Change in collateral rate - fair compensation

The transition from EFFR to SOFR as collateral rate has an important impact in term of valuation. This change is very different from the change from LIBOR discounting to OIS discounting. The LIBOR/OIS discounting was a change of valuation formula from one that was used up to then to a new one that the users though was better. It was a correction of an internal valuation process but there was not change in the term sheet of the products. The pay-off were unchanged. No compensation was required.

The collateral transition is a very different prospect. In this case, the term-sheet of the trade, through its CSA - uncleared trades - or rule book - cleared trades -, is altered and the pay-offs, at least the ones associated to the payment of interest on the VM are changed. That change of term-sheet requires a compensation.

In the uncleared work, the compensation scheme has to be agreed by both counterparties to the trade. In the CCP world, the clearing house is the calculation agent and they may have the right to do the change at their own conditions, but there is still an expectation that this will be done in a fair way for each participant. The compensation for the change of collateral rate is not a standard variation margin for which the exact formula has a small impact; this is a fundamental transfer of value. It has to be computed very precisely and is a definitive value transfer.

The change is composed of two parts: The change of level between the two rates and the specific details of the rate on each day. Historically the difference between SOFR and EFFR has been a couple of basis point on average, with SOFR higher than EFFR. That difference is reflected into the basis swap for SOFR v EFFR. The change due to daily idiosyncrasies and intra-month seasonality is more complex. The quoted rate are for monthly or even yearly periods; the liquid market does not provide information about single days. Moreover, a good forward curve should replicate the shape of historical data with steps between FOMC meetings and on top the intra-month seasonality for SOFR.

In this note we concentrate on the intra-month seasonality. We suppose that the difference of average level has been taken into account and does not need to be look at anymore.

Methods to incorporate the seasonality in the curve was described our recent blog Fed Funds to SOFR: Impact of seasonality. In this blog we look at the monetary impact of that seasonality. By definition, on average the impact is null. But that impact will be spread between the different parties in a different way and some parties may be advantaged by the methodology selected. Some parties may position themselves in such a way to take advantage of the transfer.

Historically the SOFR rates have been higher on month end, in the first days of the month and around the 15th of the month. We create positions with a total PV01 equal 0 but with an impact on the value due to expected idiosyncratic spikes. The impact on value is estimated by valuing the portfolios with one forward curve including the seasonality and one without seasonality.The seasonality we use for this analysis is the one we have described in the previous blog.

The exact mechanism is the following: we create two swaps, one with a maturity date on the last day of the month and one with a maturity on the first day of the month or shortly after. The first swap has a given notional (1 billion) and the second one has a notional slightly adapted to have the exact same total PV01 on the discounting curve.

The first example has a 6 month tenor and a fixed rate of 2.50% (not too far away from ATM). The swap is fixed semi-bond versus LIBOR-3M quarterly. The total PV01 for the discounting is by construction 0.00 USD. The total impact of the seasonality is 4.23 USD. From a pure PV01 comparison perspective, it seems that the change of discounting curve should not have any impact on the value but we still see some impact even if restricted. The bucketed PV01 is provided in Figure 1.

Figure 1. Bucketed PV01 of a short swap.

We could also have selected to have a total PV01 of 0 (not the discounting one equal to 0) or even all of them equal to 0 by adding small ATM swaps at each maturity. The results would not have been altered significantly.

In the second example, we look at a longer swap with a tenor of 2Y and a coupon of 10%. it represents the end of a long term swap that was traded some years ago when the rates were significantly higher than today. The maturities are 31-Jan-2021 and 5-Feb-2021. The bucketed PV01 is provided in Figure 2. Again the total PV01 for the discounting curve is 0. In this case the impact of seasonality is USD 1,842.38. Again that may look small but this is out of a PV01 of 0 for which the expected impact would have been close to 0.

Figure 2. Bucketed PV01 of a 2-year swap with a large fixed coupon.

We could have increased that impact by taking longer maturity swaps or focusing on end-of-year impacts. Note that the 1-Jan-2021 is a Friday and the end of year will be on a 4-day period. If we take a pair of zero-coupon swaps traded at the end of 2007/beginning of 2008 and ending one week apart around the end of 2020, we obtain a difference larger than USD 7,000. This was obtained with a end-of-month average spike of 13.5bps. If we were to use last year end-of-year spike which was above 60 bps for a couple of days, we would obtain impact larger than USD 30,000.

