Collateralisation: CVA & FVA - Murex - Alexandre Bon


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Collateralisation: CVA & FVA - Murex - Alexandre Bon

  1. 1. OTC COLLATERALIZATION, CVA AND FVA The practical challenges of untangling credit and funding costs Alexandre Bon RI$KMINDS 2011 Geneva December the 8th
  2. 2. Where have all the flowers gone?« Too big to fail » have become « too big to save »Massive re-regulation & changing standards– Basel III, Dodd Frank-Emir, IFRS 13…Where is the risk-free asset ?– OIS-LIBOR basis– Multi-curve environment– Risky sovereignsWhat about the « Law of One Price? »– Valuation adjustments– Close-out value vs. Profitability measureEvolving business models– CCPs, CVA desks, Collateral transformation… Copyright ® 2011 Murex S.A.S. All rights reserved 2
  3. 3. Introducing the Collateral AgreementA bit of terminology : Collateral, ISDA & CSA – CSA : credit support annex – Non-mandatory appendix to the ISDA master agreement (which enforces close- out netting for eligible contracts) – Defines the scope and terms of bilateral remargining agreement – CSA is the most common (but not the sole) collateral agreement for OTC derivatives – Standard templates but varied implementations (differences in clauses and jurisdictions)Main clauses – Eligibility of positions to close-out netting and collateralization – Eligibility of pledge-able assets and applicable haircuts – Remargining process : valuation, frequency, settlement, reconciliation, dispute resolution – Determination of the collateral balance: symmetry, thresholds, independent amounts, minimum transfer amounts, rounding rules… – Legal framework: pledge or title-transfer, rights of re-use & rehypothecation – Remuneration of the collateral account (most often based on an OIS rate, but not always!) Copyright ® 2011 Murex S.A.S. All rights reserved 3
  4. 4. Collateral MitigationCollateralization does not fully eliminate counterpartyrisk but reduces it greatly.A collateral contract can be seen as a derivativescontract of the portfolio value.Collateral pay-off function :– Risk-free value of the collateralized portfolio at the re-margining date– Thresholds, Minimum Transfer Amount, Independent amounts, rounding rules– Outstanding balance– Haircuts applicable to the collateral asset Copyright ® 2011 Murex S.A.S. All rights reserved 4
  5. 5. CVA - Collateral Modeling Margining Counterparties Netting Nodes NodesEligibility rules CSAExposures are ISDA - ABCmapped to Nettingand Margining sets No collateralUpon close-out the Bank ABCcollateral balance GMRA GMRAis offset againstthe netting nodepositions No netting No collateral Copyright ® 2011 Murex S.A.S. All rights reserved 5
  6. 6. CVA - Collateral Modeling Exposure at t is the difference of the Close-Out value of the portfolio and Outstanding collateral balance Considering the simulation date correspond to the close-out date following default one identify the previous effective re-margining date Common modeling options Margin Period of Risk previous grace dispute fail close-out remargining period Unsecured exposure (collateralised set) Exposure Collateral Balance ThresholdSimulation Simulation Ti - MPR date Ti-1 date Ti Copyright ® 2011 Murex S.A.S. All rights reserved 6
  7. 7. CVA - Collateral Modeling A path-dependent issue Common modeling options: – Short-cut method – Dynamically identify the previous margining date and revalue (only) the collateralized set’s positions by full simulation – Analytical (portfolio volatility) approximations – Pros/Cons Margin Period of Risk Exposure ThresholdSimulation Simulation Ti - MPR date Ti-1 date Ti Copyright ® 2011 Murex S.A.S. All rights reserved 7
  8. 8. Collateralization & typical portfolio mixAn institution’s OTC portfolio will commonly contain a mix of: – Bilateral CSAs with 0 threshold and daily margining (cash) – Positions cleared on CCPs : daily or intraday exchange of Variation and Initial Margin – CSAs with asymmetric terms • One-way with SSAs • Over-collateralized agreements (IAs, Thresholds, IM) and security collateral (e.g. PB agreements) : small funds and corporates – No CSA – Multiple “collateral sets” with a single credit entity (by products : CSA, GMRA, OSLA, GMSLA … or entities)Some local variations, but the interbank market is mostly onbilateral CSAs and daily cash marginingImperfect collateralization bears additional risks & andwarrants further valuation adjustments (credit and funding) Copyright ® 2011 Murex S.A.S. All rights reserved 8
