Multi-curve framework: double or quits?

This blog entry is a reaction to the column by Bakkar and Brigo in Risk titled Model risk in the transition to risk-free rates. While I agree with most of the column, there is a secondary issue, which is close to my heart, I would like to react to. And I certainly concur with the last sentence of the column which starts with "This should involve the quant community in an active role" as this has also been my opinion for a long time.

I would nevertheless like to present a different perspective on some side elements of their argument. To my opinion, the expanded use of overnight benchmarks will (should) not reduce the multi-curve complexity.

The pre-2007 single curve "simplicity" was coming from a combination of error and domination. Error in confusing two effects, the (pseudo-)discounting and the reference benchmark. This error was helped by the domination of a rate family: the IBOR benchmarks — the LIBOR king. The crisis emphasised the difference between the overnight benchmark used for collateral remuneration and the IBOR benchmarks and lead to the overnight discounting. A second crisis impact is that the king is dying.

Moving to overnight benchmark as the dominant benchmark may simplify the valuation of vanilla instruments by simplifying the vanilla contracts(1); both the collateral/discounting and the reference benchmark will be the same. But it will only simplify the bank balance sheets on the vanilla derivative side, there is no guarantee that it will simplify the balance sheet globally. The funding term structure of a bank will become the LIBOR of tomorrow but without its liquidity. The generalised VM/IM and its associated costs has pushed the funding issue into the valuation of derivatives (FVA, MVA). There is no need to see the LIBOR or the funding cost to appear directly in the instrument term sheet to need it in derivatives valuation.

I certainly concur with the authors that transition to new benchmark could be an opportunity to review models related to funding but I don't think it will reduce multi-curve complexities. It may lead to a name different from Multi-curve Framework, but the issue of different curves to be used for different purposes will continue to be relevant, maybe even more so with the introduction of new benchmarks. Maybe it will be called the Funding Framework(2).

Even if I concur with the authors that the transition could be an opportunity, I'm afraid that the market will have its back against the wall due to time and regulatory constraints — like in the margin changes case —, that only the minimal to survive will be realistically achieved and that the bank managements, market associations and regulators will not let the quant community play an active role.

Like for other similar issues, I sincerely hope that I will be proved wrong on the quants involvment. Don't hesitate to let me know that I'm wrong, I will enjoy it.

Don't hesitate to contact me for projects on the subject of benchmarks transition.

(1) Contract here as to be understood as a combination of the specific instruments term sheet and the generic master agreement, which govern the now mandatory associated daily variation margin.

(2) By the way, this was the name I used in my March 2007 paper on Discounting Irony, the first paper on what is today called multi-curve framework.


SOFR and clearing

The two main clearing houses for USD OTC interest rate contracts (LCH and CME) have announced that they will start clearing SOFR indexd swaps in the third quarter of 2018.

The announcement was discussed in the following Risk.net article: LCH and CME to start clearing SOFR swaps in third quarter.

Even if the clearing of SOFR swaps becomes available, users will have to wait a while for the full effects of the new rate to appear in the market. As envisaged by the Alternative Reference Rates Committee (ARRC), the Fed Funds rate will continue to be used to calculate the price alignment interest, i.e. to pay the interest on the variation margin.

This means that for the moment, one would not be able to price and risk manage SOFR OIS without having a full term structure of the Fed Funds OIS. The SOFR OIS will move from the status of non-existence to the status of second class citizen of the OTC market world, but not yet to first class citizen.

This is not a surprise as the transition from one benchmark to another is a very difficult task, the difficulty of which is well documented, in particular on this blog.

From a SOFR's derivative perspective, it means that there will be two type of derivatives, the one collateralized a zero rates (futures) and the one collateralized at fed fund rates (OTC OIS). And we will be waiting for the third type, collateralized at SOFR to appear soon.

In term of valuation, it means a multiplication of convexity adjustments. In a recent blog and working paper, I mentioned the adjustments between overnight futures and OIS collateralized at the OIS index. The situation proposed by the hybrid rate approach will require further adjustments. This may be the subject of further blogs and working papers. It will take time to develop as we need a good multi-curve model with multiple discounting and a meaningful understanding of the join dynamic of Fed Funds and SOFR.Very soon we will have, just for overnight rates in USD 2 forwards and 3 discounting. With a couple of weeks of history on the SOFR fixing and no related derivatives today, we are very far away from having that understanding. It is of note also that the secured rate SOFR is fixing above the unsecured rate Fed Fund and also that the spread has gone from 13 basis points to 4 basis points in a couple of weeks.

