Marc's answer to the consultation is now available. A link to the text can be found below.
muRisQ Advisory offers quantitative finance advisory services. Its services focus on trainings and workshops, benchmark transitions, interest rate model development and validation, product design and risk management strategies.
Thursday, 31 January 2019
Consultation on ESTER term rate - our answer
The "Second public consultation by the working group on euro risk-free rates-on determining an ESTER-based term structure methodology as a fallback in EURIBOR-linked contracts" will close tomorrow.
Marc's answer to the consultation is now available. A link to the text can be found below.
Marc's answer to the consultation is now available. A link to the text can be found below.
Wednesday, 30 January 2019
Marc's presentation at the Quant Summit Europe
Marc Henrard will present a seminar at the conference
which will take place on Wednesday 6 and Thursday 7 March 2019 in London. The agenda of the conference can be found on the organizer web site:
Marc's talk, will be titled A quant perspective on LIBOR fallback.
Talk's agenda:
Don't hesitate to reach out if you want to meet during the summit.
Quant Summit Europe
which will take place on Wednesday 6 and Thursday 7 March 2019 in London. The agenda of the conference can be found on the organizer web site:
Marc's talk, will be titled A quant perspective on LIBOR fallback.
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.
Sunday, 27 January 2019
LIBOR Fallback Transformers - historical spread impact on value transfer
On November 27, ISDA has published the preliminary results of its consultation on IBOR fallback (see Marc's comments on his personal blog).The options selected for the adjustment spread was, tothe surprise of many, the "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).
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.
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.
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!
Contact us for our LIBOR fallback quant solutions.
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.
Thursday, 17 January 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 indicated from the invitations to most of the quantitative finance conferences in Europe over the next months. Marc has been invited as guest speaker or expert panelist at the following events:
Don't hesitate to contact us if you want to discuss potential in-house training or providing expertise on this subject for your projects.
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 indicated from the invitations to most of the quantitative finance conferences in Europe over the next months. Marc has been invited as guest speaker or expert panelist at the following events:
- The future of LIBOR (CFA Society Denmark, Copenhagen, Denmark) - 24 January 2019
- CASS Financial Engineering seminar (CASS Business School, London, UK) - 6 February 2019
- Quant Summit (organized by Risk.Net, London, UK) - 6-7 March 2019
- Singapore Management University seminar - 8 April 2019
- QuantMinds International (Vienna, Austria) - 14-16 May 2019
- Risk Live (organized by Risk.Net, London, UK) - 27 June 2019
Don't hesitate to contact us if you want to discuss potential in-house training or providing expertise on this subject for your projects.
Marc's presentation at CASS Financial Engineering workshop
Marc Henrard will present a seminar at the CASS Financial Engineering workshops. The presentation will take place on Wednesday 6 February 2019 at 6:10 pm.
Marc's talk, will be titled
Talk's abstract:
Marc's talk, will be titled
A quant perspective on LIBOR fallback.
Talk's 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 ISDA consultation has been to select the ``compounding setting in arrears" option. 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. To our opinion, the option selected by the consultation fails the basic achievability criterion in many cases. Even when achievable, the option can lead to significant value transfer and risk management complexities. We also explain to which extend the fallback may transform some vanilla instruments into exotics.
Thursday, 10 January 2019
Updated Quant perspective on LIBOR fallback
The note on IBOR fallback in our series Market Infrastructure Analysis as been updated with the results of the ISDA consultation. The note, titled
is available on SSRN: http://ssrn.com/abstract=3308766
A quant perspective on IBOR fallback consultation results,
is available on SSRN: http://ssrn.com/abstract=3308766
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 ISDA consultation has been to privilege the ``compounding setting in arrears" option. This note, which can be view as the version 2.0 of a previous note, presents the different options briefly and analyses the privileged option in details. It also presents an alternative option supported by different working groups. The note's focus is on the quantitative finance impacts for derivatives. To our opinion, the option selected by the consultation fails the basic achievability criterion in many cases. Even when achievable, the option can lead to significant value transfer and risk management complexities.Tuesday, 1 January 2019
MVA and cost of funding
In the previous blog on Margin Value Adjustment (MVA), we have shown that, for linear products, the forward Initial Margin (IM) along the different paths of Monte Carlo simulation may not be very different. This was visible in Figure 2 of the previous blog.
