Profit explain explained

I was once asked to explain the P/L explain report. Something must be wrong in my story telling if I have to explain the explanation. After the failure of my story telling career, I decided to move to story writing. This note is an attempt at starting my new career.

The full text is available as PDF:

Profit explain explained


The Thalesians seminar

I will be speaking at The Thalesians seminar on

SIMM and SA FRTB: double AD

Seminar starts at 6:30pm on Wednesday 19 April 2017 at

City University Club

Champagne will be served before the seminar, around 6:00pm.

Register at Meetup:


Algorithmic Differentiation (AD) has been used in engineering and computer science for a long time. The term Algorithmic Differentiation can be explained as ``the art of calculating the differentiation of functions with a computer.
Over the last 5 years, AD has made its road to quantitative finance. The most straight forward use of AD is to compute the sensitivity of PV to market inputs. In the frame of SIMM and SA FRTB computation, those sensitivities are the main input and having an efficient way to produce them is important.
Once the IM/Capital number is computed, there are a lot of potential analysis which are handy, like marginal IM and IM attribution. Those analysis also require some form of differentiation, this time with respect to the positions.


SIMM and sensitivity based FRTB: double AD
  • Algorithmic Differentiation and computation of sensitivities
  • First AD: fast inputs for SIMM/FRTB
  • Second AD: sensitivity of the IM/Capital itself w.r.t. sensitivities
  • Second AD applications: attribution and marginal IM/Capital


Change of benchmark overnight index is a difficult task: interview

An interesting follow-up article in Risk magazine about Swiss rate reform: Swiss rate reform in race against the clock (subscription required). With respect to the previous Risk article on the same subject, it presents a more balanced view and not only the point of view of the WG on benchmark reform. At lot of the opinions expressed are closer to what could be found in my first blog on the subject.

Chris Davis, the author of the Risk article, found my blog on the subject and contacted me. We had a roughly 30 minutes discussion. He used a lot of the background information from the discussion and from my blog for the article, even if only two sentences from the discussion were quoted.

I was surprised that my blog was not explicitly cited in the references, as would be customary when the blog presented original research and analysis and was used for background information. On my side I will continue to reference Risk explicitly when I read something of interest in it.

On top of the subjects I introduced in my previous blogs, one element that I did not forecast was presented. This is that the current TOIS market already prices the change from TOIS to SARON. In some sense, this means that the TOIS market is not the TOIS market anymore; it is a blending of TOIS and expectation of conversion to SARON.

This is a quite interesting point of view from a pricing perspective. The actual market includes the "legal jump risk" from one index to the other without compensation. The pricing of the benchmark change is now impossible, the market has already been distorted by evoking the possibility of the change to a new benchmark without compensation. That creates more uncertainty for potential disputes. In some sense, the risk is becoming impossible to hedge. If you want to price or hedge pure TOIS, there is no market for it. The fact that there is a legal jump risk in the actual instrument probably make the market incomplete. Certainly it can not be treated with a diffusion process; you have to include a one-off jump.


Change of benchmark overnight index is a difficult task: follow-up

In my previous blog, I discussed the attempt by the National Working Group on CHF Reference Interest Rates to modify the CHF overnight benchmark index. Since my blog has been published, the minutes of the WG meeting have been published on the Swiss National Bank (SNB) website. The minutes also include the list of participants to the group.

In one of the documents, an ISDA representative indicates that the guidance are "non-legally binding" and "could be used as a tool for bilaterally negotiating amendments to contracts". The core of the issue is in the "non-legally binding" and "bilateral" words, but they seem to be largely ignored in the guidance.

The issues related to the change of benchmark overnight index are of three types.
  1. Contract modification. There will be changes in a lot of contracts (OIS and CSA). That will require a bilateral agreement on each of them individually.
  2. Valuation. Changing the contracts has valuation impacts. The compensation of those impacts will need to be negotiated individually.
  3. Risk management. This should probably be the first items and has maybe not entered in the discussion yet. The original objective of derivatives contracts like swaps is risk management. For example it may be used to swap some specific risk profile into an overnight unsecured funding profile. There is no way this risk management objective can be maintained if no unsecured overnight index is maintained. It would be reasonable for end used to ask not only for the monetary compensation of the change of value of the derivative but also for the lost risk management service. A compensation for forcing the end user to bear the cost of risk between secured and unsecured funding would appear reasonable to me. Beyond legal agreement and valuation impacts, there is a fundamental risk management reason for the original framework. Is the new framework covering those risk management requirements? This is an open question.
Coming back to the minutes of the meeting, they contain, to my opinion, the same misunderstanding that were analysed my previous blog.

