Tuesday, 28 April 2020

Bespoke course: 3000

We have just received an email from a large training provider. They indicate
Bespoke training for you and your team starting at GBP/USD/EUR 10,000*! *pricing dependent on topic and group size.
On our side, we can say
Bespoke training for you and your team starting at GBP 3,000/day*! *pricing not dependent on topic and group size.

The course are always provided by our in-house experts and, from our training page:

Agenda tailored to your needs. Detailed lecture notes.
Associated to open source code for practical implementation.
Training in English or French

We are an (fiercely) independent management owned advisory firm and the trainings reflect that independence. We don't have hidden agenda and are free of conflict of interest.

In the current situation, we are also happy to offer virtual/on-line courses/workshop. The configuration is even more flexible that in-person courses as participants in different locations can attend simultaneously and courses can be split in half days to avoid participants lassitude.

We have provided public and in-house workshops/courses/seminars in Europe, New York, Singapore and Africa.

Some of our courses are described in our training pages. Over the past year, the most popular ones have been
In all cases, the course are updated with the latest market information and are fully flexible.

You can check some of our introduction videos on our Youtube channel.

Friday, 24 April 2020

Fallback transformers: gaps and overlaps

The proposed IBOR Fallback Rate Adjustments Rule Book has been published by Bloomberg.

The exact details of the fallback from IBOR to compounded setting in arrears seems slightly different from the version in the latest ISDA consultation. In particular the compounding period is back from the "calculation period" to the IBOR tenor period. The period is defined with an "offset by 2 business days".

In this post, we look at the precise description of the "offset by 2 business days" as its implementation may be different from an intuition of such an offset.

The composition period is defined, first by moving froward from the fixing date by two business days to the spot date. The move forward is in the calendar of the replacing overnight index. For USD, this is already a little bit tricky as for LIBOR the fixing is in GBLO calendar, the effective date is in GBLO and USNY calendar but SOFR is fixed in the USGS calendar. We skip this question of calendar here. From the spot date, the start accrual date for the composition is computed by moving backward by 2 business day, this is the "backward offset by 2 business days" from the consultation. The end accrual date for the composition is computed from this start accrual date by adding the tenor of the IBOR index. For tenors in months, the end date is adjusted modified following.

The feature of this approach is that the backward offset is done on the start date and the end date is recomputed from the start date. Due to non-good business days, week-end in particular, there is no guarantee that the end date for the composition will actually be before the end date of the coupon period. In many cases there will be a same day payment. One example is described in the post Fallback and same day payment?.

In this post we want to focus on the impact of the way the offset is computed on the overnight risk. Because each compounded period for consecutive coupon of a swap is computed with its own offset, there is no guarantee that those periods will fit nicely next to each other. In another blog commenting on the fallback rule book, we mention one such example.

Having added the new fallback rule in our Fallback Transformer library, we can now look at the impact that those periods not fitting exactly has on the risk. Here the risk is a lot more complex that for LIBOR as each day counts, and with SOFR showing spikes at month-end, quarter-end or 15th of the month, the exact day is important.

We use the same example as the one described in the above mentioned blog: Example 1M-IBOR swap over 5-month period: 2020-03-26 to 2020-08-26. The standard accrual periods for the coupons payments are on dates 2020-03-26, 2020-04-27, 2020-05-26, 2020-07-26, 2020-07-27, and 2020-08-26. The accrual periods for RFR compositions (with 2 days offset) are [2020-03-24, 2020-04-24], [2020-04-23, 2020-05-25], [2020-05-22, 2020-06-22], [2020-06-24, 2020-07-24], [2020-07-23, 2020-08-24].

We look at the risk of the swap resulting from the fallback and the risk of a standard OIS starting on 2020-03-24 and ending on 2020-08-24. With those dates, the OIS has exactly the same start and end date as the OIS composition resulting from the fallback. This is true at least at the total swap level. What is happening at the coupon level?