The IM level is only one half of the MVA, even if this is the one that is often the most computationally intensive. The other half is the cost of funding the IM. For illustration purposes, we use in this blog a cost of funding equal to the spread between OIS over a quarterly period and LIBOR. Obviously each institution need to had some idiosyncratic spread on top of that. But for illustration purposes, this simplified approach is enough.
When we have generated the paths on which we have computed the IM, we have used an interest rate model. Even if our portfolio contained only interest rate swaps linked to a unique IBOR rate, it is important to generate the paths with a model that take into account the stochastic spread between IBOR and OIS in a realistic way. The spread is used in the valuation/IM measurement, but more importantly in our case it is also used in the cost of funding computation. This is why the model used should match the current spread, take into account the spread dynamic (volatility) and have a realistic co-dependence (correlation) between IBOR and OIS curves.
For this blog, we have used a relatively simple model that fulfills those requirements: an hybrid Model for the Dynamic Multi-Curve Framework as described in a recent Model Development document. The model includes the spread stochasticity and the correlation between rate level and spread. For the examples we provide below, the model has been calibrated to USD cap/floor for the IBOR rates dynamic and to historical spreads and correlations behavior.
We first repeat the underwhelming graph which represent the IM level of our portfolio (with a small number of paths).
For the same paths, we have computed the quarterly cost of funding as the USD-LIBOR-3M/OIS-3M spread applied over the quarter to the IM. The cost are reproduced in the graph below. The colors for each path are the same in both graphs.
As appears clearly in that graph, the spread has more impact on the MVA than the precise IM level. In modelling term, it is very important to have a realistic multi-curve model with stochastic spread to which a good understanding of the dependence of the idiosyncratic institution specific funding spread should be added.
Other blogs on IM and MVA:
The IM level is only one half of the MVA, even if this is the one that is often the most computationally intensive. The other half is the cost of funding the IM. For illustration purposes, we use in this blog a cost of funding equal to the spread between OIS over a quarterly period and LIBOR. Obviously each institution need to had some idiosyncratic spread on top of that. But for illustration purposes, this simplified approach is enough.
When we have generated the paths on which we have computed the IM, we have used an interest rate model. Even if our portfolio contained only interest rate swaps linked to a unique IBOR rate, it is important to generate the paths with a model that take into account the stochastic spread between IBOR and OIS in a realistic way. The spread is used in the valuation/IM measurement, but more importantly in our case it is also used in the cost of funding computation. This is why the model used should match the current spread, take into account the spread dynamic (volatility) and have a realistic co-dependence (correlation) between IBOR and OIS curves.
For this blog, we have used a relatively simple model that fulfills those requirements: an hybrid Model for the Dynamic Multi-Curve Framework as described in a recent Model Development document. The model includes the spread stochasticity and the correlation between rate level and spread. For the examples we provide below, the model has been calibrated to USD cap/floor for the IBOR rates dynamic and to historical spreads and correlations behavior.
We first repeat the underwhelming graph which represent the IM level of our portfolio (with a small number of paths).
Figure 1: An example of forward IM paths for a swap portfolio.
For the same paths, we have computed the quarterly cost of funding as the USD-LIBOR-3M/OIS-3M spread applied over the quarter to the IM. The cost are reproduced in the graph below. The colors for each path are the same in both graphs.
Figure 2: An example of IM cost for a LIBOR-OIS related funding cost.
As appears clearly in that graph, the spread has more impact on the MVA than the precise IM level. In modelling term, it is very important to have a realistic multi-curve model with stochastic spread to which a good understanding of the dependence of the idiosyncratic institution specific funding spread should be added.
Other blogs on IM and MVA:
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