THE FVA-DVA PUZZLE: RISK MANAGEMENT AND COLLATERAL TRADING STRATEGIES

THE FVA-DVA PUZZLE: RISK MANAGEMENT AND COLLATERAL TRADING STRATEGIES CLAUDIO ALBANESE AND STEFANO IABICHINO Abstract. In the aftermath of the crisis, valuations of fixed income derivatives have significantly diverged from the principles of arbitrage-free pricing and the law of one price. Discrepancies arise because of the incompleteness of collateral trading markets which lack of reverse REPO contracts accepting OTC derivative receivables as collateral. This circumstance forces banks to implement sub-optimal funding strategies by borrowing unsecured and passing on their own credit spread to clients. In this paper, we propose that excess collateral on OTC books should be considered as an unstable source of funding, not fungible with bank debt. As a consequence, we define the FVA as a book level, non-transactional amount computed assuming that the rate for riskless lending is OIS as opposed to being the funding rate. With this definition, the FVA does not overlap with the DVA. We discuss analytics and strategies to manage FVA risk jointly with CVA, DVA and default loss risk. We also discuss market-completing collateral trading strategies to take advantage of the FVA-DVA funding arbitrage. 1. Introduction Dealers do not receive variation margin from counterparties to unsecured derivative transactions. However, as they turn around and hedge with other financial counterparties, they have the obligation to post collateral in the form of both variation and initial margin. Financing the resulting collateral gap is costly. If markets were complete, it would be possible to finance variation margin at REPO rates by posting OTC derivative receivables in reverse REPO transactions, see Burgard and Kjaer [5]. However, since the market infrastructure for reverse REPOs on OTC deals does not exist, banks need to finance collateral at their own unsecured funding spread. It is thus an interesting challenge to understand what contractual structures could robustly support a reverse REPO market for OTC derivatives. Credit risk and funding costs are intertwined. The Credit Valuation Adjustment (CVA) is the cost dealers pass to unsecured clients to account for the potential losses resulting from counterparty default risk. The Debt Valuation Adjustment (DVA) is the benefit dealers grant clients toward which they don t post variation margin, as a compensation for the risk that the dealer himself could default. The CVA and the DVA depend on netting agreements and are additive over netting sets. The CVA and DVA can also be interpreted as the value of mutual default protection contracts embedded in derivative transactions themselves, see [2]. The Funding Valuation Adjustment (FVA) is the cost of procuring collateral to post as variation and initial margin on derivative transactions to secured counterparties, net of the OIS interest received on the collateral posted. Most CSA agreements allow for the re-hypothecation Acknowledgements: We are grateful to Martin Engblom and Alan White for giving us feedback that helped us improve on earlier versions of this paper. We are also greatful to the extensive comments of three helpful referees. All remaining errors and misunderstandings are entirely the authors sole responsibility. 1

of variation margin. Collateral deficits at the book level are financed at the bank overnight funding rate. Burgard and Kjaer [5] argue that excess collateral positions can be used to buy-back bank debt and should thus give rise to a funding benefit at the funding rate. This conclusion relies on the assumption that OTC excess collateral can be considered as a stable form of funding which is entirely fungible with bank debt. In other words, the assumption is that the rate of riskless lending for a bank equals its funding rate. This assumption gives rise to what we refer to as the symmetric FVA and was first introduced by Pieterbarg [10] in a seminal article showing that the symmetric FVA is a transactional amount which can be valued by discounting payoffs at the funding rate. As pointed out by Hull and White in [7], assuming that the rate of riskless lending is anything else but OIS embeds arbitrage opportunities at the very core of derivative valuation. In this paper, we take the view that OTC excess collateral cannot be considered as a stable source of funding which is fungible with bank debt and assume instead that OTC excess collateral represent an unstable source of funding which earns interest only at the OIS rate. The resulting asymmetric FVA is neither a transaction specific concept nor a metric dependent on netting sets. It is a global metric that is meaningful only for the whole of a trading book across which re-hypothecation of variation margin is allowed. Unlike the CVA and DVA, the asymmetric FVA is not associated to a payoff and does not have an interpretation as the value of a financial contract. The Modigliani-Miller theorem [8] stipulates that the value of a bank is not affected by its funding strategies, i.e. the FVA should be rigorously