The coupon level is described in the next two graphs. The first one is the OIS risk. In the graph, we represent only the risk associated to the forward rates (not the discounting, which is very small). We look at the risk at the (zero-coupon) rate daily sensitivity, not through a standard Bucketed PV01. The daily feature is important to understand the difference between the two instruments. The risk is viewed from 2018-08-30, this date is not important, it turns out this is the date used in previous blogs.

The swap has a notional of 1 million. Its effective date is roughly 19 months after the valuation date and the maturity date roughly 24 months after the valuation date.The risk profile is exactly what you expect. A large risk at the start, with a value of roughly 1,500 USD/bps and a large risk at the end, with a value of roughly 2,000 USD/bps in the opposite direction. Each coupon payment has a very small risk which would be cancelled by discounting risk.


The profile of the swap resulting from the fallback is a lot more interesting. Due to all the adjustments related to week-ends, the end of one coupon compounding period does not match the start of the next coupon compounding period. In this particular case, each coupon creates large positive and negative exposures at slightly different dates. In some case, there are overlaps between the periods and in other cases, there are gaps between them. Counting positive days for overlaps and negative days for gaps, we have at the 4 intermediary dates, 1, 3, -2, and 1.



Market makers will need to adapt their tools to deal with those gaps. Also, those gaps will not be completely random. Some week-ends will be more favorable for gaps and some more favorable for overlap. You cannot expect a large book to smooth those features out, to the opposite, a large book with not perfectly offsetting trades will tend to accentuate those features.


  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 
  9. Fallback transformers - A median in a crisis
  10. Fallback transformers - Gaps and overlaps  


Don't fallback, step forward!

Contact us for LIBOR fallback and discontinuation: trainings, workshops, advisory, tools, developments, solutions.

Sunday, 19 April 2020

Benchmarks in transition videos: Episode 6 - LIBOR fallback: adjusted RFR

With the increased expectation of some IBORs discontinuation, the overnight benchmark changes and the increasing regulatory requirements related to benchmarks, a clear quantitative finance perspective on the impacts for derivatives is becoming paramount.

We have created a series of introductory videos on the subject of benchmark transition. The videos are available on our Youtube channel.

The sixth episode is dedicated to the floating rate part of the fallback.




All the videos will be linked in our LIBOR transition page.



In the current situation, we are also happy to offer virtual/on-line courses/workshop. The configuration is even more flexible that in-person courses as participants in different locations can attend simultaneously and courses can be split in half days to avoid participants lassitude.

Updates on LIBOR/ON spread

Some updates on the LIBOR/Overnight compounded in arrears spreads. Posted without comments.

We refer to the previous post on Signing the LIBOR fallback protocol: a cautionary tale for the first graph, Forward looking the spread between forward looking and backward looking rates  for the second one and to LIBOR Fallback: a median in a crisis for the third one.





Using the forward ON curves for the next 3 months, the spread is 29.21 bps (computed with the median). The spread if computed with mean would be 35.34 bps, a difference of more than 6 bps.

Wednesday, 15 April 2020

Benchmarks in transition videos: Episode 5 - LIBOR fallback: overview

With the increased expectation of some IBORs discontinuation, the overnight benchmark changes and the increasing regulatory requirements related to benchmarks, a clear quantitative finance perspective on the impacts for derivatives is becoming paramount.

We have created a series of introductory videos on the subject of benchmark transition. The videos are available on our Youtube channel.

The fifth episode is an overview to LIBOR fallback. Three more episodes will be dedicated to the fallback.




All the videos will be linked in our LIBOR transition page.



In the current situation, we are also happy to offer virtual/on-line courses/workshop. The configuration is even more flexible that in-person courses as participants in different locations can attend simultaneously and courses can be split in half days to avoid participants lassitude.

Monday, 13 April 2020

Easter

This year, Easter benefits will be reduced to a small set of strange looking eggs.




When times are better, don't hesitate to contact us if you are interested by one of those golf eggs!

LIBOR discontinuation: 2 years to go and calibration

The most talked about date in the LIBOR world, or disappearance thereof, is January 2022. That is 2 years to go!

You may think that there is a problem with my calendar or that I'm still in the mist of new year celebration and I have missed the fact that there is 3 months less than 2 years to go.