It will also soon be time to offer for trading the rate quoted overnight indexed futures that I proposed some years ago. If they were traded on SOFR and the OTC clearing was done based on SOFR collateral rate, they would allow to create a full term structure with a unique design from 1 month to 30 years. It would also have very little convexity adjustment wrt OTC products, a lot less than the current offering based on 3 month futures traded with expiry up to 5 years. Don't hesitate to contact me for more detail about that design.


Overnight indexed futures

With the recent changes in market infrastructure and in the regulatory framework the importance of overnight benchmarks has increased in the last years and is expected to increase further. With that increased importance, the market will look for source of liquidity for overnight based derivatives beyond the traditional OIS. In its document on SONIA as the RFR, the The Working Group on Sterling Risk-Free Reference Rates calls for the development and promotion of interest rate derivative products which reference the RFR, including the design of a futures contract.

At a couple of days interval, CurveGlobal and CME have announced their plans to launch new overnight benchmark based futures. In the case of CurveGlobal, the futures is called Three month SONIA futures. The launch is planned for Q2 2018. In the case of CME the futures is called CME Three-Month SOFR Futures. The launch is planned for 7 May 2018. The CME futures is based on the Secured Overnight Financing Rate (SOFR). The SOFR rate is published by the Federal Reserve Bank of New York in cooperation with the U.S. Office of Financial Research. The rate publication started on 2 April 2018 and was discussed briefly in two previous blogs (here and here).

In a recent working paper, I describe the detailed futures instrument cash-flow and propose the pricing, including the convexity adjustment, of the new instrument in the collateral framework using a Gaussian HJM-like model. The paper is called

The adjustment obtained is relatively similar to the one obtained for LIBOR futures (see for example Eurodollar Futures and Options: Convexity Adjustment in HJM One-Factor Model) when the stochastic nature of the LIBOR/OIS spread is ignored. Some extra small adjustment need to be added to take into account that the futures settles only at the end of the accrual period while the LIBOR futures settle on fixing at the start of the underlying deposit period.

This futures is a new products that may help to bridge the gap between OTC and ETD in the overnight indexed products. It has still several inconvenient features that makes it difficult to be used as a building block to build an overnight yield curve up to 30 years as required by the market. Most of those drawback would be solved if the market was to adopt a design closer to the one I proposed some years ago.

I will continue to preach for the alternative design and don’t hesitate to contact me if you are interested by my sermon!


SOFR one week on

The Secured Overnight Financing Rate (SOFR) has now been published by the Fed New York for a week. Time for an early analysis.

The data published does not only consists of the benchmark rate itself which is a median rate of the data collected, but also the 1, 25, 75 and 99% percentiles. From that information, we can see that 50% of the rates captured are outside a 10 basis points band around the published rate. For the Effective Fed Fund Rate (EFFR), the 50% band is only 2 bps.

What is the origin of this larger dispersion of rates for the SOFR rate? Maybe the daily publication of the figures will increase transparency in that particular market which will lead to the narrowing of the dispersion? We will see if this is the case in a couple of months.

Another type of explanation for a larger diversity of rates could be the existence of a bid-offer in the SOFR underlying data. The Effective Fed Fund Rate is calculated on overnight federal funds transactions, which means that the transactions used are interbank transactions, transaction between are relatively homogeneous set of participants. On the other side, the SOFR transactions also include trades with clients and market-takers. The set of participants is less homogeneous. Could this 10 basis point difference be explained by bid-offer?

On a different subject, note that between the 3 April and the 4 April, the SOFR went down by 9 basis points while the EFFR was unchanged; the spread between SOFR and EFFR decreased by 9 basis points.

The spread between SOFR and EFFR is currently at 6 basis points. The secured rate still well above the unsecured rate!

The page on the Fed New York website with data related to SOFR is:

The page on the Fed New York website with data related to Federal Funds Effective Rate is:


SOFR published

The first value of the Secured Overnight Financing Rate (SOFR) benchmark has been published today by the New York Fed. The page for the rate is: https://apps.newyorkfed.org/markets/autorates/sofr

A new benchmark that is expected to play a role in the Games of Benchmarks.

The first value of the benchmark, for overnight rates between Tuesday 2 April and Wednesday 3 April, has been fixed at 1.80%. For the same period, the Fed Fund Effective rate has been fixed at 1.68%.

This means that the secured rate is 12 basis points above the unsecured rate!

Note that like for some other overnight rates,  the new benchmark is based on rates for trade on the start of the overnight period but only published the next day. It is difficult to understand why, in this era of real time and supercomputers, it takes so long for the publication of the rate. Even LIBOR that is probably not a paragon of virtue was published as soon as computed, around 11:00 a.m. London time. Note that SONIA, when it will be moved to its reformed version on 23 April 2018, will also be only published on a next day basis. Personally I would prefer an immediate publication. But it seems that timely publication is not a requirement for benchmarks.