valued as being worth zero to the bank, see [6]. More precisely, funding strategies for variation margin transfer wealth across the bank capital structure but keep constant the total value of the bank given by the sum of the value to shareholders and the value to bondholders. The asymmetric FVA of an OTC book can be interpreted as the amount of wealth transferred from shareholders to senior debt holders as a consequence of the funding strategy. Bank managers are faced with the very difficult challenge of devising a rebalancing strategy on behalf of shareholders to prevent or revert the wealth transfer to bond holders. Simple strategies are not effective, including selling protection on the bank itself or issuing new super senior debt without violating pari-passu rules. As we discuss in this paper, there are however collateral trading strategies involving third party investors that would work. Morini and Prampolini in [9] also point out that the FVA benefit resulting from the assumption that the rate of riskless lending equals the funding rate gives rise to an apparent double counting puzzle between the symmetric FVA and DVA. This conclusion does not extend to the asymmetric FVA which is orthogonal to and does not overlap with the DVA. Nevertheless, the asymmetric FVA and the DVA do have a few features in common. Firstly, also a non-zero DVA represents a transfer of wealth from shareholders to bond-holders as it is equivalent to a purchase of default protection on the bank itself, shifting cash flows from the bank before default to the bank after default when shareholders are wiped out. Secondly, if it was possible to reverse REPO OTC receivables at OIS rates, then bank managers could serve the interests of shareholders by posting back to unsecured clients, thus eliminating both the FVA for variation margin and the DVA together. Examples of transaction-specific transfer pricing formulas based on symmetric FVA are in Pieterbarg s paper [10]. In our opinion, the symmetric FVA is a faulty metric. However, transactional formulas have the merit of encapsulating a transfer pricing policy for funding costs. With asymmetric FVA, one can only look at the incremental cost in the background of a book of holdings. It appears that practitioners normally use transactional symmmetric 2

FVA formulas only as a guidance and not for book-keeping or hedging. In general, it is not possible to have a perfect match between revenue streams due to transactional FVA transfer pricing and realized portfolio total funding costs. Risk managing the funding costs/revenues mismatch necessitates a portfolio-level, risk-reward optimization analysis based on asymmetric FVA analytics. As we discuss in Section 2, FVA hedging is best accomplished holistically alongside the hedging of CVA, DVA and default losses. Because of this reason, it is fashionable among leading dealers to have a centrally managed XVA desk. Best strategies involve a combination of static positioning based on total return analysis and dynamic hedging based on sensitivities. Optimization can also be achieved by structuring transactions aimed at completing collateral trading markets with the intervention of third party investors and for which no wealth transfer occurs in the first place. These are strategies whereby collateral is supplied by third party investors absorbing first loss credit risk and providing liquidity, thus reducing or even eliminating XVA inefficiencies. As we discuss below, FVA funding arbitrage is best exploited by means of strategies involving two classes of investors. On one side, a margin lender arranges for investors to accept the credit risk of OTC portfolios by posting segregated general collateral as a guarantee to offset counterparty credit risk. By doing so, investors receive the CVA of the exposure and, unlike banks, don t suffer of CVA regulatory capital costs. Once segregated collateral in amount equal to variation margin is received by the bank to offset counterparty credit risk, the bank can then enter a nearly standard tri-party reverse REPO to upgrade the segregated collateral into cash to be posted to the hedge counterparties as variation margin. See also [2], [3] and [4]. The paper is structured as follows. In Section 2, we quantify how to calculate and risk manage the FVA in today s incomplete collateral trading markets. In Section 3, we discuss the issue of wealth transfer across the bank capital structure and the resulting arbitrage opportunities. In Section 4, we introduce a stylised two-period model demonstrating how collateral trading strategies affect the asymmetric FVA and DVA and how they can both be reduced to zero. In Section 5, we outline the proposed collateral trading strategy in a real-life situation. Section 6 concludes. 