Continuous dividend v discrete cash flows

Variation margin

With the generalization of variation margin collateral, the derivative world is not driven anymore by discrete cash flows but continuous dividend. This can be explained with the following two graphs.
Figure 1: Derivative value

Suppose that you have entered into a derivative in the past. In the graphs that date was 20 days ago and the X axis represent the time. You entered into the trade at fair price, so the initial value was 0. Time has past and the value has gone up and down. The Y axis of the same graph is the value. The current value is positive. As the party to the trade are uncertain that their counterpart will honor its derivative obligations, it is now standard to ask for variation margin related to the derivative. In this context variation margin is the exchange on a daily basis of collateral to guarantee the obligation. The party out-of-the-money (for which the value is negative) is posting financial instrument with the same value as the trade as a guarantee. In the interbank market, the legal agreement around those margins are usually described into the CSA (Credit Support Annex) between the financial institutions. The standard approach is to pay to variation margin in cash. In the graph, the multiple line for the date after today (0) represent the uncertainly around the future. For the future another concept, Initial Margin enter into account. But this is the story for another day.

Due to the legal link between the derivative and the CSA, the representation of the first graph is only partial and one could argue it is incorrect. The derivative does not exists on its own anymore. You can not look at it and compute its “value” as if the rest of the agreement did not exists. If you combine the derivative with the obligation to pay back the collateral received, you obtain the second graph. The total value is always zero, or more exactly is reset to 0 every day. There is a continuous, or more exactly daily, "dividend" payment.
Figure 2: Derivative cash flows
What is the amount of this dividend? It is the exchange of collateral, itself linked to the value of the derivative. The dividend is the change of value of the instrument minus the interest paid on the existing collateral. In continuous time, the equation is written as
dDt = dVt - ct Vt dt
(see Equation 8.1 in the Multi-curve framework book).

Margin payment in practice

In practice, today, continuous time does not exists and everything is done on a discrete basis with one day being the standard atomic amount of time. The dividend paid is thus (with time written in days)
(Vt - Vt-1) - ct-1 Vt-1
This is the amount computed at date t, but when is it paid? In theory it should be in t, but in practice you need some time to do the actual computation, agree with your counterpart the amount, send the payment message, etc. Without taking into account potential disputes, the payment is done at best in t+1. I say at best, as when institutions are not in the same time zone, t+1 becomes relative and can become t+2 in practice. To clarify the explanation, suppose that the margin is always paid in t+1.

The derivatives also have actual coupon payments; interest rate swaps have regular payments of fixed or floating coupons. How do the coupon flows interfere with the daily margin payments? Let's start with the theoretical description and introduce the t+1 payment later. As an example, suppose that the next coupon payment, in time t,  has a amount of 100 and the value of the rest of the derivative is small. Suppose the values are in
t-3 t-2 t-1 t t+1
99.0 99.5 99.8 0 0.1
Note that for the valuation in t in this table, the coupon to be paid in t is not included in the valuation.
The payments are:
Date Formula Amounts Cash flow
t-2 Vt-2 - Vt-3 99.5 - 99.0 0.5
t-1 Vt-1 - Vt-2 99.8 - 99.5 0.3
t Vt - Vt-1 + coupon 0.0 - 99.8 + 100 0.2
t+1 Vt+1 - Vt 0.1 - 0.0 0.1
Very smooth with small payments everyday. Exactly what we wanted/expected.

No introduce the t+1 payment for the margin:
Date Formula Amounts Cash flow
t-1 Vt-2 - Vt-3 99.5 - 99.0 0.5
t Vt-1 - Vt-2 + coupon 99.8 - 99.5 + 100 100.3
t+1 Vt - Vt-1 0.0 - 99.8 -99.8
t+2 Vt+1 - Vt 0.1 - 0.0 0.1
Very smooth with small payments everyday, except around the coupon where there are large spikes, positive then negative. Exactly what we don't want. We have recreated the credit risk we wanted to avoid by introducing the variation margin.

This risk related to spiked exposure is for example described in a recent paper by L. Andersen, M. Pykhtin and A. Sokol: Rethinking Margin Period of Risk.

A different approach?

To avoid this problem, the CCPs have introduced a different way to proceed; they pay the coupons also in t+1. The cash flows are then
Date Formula Amounts Cash flow
t-1 Vt-2 - Vt-3 99.5 - 99.0 0.5
t Vt-1 - Vt-2 99.8 - 99.5 0.3
t+1 Vt - Vt-1 + coupon 0.0 - 99.8 + 100 0.2
t+2 Vt+1 - Vt 0.1 - 0.0 0.1
Very smooth with small payments everyday. Only the coupon is paid on the wrong date.

