LIBOR Fallback and Quantitative Finance

With the expected discontinuation of the LIBOR publication, a robust fallback for related financial instruments is paramount. In recent months, several consultations have taken place on the subject. The results of the first ISDA consultation have been published in November 2018 and a new one just finished at the time of writing. This note describes issues associated to the proposed approaches and potential alternative approaches in the framework and the context of quantitative finance. It evidences a clear lack of details and lack of measurability of the proposed approaches which would not be achievable in practice. It also describes the potential of asymmetrical information between market participants coming from the adjustment spread computation. In the opinion of this author, a fundamental revision of the fallback’s foundations is required.


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Basics: pricing derivatives LIBOR coupon pay-off in t P : Replacement of a discontinued benchmark by an adjusted RFR and an spread adjustment (ISDA master agreement).

Fallback and quant finance
After the fallback the pricing formula will become where d is the discontinuation date, a the announcement date and S the spread. The notations X and l will be explained later.
The dates d and a are stopping times.
Pro: Interest rate, same term, similar to OIS, available? Con: Available late, achievable?, wrong period? FRA?

Fallback -Adjusted RFR options
The adjusted rate is computed between t 0 = σ and t n = τ ; is not F θ -measurable anymore, it is only F tn -measurable. In many case t p < τ . The new pay-off is not measurable on its payment date! The measurability requirement may appear as a technical term of no practical importance, but is it not; it is only the precise description of the very practical requirement that before you are able to pay an amount, you need to know what amount should be paid.

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Fallback -Adjusted RFR options

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Fallback -Forward-looking v backward-looking OIS benchmark and compounded in arrears are the same before the fixing date in term of valuation and risk management.
The floating leg amount paid is the spot OIS rate as measured at the fixing date t 0 for the period [u, v ] and it is paid in v .

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Fallback -Forward-looking v backward-looking The cash flow in the backward-looking option is also paid in v but based on the composition of the daily rates r i compounded over the period. This is similar to the floating payment of an OIS. The present value is given by Values computed just before the discontinuation's announcement.

Option 1: Forward Approach
The spread adjustment [is] calculated based on observed market prices for the forward spread between the relevant IBOR and the adjusted RFR in the relevant tenor at the time the fallback is triggered.
Option 2: Historical Mean/Median Approach The spread adjustment [is] based on the mean or median spot spread between the IBOR and the adjusted RFR calculated over a significant, static lookback period (e.g., 5 years, 10 years) prior to the relevant announcement or publication triggering the fallback provisions.
Pro: No manipulation, easy to compute and verify. Con: Value transfer. Not related to current market situation.

Adjustment Spread Computation
The adjustment spread is denoted S(X , [a − l, a]).
It depends on methodology parameters X still to be decided (mean/median, data trimming, transition period). It also depends on market data measured in the period [a − l, a]. The announcement date is unknown (stopping time) and the look-back period l is an element of the methodology parameters. All the LIBOR derivatives are now path dependent up to the discontinuation's announcement date.
N c s E X (N c J a n -1 2 J a n -1 3 J a n -1 4 J a n -1 5 J a n -1 6 J a n -1 7 J a n -1 8 J a n -1 9 J a n -2 0 Has the value transfer started?
J a n -1 7 J a n -1 8 J a n -1 9  Fallback in the language of quants -Spread The spread S(X , [a − l, a]) is F a -mesurable.
Two filtrations (or maybe many): the pure market one, that we have denoted F s , and a second one, containing the fallback methodology with material non-public information G s : F s ⊂ G s . , a])) G s . The historical spreads used to compute S cannot be manipulated.

What is the difference between
Is it possible to manipulate the methodology and G?
Is it possible to know (part of) G before the general public that knowns only F? J a n -1 9 A p r -1 9 J u l-1 9 O c t -1 9 J a n -2 0 A p r -2 0 J u l-2 0 O c t -2 0

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Vanilla becoming exotics? Cap/floor Vanilla IBOR caplet with strikeK , expiry t 0 and paid-off in v : Amount in the case of compounding setting in arrears? Amount still paid in v and is given, for a spread S, by The important difference is the the expiry date, which is now delayed to s n−1 = v − 1d. The pay-off can be writen as The vanilla IBOR cap/floor are becoming Asian options using compounding as averaging method on rates.

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Is the GBP spread curve flat? Spread (in bps)