2. Calculating the FVA The nature of OTC portfolio exposures is such that the net collateral position swings between situations where the collateral received is in excess of collateral posted and situations where the opposite happens. If there is a shortage of collateral, then the funding cost to procure it depends on the bank s own credit. Upon posting collateral the bank typically receives OIS. Hence, funding costs are measured by the funding spread over OIS. A key point in the analysis of funding costs is to decide how to quantify the rate for riskless lending in situations where hedges to unsecured OTC transactions generate an excess net collateral position. One view is that one could use excess collateral to buy-back bank debt in secondary bond markets and the rate for riskless lending should equal the funding rate, see [5]. Another view is that OTC books are an unstable source of funding which is not fungible with stable funding sources such as debt and the rate for riskless lending should be OIS. Accordingly, we have two definitions for FVA: the symmetric FVA is computed assuming that the rate for riskless lending of collateral equals the funding rate while the asymmetric FVA assumes that the rate of riskless lending is OIS. 3

The symmetric FVA is far easier to compute as it is a transactional amount, i.e. it is given by the sum of the symmetric FVAs for each individual transaction. As Pieterbarg showed in [11], the symmetric FVA of a single transaction can be computed by discounting future cash flows at the funding rate as opposed to the OIS rate. The asymmetric FVA at time 0 is defined as in the following formula: (2.1) Asymmetric FVA = E 0 [ 0 ( ( e t 0 rudu 1 τb >t max n VM n t, 0 ) s VM t + ( n IM n t ) ) ] s IM t dt. Here VM n t is the variation margin at time t due to the n-th netting set in the portfolio (counting posted margin as positive and received margin as negative) max ( n VMn s, 0) is the net excess variation margin required for the entire trading book n IMn s is the sum over netting sets of initial margins s VM t and s IM t are the spreads over OIS for variation and initial margin τ B is the default arrival time for the bank. The indicator function 1 τb >t reflects the assumption that a bank stops posting collateral upon defaulting If in this formula one omits initial margin and removes the max function, one obtains the symmetric FVA in [10] and [5]. As Piterbarg showed, the symmetric FVA is a transactional concept as it can be computed as the sum of values of individual transactions in which the discount rate is taken to be the funding rate. (2.2) Symmetric FVA = E 0 [ 0 ( e t 0 rudu 1 τb >t n VM n t ) ] s VM t. The DVA is sensitive to derivative payables, not receivables, and is linear across netting sets. [ ] (2.3) DVA = E 0 e t 0 rudu 1 τb >t max ( VM n t, 0) λ t dt. 0 where λ t is the probability rate of default of the bank at time t along a given scenario. The DVA is totally orthogonal to the FVA. There are situations where the asymmetric FVA is positive and the DVA is zero, when for instance a bank has a CSA agreement with all its unsecured counterparties that obliges it to post variation margin to all. There are also situations where the DVA is positive but the asymmetric FVA is zero, when counterparties post to the bank but the bank does post back. However, there is indeed an overlap between the DVA and the symmetric FVA, as was noticed also in [9]. Let us underline that in the definition of asymmetric FVA, we make use of OIS discounting as is normally done following the Fundamental Theorem of Finance when assessing the value of a stream of future cash flows. Exotic discount rules emerge in the analysis of the symmetric FVA but would not be consistent at portfolio level. A method for computing the asymmetric FVA is to simulate the collateral gap for an OTC trading book by evolving the price process of all unsecured netting sets while assuming that each unsecured transaction is hedged back-to-back. Since CSA agreements often include rating dependent triggers, one needs to evolve also the credit spreads of each counterparty. The asymmetric FVA is theoretically consistent with arbitrage free pricing but is much harder to compute than symmetric FVA or even the CVA. Since the CVA is additive across netting 4 n

Figure 1. Cumulative loss distribution due to counterparty defaults and CVA/DVA/FVA return distributions over monthly time intervals for the first year ahead sets, one can draw different scenario sets for each netting set. The asymmetric FVA instead requires shared scenarios across netting sets because of the possibility of re-hypothecation of variation margin. Furthermore, since collateral swings are very volatile, the time grid required to compute the FVA is much finer than the one required to compute the CVA within the same precision. The asymmetric FVA is best managed holistically together with the CVA, DVA and default losses. Since the risk profile is gamma negative and the execution of delta hedging replication is prone to leakage, static hedging strategies are a useful complement to delta hedging. The optimization of static hedging strategies necessitates nested simulation and the calculation of total return distributions for default losses, CVA, DVA and asymmetric FVA across time. A nested simulation for total return analysis typically requires generating hundreds of millions of scenarios and valueing the portfolio along each scenario a few hundred times. This is a remarkable technology challenge but is indeed possible if one makes use of the Mathematics and technology framework described in [1]. In Fig. 2 we show the graphs of the cumulative default loss distribution and the return distributions of CVA, FVA, DVA obtained with the methods in [1]. In Fig. 2 we show the total return distribution giving a complete 5