1. Termination or change of reference for existing trades. This requires the agreement of all parties, contract by contract. Given the current burden on legal and client relation resources in most banks and derivative users in relation to the changes in the regulatory landscape of the derivative market, I would be surprised if there are many resources available to start those discussions in the next months.

2. Rational for a compensation payment of zero. The rational presented in the document is inconsistent with the well documented and precise collateral discounting approach (see Chapter 8 in my multi-curve book) used by most market participants. The reference to a "risk-free rate" indicates a misunderstanding around clean collateral discounting.

The argument in the minutes that "as the SARON swap market does not exists, the determination of any non-zero compensation payment is nearly impossible", proves that the market is not ready for the change, not that no compensation is due.

The argument that compensation has not been applied in "similar situations" like "the change from single-curve valuation to muti-curve valuation", indicates that the situation is misunderstood - the situations are clearly not similar - and not that a precedent exists.

3. Internal risk approval. In the minutes, an appendix gives some argument for participants to obtain internal risk approval to start trading SARON swaps.

The first point of the proposal suggest to "start trading short maturities". It is fine for me to start prudently. But as a consequence, it means that generalized SARON discounting is impossible. To be able to have pricing of SARON cash collateralized derivatives based on market prices, you need a SARON OIS market up to the maturity of the longest traded derivative (not the longest SARON OIS). This part of the proposal invites to introduce the SARON OIS slowly, over a multi-year periods, and is incompatible with a big-bang in a short 10 months period.

The second point refers to VaR. It says that "Historical Volatility (HV) of the SARON fixing is below the HV of the TOIS fixing, which allows using the TOIS risk framework without understanding volatility". The first part of the sentence may be correct, but it applies to an index which is under review, in a very specific period of stress on the market due to central bank interventions. Moreover it applies to the index itself, not to the OIS rates associated to the index which do not exist yet. The OIS rates as risk factors is what would be important for HVaR. But what seems particularly surprising is the sentence second part. If all the OIS positions were stand alone, a lower volatility would (in a weak sense) lead to lower VaR. In a portfolio setting, a lower volatility of one component will lead to a different volatility of the portfolio; if the volatility of the portfolio is lower or higher will depend on the positions and the correlations between the risk factors. New positions on a new risk factor, the SARON OIS, will appear; at the start there will be natural basis positions. Does the working group suggest that a 0 VaR is a good proxy for the basis TOIS/SARON risk in a HVaR framework?

4. Regulation for margin on non-cleared derivatives. The new regulation impact on amending trades is not mentioned at all in the minutes. I refer you to item 8. in my previous blog. Don't underestimate this issue.

I have already written a blog scheduled to be published on the 1st January 2018. The blog is written as a couple of questions. Will the situations be closer to the one I predicted in the previous and this blog or closer to the expectation of the WG? To be continued!

Don't hesitate to let me know if any bookie is offering odds on the timing of the CHF overnight benchmark; I would probably put a fiver on one side. On which side? I let you guess!

My side for the bet is maybe more difficult to guess than you think at first sight. You know my opinion, but you don't know my current position on the bet and as a trader I'm more a market maker than a punter. I trade with my brain (and my own wallet), not my heart.


Change of benchmark overnight index is a difficult task: CHF case

In a blog published in September 2014, I claimed that a change of benchmark overnight index is a difficult task. A that time the claim was a reaction to US Federal Reserve and ISDA suggestions that changing the main USD overnight index from "Fed Fund effective" rates to a general collateral overnight index (DTCC GCF Repo Index) was easy. The reason behind that difficulty was described in that blog and, to my opinion, the misconception that it could be easy comes from a misunderstanding of what "OIS discounting" means. As you know, I'm not a fan of the terminology as it hides too many fundamental issues behind the mechanism (see Section 8.1 of my book on the multi-curve framework). People realized the difficulty of the process and in particular a US Treasury staff later commented that "Any transition away from a dominant benchmark will surely be complex and lengthy". That comment lead me to ask Did the US Treasury read my blog?

