# Signing the Libor fallback protocol: a cautionary tale

## As Orwell’s Room 101 beckons for Libor publication, muRisQ Advisory’s Marc Henrard warns of a potential pitfall in the fallback protocol

There is general consensus that Libor publication will be discontinued in the coming years. The option of last resort for existing Libor-linked derivatives is to rely on so-called fallback language, which provides alternative benchmark options, should the primary rate be unavailable.

The majority of the derivatives market is governed by International Swaps and Derivatives Association master agreements or by central counterparty (CCP) rule books inspired by the same. But the existing fallback language in both is currently not ﬁt for purpose and is being overhauled.

While the bilateral market will have to jump through various hoops to incorporate new fallback language into legacy trades being developed by the market through Isda, the path will be simpler for the cleared market.

Rules in the cleared market are CCP-speciﬁc, but in general the relationship between the CCPs and their members is very asymmetrical. For example, LCH rule 1.8.12 states that if the (Libor) rate is unavailable, LCH will determine a rate at its sole discretion.

However, the main CCPs have already announced that if the Isda fallback language is changed, they will align their house rules to it. Those changes will apply to both legacy and new trades.

With Isda fallback language now finalised for a number of currencies – and thanks to the unilateral power of the CCPs – the cleared swap market already reflects the expected future fallback language. From a quantitative ﬁnance perspective, this convergence is understandable as the current value is the expectation of the discounted payouts.

The Libor-OIS basis has moved in line with the historical median, which is the method of calculating the basis chosen as a result of the Isda consultations. As such, the implicit inclusion of fallbacks means that valuing cleared trades is relatively straightforward.

But for non-cleared trades, this is not the case.

This is a crucial point for parties trading new non-cleared swaps or contemplating signing the protocol. What compensation should be paid for signing it (or a bilateral agreement with the same intent)? By ignoring the difference, the parties may lose or gain as much as 10 basis points for long-tenor US dollar swaps.

### Spot the difference

To quantify the valuation difference between a swap with outdated and updated fallback language, we use the results described in Henrard (2019) with Lj(θ) the Libor rate fixing at date θ for a tenor j and w the payment date. The trades are under variation margin in cash with collateral interest c. The discontinuation and pre-cessation trigger dates, still unknown today, are represented by (the stopping times) d and t. The insistence of regulators and CCPs on introducing pre-cessation triggers forces this extra complexity and increases market fragmentation. The trigger’s announcement date is denoted a. With the current fallback language, the value in s is:

The indicator reflects the fact that Libor is paid only if the fixing date is before the discontinuation date and the question mark reflects the payout uncertainty in the current language. With the new fallback language, the Libor rate would be replaced by a floating rate FRj(θ) and an adjustment spread S([al,a]), computed as the median over a period of length l equal to five years. The value becomes:

To be able to value Formula 1 and compare it to Formula 2, we have to imagine what would happen on the fixing date in absence of direct agreement with our counterparty, that is: imagine what is hidden behind the question mark. In which respect, this article could be viewed as part ﬁnance and part fiction!

The parties would go to court or an arbitrator to get an independent assessment of the amount to be paid. In the contract, they agreed to payments linked to Libor, a measure of the interbank unsecured borrowing cost, including term lending and credit risk, on specific dates.

But the Isda fallback method for US dollar swaps, based on SOFR and a fixed spread, is decided on the announcement date, and therefore does not contain any bank term lending or credit risk related to the fixing dates in the contract, which can be up to 50 years later for longer tenors.

It is not even an option that a financially literate judge or arbitrator can consider.

###### By ignoring the difference, the parties may lose or gain as much as 10 basis points for long-tenor US dollar swaps

The proposed Isda spread is a one-off legal construction, not an economic or financial model of the actual required payout. As Isda’s chief executive officer, Scott O’Malia, has said, the Isda fallback creates losers and winners. It cannot be used as a reference to fairly settle non-cleared swaps.

It seems the only fair and reasonable option would be to ﬁnd a proxy for the interbank unsecured term borrowing cost. There is no guarantee that such a proxy will be available on the fixing date, but today one could use the Ice Benchmark Administration’s USD Bank Yield Index (BYI) or Ameribor.

Even if such benchmarks are not allowed today as references for financial contracts – and may not fulfil EU benchmark regulation or International Organization of Securities Commissions principles – nothing prevents a judge from using that reference to award a payment.

The absence of a compliant benchmark which can proxy Libor in fallback language does not prevent a settlement of the claims based on a proxy.