Figure 2. Total XVA return distribution including CVA, DVA, FVA and cumulative losses due to defaults over monthly time intervals for the first year ahead view of XVA risk. These graphs were obtained by running a nested simulation with 10,000 primary scenarios with 200 time points to 50 years, bifurcating off 2,000 secondary scenarios on a monthly frequency over the first year to revalue portfolio CVA, DVA and FVA. Cumulative loss distributions were also computed. The portfolio entails 50,000 fixed income trades and 2,000 counterparties, whereby each counterparty CDS curve is simulated along with all market factors and a multifactor credit-credit, credit-market and market-market correlation structure. Initial margin is simulated by valuing the value-at-risk for each netting set at each point in time of the simulation. 3. Impact of Collateral Strategies on the Capital Structure The asymmetric FVA arises from the lack of reverse REPO transactions with derivative receivables as collateral. Incompleteness per se does not invalidate arbitrage freedom and should not affect valuations. However, the asymmetric FVA arises because of a peculiar form of market incompleteness whose existence motivates sub-optimal behaviour and gives rise to macro-economic deviations from general equilibrium. To make an analogy, consider a firm wishing to finance a real estate purchase by using an unsecured loan instead of a mortgage. Unsecured funding lines have higher spreads but come with a peculiar advantage since the firm retains the title to the asset upon default. Holding the title benefits pre-existing debt holders as they have a priority claim on the asset over the unsecured lender. In other words, by the sake of entering into an uncollateralized transaction for asset acquisition, wealth is being transferred from shareholders to senior creditors. Banks have multiple classes of debt holders including depositors, bond holders, REPO counterparties and others. As a rule, asset acquisition by uncollateralized borrowing triggers wealth transfer across the bank capital structure, from equity holders to senior creditors. This is precisely what happens in OTC markets since there is no infrastructure for reverse REPO contracts 6

whereby OTC derivative receivables insured by CVA desks can be posted as general collateral to achieve a cash upgrade at OIS rates. Although a non-zero DVA does not measure an inefficiency similarly to the FVA, its existence is still intertwined with that of the FVA. The DVA arises because banks don t post collateral on out-of-the-money unsecured client transactions. The DVA is the cost of default protection the bank buys on itself from unsecured counterparties. The bank buys DVA by granting discounts at contract inception to unsecured counterparties and buys FVA by paying excess spreads to collateral lenders during the life of the transaction. However, if it was possible to reverse REPO an OTC derivative into cash, also the DVA would be zero as in this case the trading book would have no collateral shortage but only collateral surplus. In this situation, CSA restructuring whereby the bank posts back variation margin to clients would trigger a perfectly legitimate wealth transfer across the bank capital structure from bank bond holders to shareholders. The symmetric FVA would not be offset by the existence of reverse REPO transactions as the symmetric FVA would still embed a benefit generated by scenarios with net derivative payables. This is yet another indication of the spurious arbitrage opportunities arising from the symmetric definition of FVA whereby the rate of riskless lending is above OIS. Capital structure arguments are also useful to understand counterparty behaviour. Bank counterparties can be roughly divided into two categories: those which are rich of high quality collateral and those which aren t. Counterparties with collateral on their balance sheets have an interest to post as much as possible to derivative counterparties as this would decrease their DVA (i.e. the bank CVA) and transfer wealth to their shareholders. Other classes of counterparties such as corporates do not own high quality collateral on their balance sheet but instead require derivatives for the purpose of project financing. Such counterparties typically have a preference not to book derivatives on a mark-to-market basis and to deploy liquid resources for project financing as opposed to pledge collateral. The corporates preference to enter unsecured transactions is exactly the opposite of the banks preference. One should emphasize that the funding preferences of firms that do not wish to post high quality collateral could still be met if a third party which is collateral rich were to post guarantees on their behalf. Guarantees are preferable to collateral assets because they don t appear as debt on the firms balance sheet. 