But I maintain it is 2 years to go, actually a couple of weeks less than 2 years. In finance there are many conventions to compute the meaning of a tenor. Why is January 2022 separated by 2 year from April 2020 in the LIBOR world? Take a 2 year swap in the most traded currency (USD) with the most traded LIBOR (USD-LIBOR-3M). If you traded a swap on 2-Apr-2020, the effective date was 6-Apr-2020, the last LIBOR coupon will start on 6-Jan-2022 with fixing 4-Jan-2022. The 2-year swaps traded a couple of days ago, on the 2-Apr-2020 were the first 2-year swaps impacted by the January 2022 discontinuation. This justifies the "2 years to go" part of the title.

What about calibration? In a recent post, we indicated that "LIBOR Fallback is not a curve change, it is a contract change!". Does it means that I have to change the contracts/instruments used in my curve calibration? The short answer is "Yes, you do!" If the contracts are changed, with some payments in the swap changed from a "LIBOR fixed in advance" to a "SOFR compounded in arrears with 2-day shift", those details have to be included in the curve calibration. As mentioned above, we have just past the 2-year (swap) mark for the discontinuation date. This is important as it means that on a 2-year swap, now 1/8 of it embed discontinuation. Moreover, if you use 18-month and 2-year swaps in your curve calibration, 1/2 of the 6-month period between those two nodes is impacted. Is the impact large? The only way to know if is to try with actual market figures.

For this we compare three cases: 1) Ignore the existence of discontinuation 2) Take into account the existence of discontinuation for calibration and pricing 3) Take discontinuation into account for pricing but not for calibration in a hybrid way. This last method is incoherent, but may be a natural first step where the change is introduced were it is the simplest.

First we look at the no-discontinuation/no-fallback case. We just use our standard curve calibration procedure. Here to make the things simple and look at one issue at a time we use curves described by zero-coupon rates with linear interpolation on the rate. Obviously for actual market making, you would be more careful on how you calibrate curve, probably using some piecewise constant forward rate and a coherent LIBOR/OIS spread as described in a previous post on "Curve calibration and LIBOR/OIS spread". Here we want to present the difference between the three methods above and the starting point is not our focus as long as we use the same method for all cases.

How does the curve look? The calibration is done as of Thursday 9-Apr and we display the USD-LIBOR-3M forward rates (not the zero-coupon rates) and the SOFR 3-month period forward rate on the same period as LIBOR. The x-axis is the LIBOR fixing date; there is one rate for each good business day. We observe a standard pattern with kinks. The LIBOR/OIS implied spread is represented with the small dots.



We now move to the discontinuation. For that, we need to introduce a couple of hypothesis: the discontinuation date and the adjustment spread. We have selected 1-Jan-2022 for the discontinuation and 25 bps for the spread. The difference is immediately obvious. First there is a clear jump on the graph, from a market implied spread based on the economical reality of LIBOR to a legal contract implied constant spread. After the discontinuation, the spread is constant. The jump in this calibration is more than 15 basis points. This is called in some places a "cliff-effect", it is a cliff-effect only in the graph, not economically. A given instrument has a given fixing date, e.g. the dreaded 4-Jan-2022 mentioned above, you know already that date, you know that it will be after the discontinuation (under our hypothesis of discontinuation on 1-Jan-2022), so there is no surprise, there is no cliff, this will be a SOFR + spread payment. You would be surprise if, like in the first graph, someone was telling you that the value is depend on the LIOBOR economical reality on that date! The cliff can only come from ignoring reality in your calibration/valuation.



Is there a big difference between the different cases? For that we focus only on the period from 1-Jun-2021 to 1-Jun-2022. The rates are displayed in the figure below.