### Finding a proxy rate

Unfortunately, we cannot use standard replication arguments and associated risk-neutral valuation. Replication is based on hedging the risks with other financial instruments reflecting the same risks factors. Because the likely proxy rates, BYI and Ameribor, are not authorised today as underlying reference rates, it is impossible to create such replication dynamically. Nevertheless, we can value them using our best econometric judgement.

The current quotes for Libor swaps are related to cleared swaps and are contaminated by the new fallback as described by Formula 2. They cannot be used directly for non-cleared swaps.

They contain some relevant information, but only part of the required information. Because the fallbacks now dominate the cleared Libor/OIS basis, the actual credit and liquidity spread is missing, while the discontinuation date, by opposition to the trigger date, is different. This can be incorporated in a formula with:

The general level of rate for the Libor period, without including the bank credit, is traded in the market and we represent it by OIS(θ). We can use the standard risk-neutral valuation to price it. For the other part, the discontinuation date and the credit/liquidity spread, we propose to use an econometric model.

The ProxyL(θ) is our best estimate of the swap rate, which would be used by the judge to settle the claims. The proxy rate could be based on a non-compliant benchmark. Because we cannot use risk-neutral valuation, we have changed the probability to the physical or econometric probability $\mathbb{P}$.

The choice of the above split is arbitrary. We could have used the physical probability on the full Libor proxy directly, without dividing it into general level and spread. As it is possible to hedge the general level of rate, we prefer to use the econometric model – which cannot be hedged and is largely uncertain – on the smallest part possible.

The development of such an econometric model is not the main goal of this article, so we keep that part very short and very simple.

### Historical inputs

Calculating a proxy swap rate for non-cleared swaps can be done with reference to historical data and realised spreads, shown in figure 1.

The vertical red lines represent dates related to the fallback consultation process: the ﬁrst consultation publication in July 2018, its results publication on November 27, 2018, the publication of the parameter consultation in September 2019, and the parameter consultation results on November 15, 2019.

The dark blue line represents the time series of spread for cleared basis swaps between three-month US dollar Libor and Fed Funds with a 30-year tenor. We see a sharp drop on November 27, 2018, followed by a regular decline for a couple of months up to a point where the spread has been more or less stable for the last six months. Today’s spread level is in line with the historical median over a five-year lookback period.

The light blue line represents swaps with a one-year tenor not influenced by the fallback, as these positions will likely expire before Libor ceases.

Before the cleared swaps were contaminated by the fallback, the 30-year spread was above the one-year spread by an average of five basis points. Since November 27, 2018, the relationship appears to have broken. In the following days, the one-year spread went up while the 30-year spread fell. Subsequently, the difference between the two bases sat at around the same level, as they both slowly decreased up to mid-2019.

But since the middle of 2019, the one-year rate has increased by almost 10bp while the 30-year spread is largely unchanged. The one-year spread is roughly at the same level as in January 2018, but the 30-year spread is almost 15bp lower.

A possible model is to approximate the spread over SOFR of a 30-year bilateral Libor swap by taking the unpolluted one-year Libor/SOFR spread and then adding the pre-July 2018 (therefore pre-fallback discussions) 5bp spread between the one-year SOFR/Libor basis and the 30-year SOFR/Libor basis.

At the time of writing (December 2019), this would put the non-cleared 30-year Libor/SOFR basis at around 35bp, and therefore 10bp above what the equivalent cleared market is showing.

The 30-year Libor cleared swap rate is around 1.95% and our estimate for non-cleared swaps is therefore around 2.05%.

The difference between the two figures is not a modelling difference – the two rates refer to significantly different financial instruments. The market fragmentation feared by traders and regulators is already present. The pushes for pre-cessation triggers and early Libor demise will only increase that fragmentation.

The core of this article is not the quality of our econometric spread model – we concede it can be qualified as weak – but the claim is that such a model is required; the market quotes for cleared Libor swaps are mainly irrelevant for the pricing of a non-cleared swap with the current fallback definitions.

Customers with existing exposure to Libor should review their legacy books and perform such an estimate before signing the fallback protocol or entering new non-cleared swaps. Signing the Isda protocol will probably reduce their derivatives operational and legal costs, but its valuation impact could be in the tens of basis points; the monetary impact for large trading books could easily reach many millions of dollars.

The fallback impact could be larger than the one that appeared when market participants started to introduce OIS discounting. For the Libor fallback, the impact is not on discounting, but directly on the amounts paid.

The best of both worlds would be for parties to agree bilaterally on the signature value, reducing operational and legal costs with an explicit fallback and at the same time obtaining a fair value.

Marc Henrard is managing partner, muRisQ Advisory

Editing by Louise Marshall

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