4. A Two Period Toy-Model The objective of this section is to analyse in detail the form of market incompleteness at the root of a non-vanishing asymmetric FVA. For simplicity s sake, we consider a two period model with a start date t 0 in the past, a valuation date t 1 representing current time and a time horizon t 2 in the future. The commercial bank CB and unsecured counterparty UC enter in an unsecured derivative transaction struck at equilibrium at time t 0. CB hedges its derivative exposure to UC on a back-to-back basis with either an investment bank IB or an exchange CCP. The bank CB is then left with the obligation to post variation margin to either the investment bank IB or to the exchange CCP in a cash amount matching at all times the mark-to-market valuation of the derivative. Counterparty credit risk for UC is retained by the commercial bank CB. IB and CCP receive collateral and are immunized with respect to credit risk. We assume that the unsecured counterparty UC is a going concern at current time t 1 but might possibly default at time t 2. The change of mark-to-market value from time t 0 to time t 1 triggers collateral posting obligations as collateral amounts need to be updated. At time t 2, a 7

Figure 3. Unsecured collateral borrowing second update of variation margin is required and we need to consider the possibility that the unsecured counterparty UC defaults in the interim. In the following two subsections, we analyse our toy model with two time periods. For simplicity s sake, we neglect gap risk and initial margin. The unsecured collateral strategy is represented in Figure 3 while the secured one is represented in Figure 4. 4.1. Strategy 1: unsecured collateral borrowing. We assume that the commercial bank CB is a legal entity entailing a trading desk TD, a CVA desk and an FVA desk. The trading desk TD underwrites a derivative transaction with the unsecured counterparty UC. For simplicity s sake, we assume that the transaction makes reference to a CSA agreement whereby the parties post collateral to each other only for the variation margin in excess of a pre-set trigger level depending on the credit of either party. At the start date t 0, the transaction is at equilibrium and TD buys default protection from the internal CVA desk against the default of UC. The unsecured counterparty UC pays to TD the fair value of the derivative in addition to the CVA and FVA price adjustments. In addition, the unsecured counterparty receives DVA in the form of a discount on the transaction price at inception. At start time t 0, the trading desk TD: hedges the transaction with an offsetting trade with the hedge counterparty HC, which can either be an investment bank or a CCP; buys counterparty credit risk protection on itself by paying DVA to the unsecured counterparty UC; buys counterparty risk protection from the CVA desk internal at TD by passing the CVA premium received from the unsecured counterparty; no collateral is posted as the transaction is initially at equilibrium at time t 0. At current time t 1, assuming as we explained that the unsecured counterparty UC is not in a state of default, the trading desk TD does the following: 8

if the fair value of the derivative transaction to UC at time t 1 is negative, then CB receives variation margin from the hedge counterparty HC and keeps it on its balance sheet, without handing it over to UC; if the fair value of the derivative transaction to UC at time t 1 is positive, then the FVA desk of CB borrows variation margin on an uncollateralized basis at the credit spread of the bank CB and posts it to the hedge counterparty HC. HC pays to CB the interest on variation margin at risk free rate (OIS). At current time t 2, the trading desk TD acts as follows: In case neither the unsecured counterparty UC nor the bank are in a state of default, then variation margin is updated as it had been at time t 1 ; In case the unsecured counterparty UC happens to be in a state of default at time t 2 while the bank CB is a going concern and the transaction is in-the-money for the bank, then: the CVA desk pays the transaction value to the desk TD; the trading desk TD closes the transaction with the hedge counterparty that keeps variation margin; TD closes the loan from the FVA desk with the funds received from the CVA desk; In case the unsecured counterparty UC happens to be in a state of default at time t 2 while the bank CB is a going concern and the transaction is out-the-money for the bank, then the trading desk TD closes the transaction with the hedge counterparty and pays the received margin to the liquidator of the unsecured counterparty UC. In case the bank CB happens to be in a state of default at time t 2 while the unsecured counterparty UC and the transaction is in-the-money for the bank CB, then: the unsecured counterparty UC novates the