation in the literature (but not directly by the WGSRFRR and ISDA, who reported approximation of only 0.10 bps or less).

What does that mean for our trade? Suppose that we have a receiver with strike 2.50% (250 bps) and the rate at the exercise date is close to that level. If you don't like that level, pick any other level, as seen in Figure 1, the level impact is very small. In Figure 2, we reported the fallback ISR rate level for a set of curves with the levels and slopes indicated. Those rates are indicated by level curve in color with the level indicated. We also reported the actual exercised swap (the one resulting from the LIBOR fallback) in black. The curve don't match; this is expected from Figure 1.

**Figure 2. Level for the two swap rates.**

What is happening between the curves? Let's color the curve space according to the exercise and value situation. Above 250 bps fallback ISR rate, the swaption is automatically exercised; this is the non-white part of Figure 3. But (yes there is a but), the swap value depends on the fallback LIBOR swap, which has a positive value only for the part in yellow. The blue band is the set of curves where the swaption has been exercised but you have received a swap with negative value!

**Figure 3. Color representation of the level/slope domain where one lose money by being long the option.**

You have lost money, automatically!

You don't lose money all the time (I never promised that), only in some circumstances. The probability of that depends on the current curve shape and the volatility, but it is certainly not null.

How do you value such an option? That will be the subject of a (hopefully forthcoming) follow-up blog.

In the mean time, enjoy the money you have been making thanks to this blog while it last!

**Figure 4. Approximated formula proposed by the WGSRFRR for ICE Swap Rate fallback.**

I plan to collect the blogs related to the ICE Swap Rate transition/fallback into a more serious looking working paper. I still need to add some pricing discussion.

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