In the present blog, I will present similar arguments, but this time in relation to the proposed changed of the CHF reference overnight index. The proposed changed is described in a recent article in Risk magazine: Swiss rate reform set to trigger swap value change (subscription required).

The current main reference rate in CHF for overnight rates is the TOIS published by COSMEREX AG. The above sentence contains a contradiction on a contradictory term, as I wrote "overnight rate" and "TOIS" means "Tom/next rate used in Overnight Index Swaps", but I will ignore that detail here. The proposed replacement is the SARON ® (Swiss Average Rate OverNight) developed by the Swiss National Bank (SNB) and SIX Swiss Exchange. The SAR family of rates are based on CHF repo transactions. There are indices with tenors from ON and T/N up to 12 months.

The situation is very similar to the USD one that I analyzed a couple of years ago; some people estimate that the replacement of an unsecured overnight rate (or tom/next) rate by a secure rate based on transactions would be better.

As before, I certainly agree that using a secured rate as a reference rate for collateral remuneration would be a logical step. In the OTC derivative market, where Variation Margin (VM) will become mandatory in a couple of weeks (on 1 March 2017), having a good reference rate will certainly be more paramount than ever. The collateral posted for VM is done mainly in cash, and is equivalent in some sense to collateralised lending. The cash collateralises the derivatives as much as the derivatives collateralise the VM cash.

Is a secured rate better as a reference for the OIS in the OTC derivative market? That is entirely another question. The answer depends on what you want to use the derivative market for. Is it to hedge the interest rate risk of a book to align it to a secured or an unsecured borrowing? I'm sure there are plenty of situations where secured borrowing hedging will be the correct one and plenty of other situations where unsecured borrowing hedging will be the correct one. As much as I strongly prefer the secured rate as a reference for the collateral, as much I don't have a preference in the case of the reference rate for the derivative market. Or more exactly I believe the ideal solution would be to have a market for both, but if there is only one market I don't have an economical preference for either of them.

I don't have an economical preference, but I have a strong mathematical/quantitative finance simplicity preference; I would prefer to have the same rate for collateral and swap reference. That preference is strongly linked to the subject of the above mentioned Risk article and lies in the in depth understanding of what "OIS discounting" means. To my opinion, most of the article and the people interviewed for it got the foundation of OIS discounting wrong.

The goal is to reform the SARON definition and completely replace the TOIS index, including discontinuing it, for collateral remuneration and OIS reference by the end of 2017. To achieve that the following steps must be taken (this is a reworked list from my 2014 blog).
  1.  Create the reformed version of SARON.
  2.  Create a liquid OIS market linked to SARON.
  3.  Make sure that bilateral traded new OIS refers to a (new) CSA related to SARON collateral interest.
  4.  All dealer have to sign new CSA agreements for the new trades.
  5.  CCPs create a new category of trades with SARON collateral; it is not possible to net the existing trades and variation margin as the trades have different reference collateral rates and no full netting is possible. Cross margin for new and old indices are not possible. Or more exactly a payment netting is possible but not a netting of new and old instruments in term of positions.
  6. Run, up to the maturity of the longest trade existing in the world linked to TOIS, two parallel markets, one for the TOIS trades and one for the SARON related trades. This includes computing convexity adjustment between the different trades (good for me, more work for quants, see Theorem 8.11 in my book). The dual collateral rules require each user to run a double set of multi-curve framework with collateral, one with each collateral. In total, one can expect four OIS markets to run in parallel: TOIS swaps collateralised at TOIS (current market), TOIS swaps collateralised at SARON (target collateral with current liquid underlying), SARON swaps collateralised at OIS (target underlying with current collateral), and SARON swaps collateralised at SARON (target market). Obviously there would also be multiple Libor markets.
  7. As an alternative to 5/6, users with existing position could decide to cancel the existing trades. That would require each individual user to agree on the valuation of each position and agree to cancel it for that price. The cancellation could be replaced by an alternative move from one collateral to the other, but in the same way all the parties have to agree on the valuation (as an up-front fee or a fee over the life of the trade) impact of the transfer.
  8. Analyses if the changes of collateral rules or of reference index means that all CHF related trades should be considered as new trades. Due to the rules on mandatory margin the answer to this has a huge impact. It would mean that all trades on TOIS and all trade with a CSA referring to TOIS will fall in the category of trades for which the bilateral margin is mandatory. The mandatory margining does not only apply to completely new trades, but also to any amendment of a trade, even a change of reference ID is considered as a new trade.
  9. Discontinue TOIS publication.
The numbers above are not an order in which the steps need to happen; it is just a list of them. It is better if 1. happens before 9., but for the rest there are plenty of permutations possible, all of them with some kind of inconveniences.

