## Episode 2: Zero rate collateral

There is certainly a push for more standardisation of financial products and their collateral terms – Credit Support Annexe (CSA) and margining process in particular. One particular discussion is around the CSA collateral remuneration and its equivalent Price Alignment Interest (PAI) used by Central Counterparts (CCPs). In the current standard terms an overnight rate (Fed Fund, EONIA, etc.) is paid in the currency of the trade in most cases. One potential solution to simplify the term of the CSAs, that I propose as my next fiction, would be to pay interest at a rate of 0 on the collateral. This would certainly simplify the computation of the interest part of any variation margin.

This proposal would align collateral and CCP process to the margin process used for exchange-traded futures. The amount paid as variation margin on futures, on OTC and on cleared trades would not include any interest any more and would be in line. As a secondary benefit, the overnight indexes fixing importance would have the role it should not have lost as an indicator of the economy and not as a main part of the economic process.

Suppose that there is a continuous perfect collateral, a collateral paid in cash in the currency of the instrument and a rate paid on the collateral of 0. From a valuation perspective, the valuation under collateral would become similar to the margining on futures: the difference of value with the previous valuation is exchanged and no interest is paid on that amount. The general futures price process theory, or the multi-curve and collateral framework as described in Chapter 8 of the book, both apply in this case.

What is the value of an Ibor coupon with CSA at rate 0? The answer in term of futures is easy (if we forget about notional and accrual factor)

This proposal would align collateral and CCP process to the margin process used for exchange-traded futures. The amount paid as variation margin on futures, on OTC and on cleared trades would not include any interest any more and would be in line. As a secondary benefit, the overnight indexes fixing importance would have the role it should not have lost as an indicator of the economy and not as a main part of the economic process.

Suppose that there is a continuous perfect collateral, a collateral paid in cash in the currency of the instrument and a rate paid on the collateral of 0. From a valuation perspective, the valuation under collateral would become similar to the margining on futures: the difference of value with the previous valuation is exchanged and no interest is paid on that amount. The general futures price process theory, or the multi-curve and collateral framework as described in Chapter 8 of the book, both apply in this case.

What is the value of an Ibor coupon with CSA at rate 0? The answer in term of futures is easy (if we forget about notional and accrual factor)

*PV*

_{0}= 1 - Φ_{0}
with Φ

Note that the fact that the coupon pays at the end of its actual period has no impact anymore on the valuation. The quote (to use the terminology of the book) is known at the fixing date of the Ibor index and from that date on, the required collateral is known and transferred. The payments in advance or in arrears have the same quote. Maybe there would be a legal distinction between the amount paid as collateral and the amount paid as coupon, but if we ignore that legal distinction, from a pure cash flow exchange perspective, everything is exchanged as soon as the cash flow is known; present value equals futures value (pun intended).

The general collateral principle is still valid: a promise to pay tomorrow is fulfilled by paying today the discounted forward value and adapting the amount up to the final payment. The difference here is the discounting is done at a rate of zero and the fact that no adaptation is required after the last fixing.

There is no convexity adjustment due to the difference in timing of the payments between futures and cleared swaps. This is a world where convexity adjustment becomes an exotic feature for non-standard collateral practice, not a vanilla characteristic of every curve calibration.

It is important to clarify that zero-rate collateral is not equivalent to zero collateral. The collateral is paid, there are cash-flows every day. The cash flow paid every day does not include any interest for previously paid cash flows. What has been paid is paid and we do not adjust the payment subsequently by added some interest to it. That may seems an extravagant proposal, not receiving interest on cash deposited. Looking at it from another point of view, in the futures market, which is probably the most liquid and oldest derivative financial market, used by banks, hedge funds, asset manager, pension funds, and corporates, nobody complains about the absence of PAI (or interest on previously paid profit). The usage of interest on collateral is more an habit (or maybe addiction?) than a fundamental economic necessity.

In interesting to note that the EONIA rate, which is computed in the afternoon of the starting date of the overnight period, is not publicly available anymore on a same day basis; it is available only on the next day. If a figure is used for general process and the regulator forces in some way market participants to use that process, the least we could hope from the regulator is to insure the minimal transparency and make sure the figures are publicly and fee-free available to all. To my opinion, this is a part of the "fixing scandal" that regulators have not addressed properly, if indexes are used for

_{0}the price of the STIR futures in 0.Note that the fact that the coupon pays at the end of its actual period has no impact anymore on the valuation. The quote (to use the terminology of the book) is known at the fixing date of the Ibor index and from that date on, the required collateral is known and transferred. The payments in advance or in arrears have the same quote. Maybe there would be a legal distinction between the amount paid as collateral and the amount paid as coupon, but if we ignore that legal distinction, from a pure cash flow exchange perspective, everything is exchanged as soon as the cash flow is known; present value equals futures value (pun intended).

The general collateral principle is still valid: a promise to pay tomorrow is fulfilled by paying today the discounted forward value and adapting the amount up to the final payment. The difference here is the discounting is done at a rate of zero and the fact that no adaptation is required after the last fixing.

There is no convexity adjustment due to the difference in timing of the payments between futures and cleared swaps. This is a world where convexity adjustment becomes an exotic feature for non-standard collateral practice, not a vanilla characteristic of every curve calibration.

It is important to clarify that zero-rate collateral is not equivalent to zero collateral. The collateral is paid, there are cash-flows every day. The cash flow paid every day does not include any interest for previously paid cash flows. What has been paid is paid and we do not adjust the payment subsequently by added some interest to it. That may seems an extravagant proposal, not receiving interest on cash deposited. Looking at it from another point of view, in the futures market, which is probably the most liquid and oldest derivative financial market, used by banks, hedge funds, asset manager, pension funds, and corporates, nobody complains about the absence of PAI (or interest on previously paid profit). The usage of interest on collateral is more an habit (or maybe addiction?) than a fundamental economic necessity.

In interesting to note that the EONIA rate, which is computed in the afternoon of the starting date of the overnight period, is not publicly available anymore on a same day basis; it is available only on the next day. If a figure is used for general process and the regulator forces in some way market participants to use that process, the least we could hope from the regulator is to insure the minimal transparency and make sure the figures are publicly and fee-free available to all. To my opinion, this is a part of the "fixing scandal" that regulators have not addressed properly, if indexes are used for

*public*processes, and anything mandatory by regulator rules should be considered as public, all the relevant related information should be public. The relevant information refers at the very least to the index value as soon as known and its full historical data. In the absence of public availability of the figures used currently, the proposal of a public and transparent rate a zero (0) would be a good improvement.