Sunday, 23 June 2019

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.

Wednesday, 12 June 2019

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.

Saturday, 1 June 2019

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.

muRisQ Advisory is specialized in interest rate derivatives. Our experience related to Initial Margin includes commenting on the regulatory consultations, implementing the first versions of SIMM™and comparing CCP models to uncleared regulatory requirements and SIMM. We have used the SIMM methodology 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.

Sunday, 19 May 2019

Fallback, historical spreads, and market convergence

Marc has been active on its personal blog trying to answer the question "Has the value transfer already started in the LIBOR fallback?". From the market data, it seems that the answer is yes. Once there is a value transfer, one can try to take advantage of it. Since November, he has published regular updates on the question, the most recent of them being Making money on LIBOR fallback (5).

We have developed a tool to systematically analyze this idea. In this blog we summarize its results for only one benchmark through a single graph. The benchmark is GBP-LIBOR-3M which could fallback to SONIA compounded setting in arrears. For that benchmark we looked at a total of 48 scenarios. Those scenarios where created using 8 announcement dates, 3 lookback periods (10Y, 7Y, 5Y) and the mean/median options.

The first item represented in the graph is the historical data of the market quoted spread on basis swaps GBP-LIBOR-3M v SONIA for a tenor of 30Y. We also represented the 48 scenarios. For each of them the running measure on each day over the last year has been computed. So each scenario has been run roughly 250 times to generate the curves.


This market has moved by roughly 5 basis points since the July 2018 consultation results announcement on 27 November 2018. The different scenarios still leave a range of 7 basis points for the fallback. The market is now at one of the bounds of the range that we have computed. This range should close when the exact methodology for the spread computation is published by ISDA.

On which side of the value transfer will you be on the next market move?


Related blogs:
  1. Fallback transformers - Introduction
  2. Fallback transformers - Present value and delta
  3. Fallback transformers - Portfolio valuation
  4. Fallback transformers - Forward discontinuation
  5. Fallback transformers - Convexity adjustments
  6. Fallback transformers - magnified view on risk
  7. Fallback transformers - Risk transition
  8. Fallback transformers - historical spread impact on value transfer


Don't fallback, step forward!

Contact us for our LIBOR fallback quant solutions.

Saturday, 11 May 2019

Panel expert - Risk Live 2019

Marc Henrard has been invited as an expert panelist at the inaugural

Risk Live


organized by Risk.Net that will take place on June 2019 in London. The agenda of the conference can be found on the organizer web site:




Marc will contribute to the panel

What could go wrong in Libor reform?



You can get a discount on the event with the speaker discount code below


Register from the link: https://bit.ly/2vm3lQe


Don't hesitate to reach out if you want to meet during the event.

Thursday, 9 May 2019

Planning for the end of LIBOR - Cass Business School one-day workshop


Marc Henrard will present a seminar at the conference

Planning for the end of LIBOR

organized by Cass Business School in London on Wednesday 19 June 2019. The details of the workshop can be found on the organizer web site:


The event is free, but limited number of places are available. You have to register from the organizer's site referenced above. The registration is now open.


Marc's talk, will be titled LIBOR fallback: a quant perspective. It will be the opening session and will start at 10:00 am.

Abstract
With the increased expectation of some IBORs discontinuation and the increasing regulatory requirements related to benchmarks, a more robust fallback provision for benchmark-linked derivatives is becoming paramount for the interest rate market. Several options for such a fallback have been proposed and ISDA held a consultation on some of them. The results of the consultation has been to privilege the compounding setting in arrears and historical mean/median options. We present those options and emphasize their drawbacks. In particular the compounding setting in arrears lack of details and lack of measurability and they would make it not be achievable in practice. We also present an alternative option supported by different working groups. The historical option can lead to significant value transfer, some of them having already taken place.



Don't hesitate to reach out if you want to meet during the workshop.

Sunday, 5 May 2019

LIBOR fallback: a recognised expertise

Over the coming years, one of the main issues in interest rate trading and risk management will be the emergence of new benchmarks and the potential IBORs fallback.

In the past year, we have looked at those issues from a theoretical and from a practical point of view. Some of the theoretical issues are detailed in a note that Marc published recently called "A Quant Perspective on IBOR Fallback Consultation Results" (https://ssrn.com/abstract=3226183). On the practical side we have implemented different fallback options, curve calibration mechanism and convexity adjustment to analyze the impacts on large portfolios. Some descriptions of the tools are available in a series of previous blogs.

Our expertise has been recognized by the market as documented from the invitations to many practitioner and academic finance conferences and seminars. Marc has been invited as guest speaker or expert panelist at the following events:
We are also presenting in-house workshops on similar subjects (see our training page on LIBOR) at different financial institutions in Europe.

Don't hesitate to contact us if you want to discuss potential in-house training or providing expertise on this subject for your projects.

Monday, 1 April 2019

Marc's presentation at QuantMinds International

Marc Henrard will present a seminar at the conference

QuantMinds International


which will take place from 14 to 16 May 2019 in Vienna. The agenda of the conference can be found on the organizer web site:


See also Marc's page on QuantMinds site.


Marc's talk, will be titled A quant perspective on LIBOR fallback and will take place on 16 May at 9:50.

Talk's agenda:
  • The current status of the fallback improvements 
  • Potential difficulties with the proposed compounding in arrears option 
  • Value transfer in the fallback 
  • The RFR term rates


Don't hesitate to reach out if you want to meet during the summit.

Monday, 25 March 2019

Seminar at Singapore Management University

Marc Henrard will present a seminar at the

Singapore Management University

on Monday 8 April in Singapore. The details of the seminar and registration can be found on SMU website:




Marc's talk, will be titled A quant perspective on LIBOR fallback.

Talk's summary:

With the increased expectation of some IBORs discontinuation and the increasing regulatory requirements related to benchmarks, a more robust fallback provision for benchmark-linked derivatives is becoming paramount for the interest rate market. Several options for such a fallback have been proposed and ISDA held a consultation on some of them.
The results of the ISDA consultation has been to select the "compounding setting in arrears" adjusted rate and the "historical mean/median" spread approach. We analyse the proposed option in details and present an alternative option supported by different working groups. The presentation focuses is on the quantitative finance impacts for derivatives.



Don't hesitate to reach out if you want to meet at the seminar.