transaction with another bank, receives fair value from the novation counterparty and passes it on to the liquidator of CB; the hedge counterparty HC novates the transaction while keeping the variation margin received; CB liquidators distribute the proceeds from UC to the universe of all its debt holders in order of seniority, not favouring collateral lenders unless their contract explicitly states otherwise. As a consequence collateral lenders have a limited recovery R ULC (V M) +. In case the bank CB happens to be in a state of default at time t 2 while the unsecured counterparty UC is not and the transaction is out-of-the-money for the bank CB, then: the unsecured counterparty UC novates the transaction with another bank by paying the fair value of the transaction in case UC is out-of-the-money; the hedge counterparty HC novates the transaction and CB keeps the variation margin received from HC; CB liquidators distribute the cash collateral from the hedge counterparty HC to the universe of all its debt holders in order of seniority, not favouring the derivative counterparty UC unless their contract explicitly states otherwise. As a consequence, the derivative counterparty has a limited recovery R UC (V M). In case the bank CB and the unsecured counterparty UC are both in a state of default at time t 2, then: the hedge counterparty HC novates the transaction while keeping the variation margin received; 9

the bank CB liquidates the defaulted derivative assets and distributes the proceeds to the universe of all its debt holders in order of seniority (not favouring collateral lenders unless their contract explicitly states otherwise); derivative transaction between CB and the unsecured counterparty UC give rise to recovery rights that need to be identified and settled during the bankruptcy process. Figure 4. Secured collateral borrowing 4.2. Strategy 2: secured collateral borrowing. The setup of this scenario is similar to that of the previous case except for a key difference: at start time t 0, the trading desk TD buys default protection not from the internal CVA desk but from an external margin lender ML which accepts the obligation to post segregated collateral on behalf of the unsecured counterparty UC in an amount equal to the fair value of the transaction at all times. At current time t 1, assuming that the unsecured counterparty UC is not in a state of default, the FVA desk funds the variation margin required by the hedge counterparty by entering into a reverse REPO transaction to transform the segregated collateral posted by ML into overnight cash. The rate for upgrade to cash is the prevailing REPO rate for GC collateral. Since the GC REPO rate and OIS are separated by a very small spread of a few basis points, the cost of the cash upgrade to the FVA desk is nearly offset by interest rate receipts from the hedge transaction counterparty HC which pays OIS. At current time t 2, the trading desk TD does the following: In case, the unsecured counterparty UC is not in a state of default, then variation margin is updated; In case the unsecured counterparty UC happens to be in a state of default while the bank is not defaulted, then: the margin lender ML liquidates the segregated collateral and the FVA desk makes whole the reverse REPO counterparty with these funds; the trading desk TD closes the transaction with the hedge counterparty by allowing them to keep the variation margin. 10

In case the bank CB happens to be in a state of default at time t 2 while the unsecured counterparty UC is not defaulted, then: the unsecured counterparty UC novates the transaction with another bank by either passing the variation margin received or instructing the margin lender ML to re-post the segregated collateral to the novating bank; the hedge counterparty HC novates the transaction while keeping the variation margin received. In case the bank CB and the unsecured counterparty UC both default at time t 2, then: the hedge counterparty HC novates the transaction while keeping the variation margin received; the margin lender ML liquidates segregated collateral in an amount equal to the fair value of the derivative transaction and makes the counterparty of the reverse REPO transaction whole. 5. Strategy implementations A real life strategy along the lines discussed in this paper is illustrated in Figure 4. In an efficient and realistic implementation, instead of configuring the CVA desk as an internal operation, one would have a margin lender as an arm s length financial entity that sells insurance to trading desks. The margin lender backs up the default protection with collateral in full for a pool of names, up to a cap negotiated with the bank. The bank would then lend cash as needed to cover the excess amount whenever needed, with the understanding that the margin lender would still cover all losses arising from default up to the cap. Margin lending for OTC contracts can be structured over various maturities. We believe that the most efficient structuring strategies involve rather short maturities of around 6 months as one