The amount above were obtain with a notional of 2 billions (1 billion in each direction). Given that the total outstanding amount at LCH is 150 trillions, the theoretical potential impact on valuation of the seasonality could be above 100 millions if the feature of dates of the second example was representative of the composition of the CCP book.

What is the impact of seasonal adjustment on your book? Do you have tools to incorporate the seasonality in your valuation mechanism and check if the proposed compensation for change of collateral/discounting is a fair compensation for your own book?

Don't hesitate to contact us to discuss how we can help in this process.

Fed Funds to SOFR: Impact of seasonality

The USD market is in transition between Effective Fed Fund Rates (EFFR) and Secured Overnight Financing Rate (SOFR) as the main overnight benchmark.

Once the transition will be completed, the main source of liquidity for OIS will be based on SOFR. For the OIS transition, the change will be gradual. The new OIS trades will be more and more linked to SOFR, but the legacy trade already entered into and linked to EFFR will not be directly affected.

Currently, the EFFR is not only used as the underlying for OIS but also, and maybe more importantly, used as the reference rate for the payment of interest on the Variation Margin (VM). The rate for VM is usually described in a CSA (non-cleared) or the house rule book (cleared). For the usage of the overnight benchmark in collateral, it is expected that the transition will be more "brutal". For example, LCH and CME have announced that they plan to switch from EFFR to SOFR at some stage in 2020. The switch will be done on one day, without gradual transition and without possibility for the members to switch from one to the other at their own pace.

The change of collateral rate impacts the present value of all the trades through the discounting. The exact details of the collateral discounting approach can be found in (Henrard 2014, Chapter 8). The collateral rate is part of the term-sheet of the trade (through the CSA or the rule book) and a change of term-sheet must be compensated in some way. To estimate the compensation, you need two ingredients: the difference of average between the two rates and the difference of "local behavior". In the case of EFFR v SOFR the difference of local behavior is the intra-month seasonality. As can be seen in Figure 1, the SOFR rate, based on a wider market, has some very clear seasonal behavior. In particular, one can see sharp rate increases at month-end that subside for a couple of days and some sharp increase around the 15th of the month, even if to a lesser extend.

Figure 1: Historical data comparison between EFFR and SOFR (most recent data missing due to issue with the Fed website).

In this blog we will look at the seasonal adjustment and how it can be incorporated in the curve calibration. In a forthcoming blog, we will look at the impact of the seasonality on the valuation.

The first step of this intra-month seasonality analysis is to quantify it. For this we used the historical data, which is now a little bit longer than one year, and estimated a couple of effects. We use a relatively simple method. We split the month is 6 parts: First business day of the month, second business of the month, the day starting on the first business day on or after the 15th, the second lasst business day of the month, the last business day of the month and the rest of the month. For each of this parts, we estimate the difference between EFFR and SOFR since the publication of SOFR. The results we obtained are provided in Table 1. One can see that the seasonal effect is significant with the month end reaching 13.5 bps above average, the peak subside over a couple of days (8 bps and then 4.5 bps) and a second, smaller, peak appear on the 15th of the month with a level of 4 bps. We have not found any specific impact on the second last day of the month. We do not claim that this is the best way to estimate the intra-month seasonality; each firm will have his own approach(es). We use those simplified number as an example of the impact on curve calibration

Description	Spread EFFR-SOFR (bps)	Adjusted to other	Adjusted to average
First	10.4	9.3	8.0
Second	7.0	5.9	4.6
15th	6.3	5.2	3.9
Second last	0.9	-0.2	-1.5
Last	15.9	14.8	13.5
Other	1.1	-	-1.3
Average	2.4	-	-

Table 1: Average of specific intra-month seasonality.

How to incorporate this information in the curve calibration? Obviously the curve after calibration should match the market exactly, so it is not a valid method to calibrate the curve with you favorite method and then to manipulate the result to incorporate those seasonality. After the manipulation, the curve would not match the market perfectly anymore. The seasonality has to be incorporated in the calibration step.