Base on that list, I would like to point to a number of issues that seem misunderstood in the above Risk article.

Consensus: The article states that "The consensus is moving towards the view that no compensation payments will be made". That may be true, but it is irrelevant. The derivatives market is driven by the individual contracts signed by each party. The consensus opinion of the working group is irrelevant to those contract. Each party will need to review its rights and obligation in each contract (individual trades, CSA, CCP agreements, etc.) and see what is applicable to him; no working group, trade body or regulator can decide the fate of existing or forthcoming contracts. As mentioned in the article by an ISDA representative: "parties to make changes to their contracts on a bilateral basis". And, I'm sure you had guessed it, I'm not part of that "consensus opinion".

Risk-free rate proxy: The fact that the OIS rate is in some circumstances associated to a risk-free rate proxy is mentioned in the article. Again, that may be true but irrelevant. For actual fixing, we are not looking at a proxy, but at the actual term sheet, what is legally binding. For discounting of collateralised trade (and all of them will be collateralised from next month), the number of interest is the collateral remuneration rate in the collateral agreement and the risk management procedure of each market participant, not a theoretical risk-free rate.

Libor to OIS discounting: One quote in the article assimilates the change between TOIS and SARON to the change from the Libor to OIS discounting from 2007/2008. The situations are completely different and no parallel can be drawn between the two. The Libor v OIS discounting changes refer to a change in the internal valuation policy of some market participant due to a change of the market levels (change of spreads). The economics of the trades themselves or of their related CSA where not changed. There was no externally forced changes to the term sheets. For some people, the Libor v OIS discounting changes were only a general recognition of a practice that was already used internally by some traders.

Terminate TOIS swaps: "The Swiss working group suggests market participants either terminate existing swaps, or have their floating leg moved to Saron." The above proposal is obviously incomplete, there are many other possibilities, like creating a proxy TOIS, move to SARON + spread, modify the terms of the existing swaps to LIBOR, etc. But even if only the above two possibilities are envisaged, it leads to the "one (or more exactly many) million CHF question": At what price do you do that?

By year end: The article mentioned that some people expect to have all this finished by year end. At this stage, it appear that no trade based on SARON has been done, no ISDA definition exists (expected by end of Q1) and no clearing house has definitively announced it will clear those trades (some potential clearing is expected by year end).

New trades: That very important issue of modified trades considered as a new trades from a regulatory perspective is not even mentioned!

Conclusion: Some market participants still strongly misunderstand the OIS discounting concept, which is not a quant shiny toy but something ingrained in market trading and legal practice. Due to foundations, evolution and implementation of the market, changing any part of its functioning, even the reference overnight index of one currency, is a huge undertaking.

I strongly doubt it will be done in less than a year. To my knowledge, since the September 2014 burst of noise on the similar subject in USD, no real progress has been made. If a "consensus" is forced on the market over that period, I predict many years of legal litigation. I will report on the evolution of the question when I have more information. I already pin a 1st January 2018 blog with a status report.

As usual, my contact details are available in the Book details section of the blog. I'm happy to discuss those  issues with industry representatives, regulators, investors and journalists.