Can we do better? Certainly! Obviously you can not forecast the market perfectly and know in t-1 what the market will be in t, but you can certainly compute a forward value. The exact meaning of this forward value and how the forward market is estimated is not very important, what is the most important part is to include the cash flows in that valuation. The new valuation are

Computation t-4 t-3 t-2 t-1 t
Value date t-3 t-2 t-1 t t+1
Value 99.1 99.6 99.9 0 0.1

The cash flows are in this approach
Date Formula Amounts Cash flow
t-2 Vt-2 - Vt-3 99.6 - 99.1 0.5
t-1 Vt-1 - Vt-2 99.9 - 99.6 0.3
t Vt - Vt-1 + coupon 0.0 - 99.9 + 100 0.1
t+1 Vt+1 - Vt 0.1 - 0.0 0.1

To have this approach working, it is important that in t, the two parts of the cash flow, the one related to the variation margin and the one related to the coupon are paid on a netted basis. If not you introduce a "Herstatt"-like settlement risk even in single currency. To be netted, the payment of the two parts have to be in the same currency. But this is the case for most of the market (in traded notional), the variation margin and the instrument are denominated in the same currency.


The requirements to obtain this clean margining process are at the same time easy and difficult. The CSA have to be rewritten to incorporate this forward approach to margin related valuation and payment processes for coupons and collateral have to be merged into a unique process. This require rewriting all CSA agreements. A huge process, but this need to be done anyway in the coming months to take into account the new regulation related to bilateral margining. A good time to introduce the changes. The second part require changes in back-office processes and a more global approach to risk management processes. This is maybe where the resistance will be the largest.

Note that the new regulation on bilateral margin impose to compute initial margin related to a 10 days margin period of risk or close-out period. If no mechanism is introduced to smooth-out the exposure spikes, this amount at risk will need to be included in the IM computed. That would introduce a new spike, an asymmetrical in IM this time to protect for the spike in VM/coupon payment. That spike will be worst as the IM has to be in segregated accounts and no netting or reuse of funds is allowed. It will be "interesting" to see if the regulators take into account that type of exposure in their validation of bilateral internal model. The mandatory bilateral margin takes effect in September 2016 for the largest derivative users; their models will need to be validated (by regulators in Europe, US, etc.) by that date. A lot of validation activity will take place in the coming months.

In summary

Timing difference between variation margin and coupon payment reintroduce a temporary credit exposure that is supposed to be remove by the variation margin procedure. This residual risk can be removed by relatively small changes in the margin procedure. Those small changes involve changes in CSA wording and changes to payment processes that should be unified inside a financial institution. This is probably the right moment to do it as CSA and procedure have to be fundamentally reviewed to cope with regulatory changes taking place in less than 6 months.

As usual, don't hesitate to contact me for advisory work around market infrastructure changes, derivatives valuation or  risk management.


Workshop on Margin

In the last years, I have reviewed the methodologies of the world largest OTC swap CCPs, read most of the recent related regulatory changes, research the impact of those changes on valuation and implemented most of them in libraries. Those exercises combined with my background in quantitative analysis and trading give me a unique perspective on the changes in the derivative market infrastructure.

As part of the recent advisory engagements related to the above subjects, I ran several workshops on margins in Europe and in the US. Those workshops have been offered as one day or two days programs.

Below are a short summary and the agenda of a typical workshop. The workshops are always tailored to the audience. Don't hesitate to contact me for more information or to request a similar workshop in-house.


One impact of the crisis has been the increase of the spread between different reference rates. Another impact has been the regulatory efforts to try to reduce the systematic credit risk in the inter-dealer market. One direction has been to push vanilla instruments to central counterparties (CCPs) for central clearing and another one is the mandatory bilateral margin for transaction. Those changes have generated a new approach to the valuation and risk management of derivatives, in particular to the vanilla one. The first part of the workshop describes the impact of Variation Margin on the valuation. This is often referred to as the collateral discounting framework and has ramification in swap valuation, curve calibration, risk management in presence of collateral, with the foreign collateral case an important example. In the second part we focus on Initial Margin (IM). IM is one of the CCPs risk management tools; we analyse the specific methodologies used by the main CCPs. IM will become an important part of bilateral relation as it will made mandatory from September 2016; we analyse different current proposal for a standard market methodology.

Previous delivery agenda


Part 1: Variation margin

  • Margin: terminology and fundamentals
  • Clearing/variation margin/initial margin/capital: a regulatory time table
  • Multi-curve framework
  • Valuation under (variation margin) collateral: Overnight rate collateral, Foreign currency collateral, Bonds collateral
  • What information about change of collateral valuation is available in the market?
  • Curve calibration under collateral: OIS discounting and foreign currency collateral
  • Risk management of interest rate risk with foreign currency collateral - sensitivities, basis / Impact on IM methodologies


Part 2: Initial margin

  • CCP specific initial margin methodologies: LCH, CME, Eurex ; CME/LCH basis
  • Bilateral margin: regulatory requirements (focus on Europe/EMIR and/or US regulation)
  • ISDA(R) SIMM proposal (related to FRTB SBA standard approach): main feature, implementation
  • Comparison between CCP margin and bilateral requirements/SIMM
  • Pro-cyclicality features of CCP methodologies - volatility stress-test / Estimation of future Initial Margin
  • Cost of clearing: New member of the xVA family: MVA
  • Numerical challenge of the MVA computation; some methods to reduce the numerical burden
  • Conclusion: Review of the regulatory time-table and the impact on the workload for financial institutions and regulator

Slides and lecture notes are made available to participants at the end of the day.