For the calibration presented here, we used OpenGamma's Strata library as the starting point. The library is very flexible in term of curve calibration and it is easy to extend and incorporate your own curve mechanism in it.

We have added a new type of curve. It consist of a "fixed curve", in which we incorporate the seasonality, and a variable main part. The two parts put together form a unique curve. We call the first curve fixed as we have created it from our historical data analysis and it will not be changed in the calibration procedure. The variable part is the one that will be calibrated.  Just to reiterate, we have one curve, which internally is divided in two parts, and we calibrate that one curve to the market. There will be no adjustment after the calibration. The one step calibration include both the general shape and the seasonal adjustment.

To match the usual shape of the overnight rate behavior, the main curve is interpolated using log-linear interpolation on the discount factors with node on the FOMC date. In that way the overnight forward rates follow a piecewise constant shape with jumps at the FOMC meeting dates (see Henrard 2014, Chapter 5 for the details).

We did the calibration described above with and without adjustment for seasonality. The calibration was done with market data from 21-Jun-2019. The non-adjusted curve is presented in Figure 2 and the adjusted one is added in Figure 3. Figure 4 depict the difference between the two.

Figure 2: Forward overnight rates implied by the curve calibration without adjustment to intra-month seasonality.

Figure 3: Forward overnight rates implied by the curve calibration with adjustment to intra-month seasonality.

Figure 4: Spread of forward overnight rates implied by the curve calibration with and without adjustment to intra-month seasonality.

In the difference one can see clearly the month-end and first days of the month impact and also the 15th of the month impact. Even if the above impacts have a fixed amplitude, the impact on the other part is not always the same. The reason is that the length of the months are different and in some cases, some of the dates above span a three calendar days period instead of one.

The code will be added to the muRisQ-ir-models open source library at a later stage.




Henrard, M. (2014). Interest Rate Modelling in the Multi-curve Framework: Foundations, Evolution and Implementation. Applied Quantitative Finance. Palgrave Macmillan. ISBN: 978-1-137-37465-3.

Is the LIBOR/SONIA spread curve flat?

In a recent blog we described the apparent convergence of the market basis spread to historical spot averages. This would be a consequence of the new fallback language based on historical mean/median. To illustrate this we have used USD 30Y EFFR/LIBOR basis swaps data and previously GBP 30Y SONIA/LIBOR basis swaps.

An argument that we have heard against our description of this convergence is that the spread curve is not flat. The argument is that if there was a convergence to historical mean, it should be the same for all tenors and the curve should be completely flat. If you look at the curve as of the end of May, you can see that the curve is not flat at all; the spreads are between 9 and 17 basis points. The graph of the GBP SONIA/LIBOR-3M basis spread for different tenors is displayed in Figure 1.

Figure 1: Shape of the GBP SONIA/LIBOR-3M basis spread curve as of 24 May 2019

Our answer is the following: The argument is correct but incorrectly applied. Yes, if the market has already incorporated the fallback on an average spread, the spread should be the same for all tenors and the curve should be very flat. But this argument applies only for swaps after the discontinuation date. The discontinuation is expected to take place at the start of 2022.

Now we can look at the same data with the correct glasses. What are the spreads for basis swaps starting somewhere after 2022 and with different tenors? We have not looked only at starts in 2022, but at forward starts with starting dates every 6 months for the next six years. The results are displayed in Figure 2.

Figure 2. Shape of the GBP SONIA/LIBOR-3M basis spread curve and several forward starting curves as of 24 May 2019

From that figure we can see two things. 1) the curve is (almost) flat for forward swaps starting after 2022. 2) The curves are not flat for swap starting in the next 18 months.

Not only is the market really pricing a flat curve in line with the convergence arguments but we can also infer that the market is not expecting a discontinuation in the next 18 months. The shape of the curve seems more an evidence for the convergence as described in previous blogs than against it.

Overnight benchmark collateral transition: delta impact

In USD and EUR, the main overnight benchmarks will be transitioning from a long serving benchmark to a relatively new benchmark.