needs to accommodate for the natural flow of positions. In this situation, the margin borrower is liable for the payment of floating CVA premia which are linked to its credit spread (or a proxy thereof) and the expected amount of collateral required. The CVA volatility risk can be ameliorated by negotiating caps on the CVA floating payments. Since margin lending eliminates both the cost of CVA regulatory capital and the cost of FVA and since long term CVA is typically well in excess to short term CVA, even striking a cap at the current level of cumulative CVA and FVA fees would result in a substantial reduction in running spreads for the client. Initial margin that the counterparty needs to post can also be reduced at the condition that the margin lender accepts to post collateral past the time of default and until the close-out process and liquidation is completed. This assumes that the margin lender providing variation margin is a fully collateralized pass-through vehicle with potential liabilities matched by his collateral assets up to a cap and that the bank accepts the risk liabilities may exceed the cap. Reducing initial margin posting obligations by the bank and the FVA for variation margin cannot be achieved by a third party margin lender focused on providing collateral to counterparties. However, relief could be obtained by means of a segregated liquidation fund selling globally capped gap risk protection to all bank counterparties. In this paper, we focused exclusively on bilateral derivative transactions. However, most constructions and concepts extend and apply to the multi-lateral case whereby CB is replaced by a Central Counterparty Clearing House or CCP. From a regulatory angle, we believe that banks would obtain capital relief within current regulations if this scheme were implemented. The key consideration is that this scheme involves 11

repapering CSA agreements in such a way to oblige counterparties to post variation margin, while allowing them to rent the collateral from investors that would post it on their behalf through a combination of segregated funds and cash upgrades. Failure to post collateral by counterparties would trigger a failure to pay condition and a default event. 6. Conclusions We introduced the asymmetric FVA as metric for funding costs to procure variation and initial margin for OTC books. The asymmetric is a book level metric which, unlike the more commonly used symmetric FVA, has no overlap with the DVA. A non-vanishing asymmetric FVA is the indication of existence of funding arbitrage. Whenever a dealer raises unsecured collateral under its own credit, it generates spurious payoffs after the bank default, thus transfering wealth across its capital structure from shareholders to bond holders. Further transfering costs to clients reduces macro-economic welfare. In this paper, we discuss market-completing collateral trading strategies based on margin lending that theoretically reduce the asymmetric FVA due to variation margin possibly down to a theoretical limit of zero. Once a market infrastructure for such strategies is established, derivative markets will be more efficient, the law of one price will be restored and risk neutral valuation at OIS discounting will again prevail. References [1] C. Albanese, T. Bellaj, G. Gimonet, and G. Pietronero. Coherent Global Market Simulations and Securitization Measures for Counterparty Credit Risk. Quantitative Finance, 11-1:1 20, 2011. [2] C. Albanese, D. Brigo, and Frank Oertel. Restructuring Counterparty Credit Risk. SSRN: http://ssrn.com/abstract=1969344 or http://dx.doi.org/10.2139/ssrn.1969344, accepted for publication on IJTAF and on the Working Paper Series of the Deutsche Bundesbank, 2011. [3] C. Albanese and G. Pietronero. A Redesign for Central Clearing. Credit Flux, August, 2011. [4] C. Albanese, G. Pietronero, and S. White. Optimal Funding Strategies for Counterparty Credit Risk Liabiliies. Available at SSRN: http://ssrn.com/abstract=1844713, April 18, 2011. [5] C. Burgard and M. Kjaer. Partial Differential Equation Representations of Derivatives with Counterparty Risk and Funding Costs. Journal of Credit Risk 7(3), pages 119, 2011. [6] J. Hull and A. White. Is FVA a Cost for Derivatives Desks? Risk, pages 83 85, 2012. [7] J. Hull and A. White. Valuing Derivatives: Funding Value Adjustments and Fair Value. preprint, 2013. [8] F. Modigliani and M. Miller. The Cost of Capital, Corporation Finance and the Theory of Investment. Economic Review, 48:261 297, 1958. [9] M. Morini and A. Prampolini. Risky Funding: A Unified Framework for Counterparty and Liquidity Charges. Risk Magazine, March, 2011. [10] V. Piterbarg. Funding beyond discounting: collateral agreements and derivatives pricing. Risk Magazine, pages 97 102, 2010. [11] V. Piterbarg. Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing. Risk Magazine, February, 2010. E-mail address: claudio.albanese@global-valuation.com Global Valuation Limited, London, EC2M 4YF, UK E-mail address: stefano.iabichino@global-valuaiton.com Global Valuation Limited, London, EC2M 4YF, UK 12