Before that period, all the methods give the same results. The swaps up to 18-month tenors are not affected by the fallback. If we look at longer term, there will be an impact, but a lesser one. It is really around the discontinuation date that the difference is clear. In the graph we have added also the hybrid result with fallback on the pricing but not on the calibration. We see that around the discontinuation date, before it, the no-discontinuation approach is overestimating the rate and after it, it is underestimating it. The difference between the different cases is up to 10 basis points. The market rates are matched perfectly, so you don't see the difference on standard tenor swaps. But if you have to price a non-standard instrument, e.g. a FRA with a start date just before or just after the expected discontinuation date, you may mis-price it by as much as 10 basis points.

Conclusion: Calibrate wisely and make sure that the instruments you price and those you are calibrating to are taking the LIBOR fallback/discontinuation into account for the contract description.

Saturday, 11 April 2020

Benchmarks in transition videos: Episode 4.b - CCP big bang - USD

With the increased expectation of some IBORs discontinuation, the overnight benchmark changes and the increasing regulatory requirements related to benchmarks, a clear quantitative finance perspective on the impacts for derivatives is becoming paramount.

We have created a series of introductory videos on the subject of benchmark transition. The videos are available on our Youtube channel.

The fourth episode (part b) describes the PAI and discounting big bang at CCPs for USD.




All the videos will be linked in our LIBOR transition page.



In the current situation, we are also happy to offer virtual/on-line courses/workshop. The configuration is even more flexible that in-person courses as participants in different locations can attend simultaneously and courses can be split in half days to avoid participants lassitude.

Wednesday, 8 April 2020

Benchmarks in transition videos: Episode 4.a - CCP big bang - EUR

With the increased expectation of some IBORs discontinuation, the overnight benchmark changes and the increasing regulatory requirements related to benchmarks, a clear quantitative finance perspective on the impacts for derivatives is becoming paramount.

We have created a series of introductory videos on the subject of benchmark transition. The videos are available on our Youtube channel.

The fourth episode (part a) describes the PAI and discounting big bang at CCPs for EUR.




All the videos will be linked in our LIBOR transition page.

Monday, 6 April 2020

Benchmarks in transition videos: Episode 3 - New ON benchmarks

With the increased expectation of some IBORs discontinuation, the overnight benchmark changes and the increasing regulatory requirements related to benchmarks, a clear quantitative finance perspective on the impacts for derivatives is becoming paramount.

We have created a series of introductory videos on the subject of benchmark transition. The videos are available on our Youtube channel.

The third episode describes the new overnight benchmarks in USD (SOFR) and EUR (ESTR).




All the videos will be linked in our LIBOR transition page.

Sunday, 5 April 2020

Mandatory IM: Category 5 and 6 delayed by one year

The BCBS has proposed a deferral of final implementation phase of the mandatory IM requirement for non-centrally cleared derivatives. The BCBS press release can be found at: https://www.bis.org/press/p200403a.htm

The BCBS deferral is in line with the proposition that Marc made at the QuantSummit and quoted in the press.

As mentioned previously, we have developed our own code related to a Standard Initial Margin Model (SIMM) used by most of the banks under mandatory IM (currently category 1 to 4). Our implementation is AD compatible and provides the derivatives/sensitivities with respect to all the inputs (all the input amounts).

Note added: By doing some reviews, we have also noticed that some open source code for its computation contains bugs related to the computation of correlations (string comparison bugs).

Benchmarks in transition videos: Episode 2 - Why?

With the increased expectation of some IBORs discontinuation, the overnight benchmark changes and the increasing regulatory requirements related to benchmarks, a clear quantitative finance perspective on the impacts for derivatives is becoming paramount.

We have created a series of introductory videos on the subject of benchmark transition. The videos are available on our Youtube channel.

The second episode is dedicated to the description of why a transition is required.




All the videos will be linked in our LIBOR transition page.

Saturday, 4 April 2020

Benchmarks in transition videos: Episode 1 - Introduction

With the increased expectation of some IBORs discontinuation, the overnight benchmark changes and the increasing regulatory requirements related to benchmarks, a clear quantitative finance perspective on the impacts for derivatives is becoming paramount.

We have created a series of introductory videos on the subject of benchmark transition. The videos are available on our Youtube channel.

The first episode is dedicated to the description of Ibor and Overnight benchmarks.




All the videos will be linked in our LIBOR transition page.