In USD the current main benchmark is the Effective Federal Fund Rate (EFFR). The Secured Overnight Financing Rate (SOFR) which should replace it is published since April 2018. The transition to SOFR is relatively slow with only 0.2% of the notional traded in SOFR swaps with respect to LIBOR swaps year-to-date according to ISDA data.

In EUR, the current main benchmark is the EONIA. The Euro Short Term Rate (ESTER) which should replace it will be published from 2 October 2019. Due to the recalibration of the EONIA rate to ESTER plus a spread on the same date, it is expected that the EUR transition to the new benchmark will be a lot faster than the USD transition.

Once those new benchmarks are in place, one of the the most important change in the market will be to transition to that benchmark as reference rate for cash collateral. This is very important as the collateral rate is used in the valuation of all derivatives subjects to the Variation Margin (VM) in cash with the rate paid on the collateral referencing the benchmark. The details of the pricing mechanism in this context can be found in (Henrard 2014, Chapter 8).

Even if the main benchmark for collateral and the OIS market has switched to the new benchmark, there will still exists legacy trades referencing the old benchmark. Also we can expect that the most liquid market for the old benchmark will be based on overnight/overnight basis swaps.

If the market is moving in that direction, what will be the impact on delta risk of an OIS? We have tried to answer to that question with a simple example.

We used a USD 10Mx5Y OIS referencing EFFR. If we look at it in the current framework with EFFR collateral and with the most liquid market based in vanilla EFFR OIS, the risk is straightforward. It is displayed in Figure 1 below.

Figure 1: Delta for an OIS with cash variation margin and interest computed on the same benchmark as the OIS.

The main risk is between 5Y and 7Y at the maturity date and there is some risk between 9M and 12M at the effective date in the opposite direction.

If we look at the same trade in the expected new configuration, two things will change: the discounting will be done on SOFR and the most liquid market for EFFR will be based on basis swaps. The current standard for the SOFR/EFFR swaps is to quote the spread on the SOFR leg; this may change at some stage when SOFR becomes the standard. The delta risk in the new configuration is displayed in Figure 2.

Figure 2: Delta for an OIS with cash variation margin and interest computed on a different benchmark than the OIS. The market quotes the benchmark underlying the OIS through basis swaps.

The risk still appear on the same tenors. But now we see two risks. The SOFR risk and the basis risk. When a SOFR OIS rate increases and the spread is unchanged, EFFR rate increases through the basis swap. When the SOFR OIS rate is unchanged and the spread increases, EFFR increases also. This is why is seems that there is a duplication of the risk. The pure discounting (the coupon is not ATM) explain the small figures in the nodes 2 to 4 years. That risk appears only in the discounting and not in the forward. It is visible in Figure 1 in the EFFR column and in Figure 2 in the SOFR column.

The code that produced the above delta ladders can be found in the OvernightOvernightNodesCalibrationAnalysis class of the Analysis repository on Marc's Github repository.




Henrard, M. (2014). Interest Rate Modelling in the Multi-curve Framework: Foundations, Evolution and Implementation. Applied Quantitative Finance. Palgrave Macmillan. ISBN: 978-1-137-37465-3.

Mandatory IM: category 5

The mandatory bilateral Initial Margin for derivatives is approaching for financial institution in the Category 4 (aggregate month-end notional amount in March, April and May 2019 greater than EUR 0.75 trillion), with an implementation date of September 2019.

It is time for the institutions in Category 5 (aggregate month-end notional amount in March, April and May 2020 greater than EUR 8 billion) to prepare for the September 2020 deadline.

muRis_Q Advisory is specialized in interest rate derivatives. Our experience related to Initial Margin includes commenting on the regulatory consultations, implementing the first versions of ISDA SIMM and comparing CCP models to uncleared regulatory SIMM and ISDA SIMM. We have used the SIMM methodologies in many contexts. Our implementation for interest rate includes Algorithmic Differentiation features for efficient computation of IM differentiation (see our blog on Initial Margin and double AD).

On top of spot IM computation we have also worked on Margin Valuation Adjustments (MVA) from an academic and practitioner perspective. Some examples of our research can be found on our "Forward Initial Margin and multiple layers of AD" blog.

Don't hesitate to contact us for quantitative advisory on projects related to the mandatory uncleared IM framework, technical questions related to SIMM and associated MVA questions.