I first discussed collateral square in my 2013 paper Multi-Curve Framework with Collateral. The name collateral square itself had been suggested by Damiano Brigo during discussion on the paper first draft. To my knowledge, the theory behind the pricing of derivatives collateralised by assets that can themselves be repoed was first described in the above paper. It is also described in my multi-curve framework book.
The origin of the term "collateral square", which reminds the CDO square terminology, is that the bonds are provided as collateral to the derivative and then the bond is provided a second time as collateral to obtain the required cash; the collateral to the derivative is provided as collateral to a term deposit.
A recent article in Risk, titled The price is still wrong: banks tackle bond CSA discounting, describes the recent evolution in the EUR market in which the ON repo rates (for high quality bonds) are well below the EONIA rate, up to 40bps and even several percent at quarter end.
As often the case when there is a discussion about collateral and discounting, I would like add some personal comments and analysis.
In general, to price collateralized derivatives, the "discounting" is done using the "collateral rate". The discounting is done using the overnight rate - or overnight repo rate of the asset in case of asset collateral - cash account. It is only in exceptional circumstances that the overnight compounded of the cash account can be transformed into an actual know long term discount factor. This very special circumstance is realized in the main currencies for the overnight main indices through the OIS market. As this special case is the standard for all the main currencies, one tends to forget it is an exceptional circumstance; my dislike of the term "OIS discounting" and regular rants about potential changes in the related markets comes from the use of a common place name for an exceptional circumstance. The OIS market transforms a compounded overnight into a fixed rate over a potentially long period. Overnight rate discounting can be transform into OIS discounting by a change of numeraire, and the market provides us a practical tool to realize the change of numeraire!
The article mentions the long term repo rate that would be used (after change of numeraire) to discount the long term derivatives cash-flows. What the article does not mention is how to transform the ON compounded repo rate into a long term repo rate in the market. This can be achieved in the following way: Receive the bond in a long term repo transaction in which you provide the cash for a long term and received the associated long term repo rate. At the same time, repo out the bond overnight, receive the cash overnight and pay the overnight repo rate. This look theoretically, from a derivative pricing perspective, like the OIS case, transforming an overnight rate into a long term rate. The first big difference, often mentioned, is the absence of long term repo market. The second big difference, less mentioned, is the balance sheet impact of the repo transformations. As I mentioned in one of my previous blog, I have grown-up from a derivative quant to a balance sheet quant; before using a pricing formula I have to look at how to implement the hedging strategy (derivative quant) and its impact on balance sheet (balance sheet quant). To realise the EONIA overnight to long term transformation, a single clearable and balance sheet cheap OIS is enough. For the repos, the transformation involving a repo and a reverse repo described above is required. The cost in term of capital to put those two transactions in place is a lot higher than the OIS; probably nobody would enter is such a costly hedging scheme only to hedge the discounting risk.
In term of pricing a new ATM vanilla IRS, what is the impact of the cash v bond collateral, i.e. overnight EONIA v overnight repo discounting? Personally I have no way to estimate the exact difference. It would require to estimate the convexity adjustment between the EURIBOR forward rate under EONIA discounting and repo discounting. Remember what the forward rate is. It is not a economic quantity that is measured on its own, it is the number to be put in a old formula to obtain the right price (Definition 2.1 in my multi-curve framework book). The forward is defined from the price, not the opposite. You cannot compute the price in a new circumstance from a forward rate estimated somewhere else without theoretically justified adjustments. This requires a three curves model for EONIA, ON repo and EURIBOR, including all the co-dependence (correlation) between them. Moreover, there is no way to hedge any of the model risk generated by those multi-factor model, due to the absence of liquid market. If I have to market make a swap book and I'm asked to quote a bond collateralized swap, my only protection is a large bid/offer spread. I can compute my PV01 risk with respect to EURIBOR collateralized at EONIA, EURIBOR collateralized with bonds, the associated discounting, but I don't have liquid hedging instruments. My strategy would be to try to balance the book with other bond collateralized IR derivatives and take a large bid/offer spread protection when quoting those trades to be able to survived unhedged market movements.
The article seems to indicate that banks have ignored the difference between bond collateral and cash collateral in part "because there is no liquid term-repo market that can be used to accurately price long-dated trades". As a former swap trader, this would be a supplementary reason for me to take it into account! If there is no way to accurately price and hedge the trade, that is where I would put more risk management and pricing efforts, not less. I may use OIS levels to estimate the shape of the long term repo curve, but I will certainly have a specific repo curve and spend a good amount of time analyzing the non-hedgable model risk of that curve.
Now if we ignore the known unknown that the convexity adjustment between forward rates is, what would be the change of ATM rate for a vanilla EURIBOR IRS? Currently the repo rates are lower than the EONIA rates and the EUR curves are upward sloping. The curve being upward sloping, this means that in a receiver IRS, on the short term part of the IRS we will receive a net cash flow (fixed higher than forward) and on the long term part of the IRS we will pay a net cash flow (fixed lower than forward). Discounting at a lower rate is increasing the value of all the cash flows but the impact is larger on the longer term. The impact is higher where we net pay; the IRS with the same fixed coupon has less value. To obtain a fair ATM IRS, the fixed coupon received has to be increased. In summary, given the current upward shape and negative repo spread, ignoring convexity adjustments, the IRS should have a higher fixed coupon for bond collateral.
When trading IRS with clients under a symmetrical bond-only CSA, the banks will receive and post collateral, depending of the market movements. The higher cost of collateral is potentially in both directions, it is not necessarily a gain for the bank; it is no "keeping the benefit", it is "keeping the risk", positive of negative. But this is fair, one of the raison d'être of banks is to manage financial risks, not to avoid them. Probably certain categories of clients have a derivative portfolio which is mainly made of receiver swaps. Feigning of ignoring the impact of bond-only collateral will allow to underpay the fixed rate as described above. But once that initial mis-pricing has been realized, during the life of the trade, the spread can generate a monetary gain or loss; but what is certain is that dealing with the repo market to align the trade arrangements to the main liquid market based on cash collateral will be a cost in term of operation and balance sheet. For that part it is "keeping the cost".
The Risk article also repeats the traditional view that OIS discounting appeared in 2007 following the divergence between EURIBOR and OIS. There has always been a decently large spread between EURIBOR and OIS, even before the crisis. Before the crisis, the spread was lower and more stable at around 10 to 12 bps. Moreover the OIS discounting, even if under a different name and with less theoretical developments than today, as been used well before the August 2007 start of spread volatility. I have used similar technique for trading as early as 2004 or 2005 and my first 'irony' article was published in Wilmott magazine in July 2007, before the start of the crisis.
An interesting question that could be asked, is the potential for a segmented market with a bond-only collateral market developing in parallel to the main cash collateral market. Part of the answer could be present in the potential move by Totem to start benchmarking that segment. The market segmentation of bilateral trades has to be put in parallel with the segmentation of the cleared market, e.g. the existence of a LCH v EUREX spread in EUR IRS. The spread exists not necessarily for fundamental difference between the economics of each market, but because of the difficulty to cross the markets. The regulations, balance sheet constraints and market infrastructures are creating barriers in a global market. Could it be that the world is becoming geographically global but local in term of classes, not social classes but market infrastructure classes?