*historical mean/median approach*". This was surprising as this approach has an embedded value transfer implication that was explicitly mentioned in the consultation and agreed with by most participants.

What was not clear is when this value transfer would take place. From a "rational expectation" arguments and confirmed by market data, our expectation was that a good part of the value transfer has happened just after the fallback methodology was announced last November. Some figures have been detailed in the blog "Has value transfer in LIBOR fallback started?"

The value transfer has started but is not finished. It will continue up to the moment when the exact methodology is defined (look-back period, mean/median choice, linear transition period) and the exact discontinuation date is known. This is particularly true for USD and EUR that were officially not part of the consultation and where the target indices are very recent or have not been published yet. It is not clear if a historical approach could be used for those main currencies. Maybe a term fallback rate will be applied depending of the ongoing work of several working groups.

Among the tools useful to be prepared for the fallback, we have described our Fallback Transformers which is part of our (Java) library and which can transform a portfolio of legacy trades into an after fallback portfolio, taking into account the different options and variants, those proposed in the ISDA consultation and some additional ones.

In this new installment of the fallback transformers, I will apply that tool to a USD portfolio using the historical spread approach with transition period. The historical spread being largely unknown (there is very little history for SOFR), this leave a large uncertainty on the range of spreads.

In the historical mean/median with transition period, there are two unknowns in the fallback spread function. The first one is the historical average used over the long term and the second one is the spot spread used to transition from the current level to the historical average level.

The transition period in some sense reintroduce the

*spot-spread approach*that has been rejected, with good reasons, by the vast majority of the respondents to the consultation. That approach is prone to "

*manipulation, extreme conditions and arbitrage*". If the historical approach has created forward long term spreads in line with historical data, as evidenced in the blog referenced above, the introduction of the transition period would actually create a (one year) cliff effect that it is supposed to remove.

While waiting for the details of the exact fallback methodology on the spread, market participants can already analyse the different spread impacts on their portfolios. We have done so with the 1000 swap portfolio we have used in previous installments of the series. This is a portfolio composed of USD OIS and IRS v LIBOR-3M semi-randomly created for demo purposes.

In this case the valuation date is 25 January 2019. For the first scenario analysis, we suppose that the discontinuation date is 1 January 2022. The fallback options are compounding setting in arrears (with small arbitrary adjustment to dates required as the method is currently ill-defined as documented the "quantitative perspective") and historical mean/median with one-year transition period. The scenarios are the sizes of the historical and spot spreads. We looked a quite wide range of spread, from 20 to 40 basis points for the historical spread and 10 to 50 points for the spot spread. The spot spread has a larger range has it can be more volatile. Note that the spot range is not randomly selected but correspond to the range for LIBOR-3M / SOFR-compounded-in-arrears-over-3-month using actual LIBOR and SOFR data. The graph of the historical data is provide below. Note also that the spread is between a forward looking LIBOR and a backward looking SOFR composition. It includes some credit component and some change of market perception component. This last part is clear in the last month where the realised spread is very low (down to 11 bps) when the expectation of rate hikes by the fed have decreased (no December hike?) but at the same time the LIBOR/OIS spreads have been larger (between 20 and 30 in the September/October period).

**Figure 1: Historical data for USD-LIBOR-3M and USD-SOFR compounded in arrears over 3 months.**

With those ranges in mind, we can run our scenario analysis. We look at a grid of historical and spot spreads in the ranges described above. For each spread pair, we compute the P/L (value transfer) that would be generated if that pair of spread was to be used for a discontinuation on 1 January 2022. The result is presented in the graph below. The underlying portfolio is made of linear instruments, hence the almost linear appearance of the graph. What is of more interest is the vertical axis, with profits ranging from -200 million to +200 million. Also of interest is the fact that the profit is increasing with the spot spread but decreasing with the historical spread. The exposure to the spread impact is not in the same direction in the one year transition period and in the after transition period.

**Figure 2: Scenarios for the historical and spot spreads. Discontinuation date 1-Jan-2022.**

This lead naturally to the question of the impact of the discontinuation date. The portfolio exposure with respect to LIBOR is not the same for every period. One can look at the exposure on a very detailed basis, like describe at the end of the "LIBOR Fallback transformers - magnified view on risk" installment or we can also apply some scenario analysis to this issue. In the following graph, we have looked at possible discontinuation date from 1 January 2020 to 1 January 2060. For each possible date (with a 2-month step), we computed the impact of the fallback using three spread scenarios (27.5, 30 and 32.5 bps). The date of the impact can have an important effect on the value transfer. In our example, for the middle scenario (30 bps spread), the value transfer is between -25 and +33 million, depending of the discontinuation date. Obviously the impact is getting small for discontinuation very far in the future.

**Figure 3: Scenarios for the discontinuation date between 1-Jan-2020 and 1-Jan-2060. Three spread scenarios.**

In all cases the computation time is relatively small. Even for the full time profile (241 dates) and the portfolio of 1000 swaps, the computation time was around ten seconds on a laptop. A couple of ten seconds of computation times is a very small price to pay to have a multi-scenario analysis of the fallback that can cost you hundred of millions!

- Fallback transformers - Introduction
- Fallback transformers - Present value and delta
- Fallback transformers - Portfolio valuation
- Fallback transformers - Forward discontinuation
- Fallback transformers - Convexity adjustments
- Fallback transformers - magnified view on risk
- Fallback transformers - Risk transition
- Fallback transformers - historical spread impact on value transfer

Don't fallback, step forward!

Contact us for our LIBOR fallback quant solutions.