  9. 9. CVA – Collateralization EfficiencyMain collateralization risks and issues: Lack of standardization across CSAs Costs and risks of operation (bilateral & 0-threshold) Concentration risk Credit dependent clauses Eligibility of collateral assets & haircuts Execution : rounding, split differences, disputes – In practice collateral amount will never exactly match the exposure levels – The former are typically ignored in the model, the latter managed by adjusting the MPR of problem counterparties (dispute history). Rehypothecation and re-characterization risks Gap Risk – Model risk & close-out value – JTD & Wrong way risk Copyright ® 2011 Murex S.A.S. All rights reserved 9
  10. 10. RehypothecationRehypothecation: – The collateral taker uses pledged assets as security for his own obligations to a third partyRight of re-use: – Covers rehypothecation as well as any use of the collateral asset in line with ownership of the property (e.g. sale, lending to a third party)Depending on the jurisdictions and legal phrasing, collateralexchange can be performed under: – A Title Transfer Arrangement (implicit re-use rights) – A Pledged Collateral Agreement, where the rehypothecation right may be explicitely granted (often the case with non-bank counterparties)Similar question with cash collateral and margin segregationSome remarks: – Rehypothecation and “re-pledging chains” have played an essential part in providing liquidity (and leverage) to the financial markets – The GFC showed how damaging the combined effects of reduced collateral velocity (cf. Lehman close-out) and collateral squeeze (haircuts) can be in a systemic shock. – Not a desirable feature from a CCR mitigation point of view, but forfeiting this right represents a funding cost. Copyright ® 2011 Murex S.A.S. All rights reserved 10
  11. 11. Risk-free or risky close-outISDA documentation not 100% clear on how weshould price the liquidation value of derivatives.Open issue for default close-out as well asvaluations for Unwinds and ATEsIntroduces a recursive pricing issueTheoretical justifications for both approaches: theneed for another Valuation Adjustment(RVA/ATEVA) ?Practical questions:– Pricing of DVA or funding cost in distressed markets– Joint-default– Going-concern collateral balance is determined based on risk-free valuation Copyright ® 2011 Murex S.A.S. All rights reserved 11
  12. 12. One-Way Collateral Agreements Part I Sovereigns, Supranationals and Agencies (SSAs) Small non-bank counterparties without a collateral management function Potentially large exposures for the un-collateralized party Bilateral CVA ~ Unilateral CVAExposures vs. Liabilities distributions Copyright ® 2011 Murex S.A.S. All rights reserved 12
  13. 13. Collateral gap riskInstantaneous jump in exposure and counterparty defaultleaving a portion of the portfolio un-collateralized• More prevalent with imperfect CSAs (large thresholds & MTAs, longer remargining frequencies)• Credit protection bought from related entity• Simply settlement effects (warrant special treatment?)• Liquidity effects upon counterparty default Copyright ® 2011 Murex S.A.S. All rights reserved 13
  14. 14. A Familiar Horror StoryA SME wishes to hedge away the FX risk of itsexports against the steady appreciation of itslocal currency against USD: => a right-way situation Copyright ® 2011 Murex S.A.S. All rights reserved 14
  15. 15. A Familiar Horror StoryA SME wishes to hedge away the FX risk of itsexports against the steady appreciation of itslocal currency against USD:We can sell him a strip of put optionsWe make the product cheaper by limiting ourdownside (KO)The product is very popular but the market ishighly competitive: we can make it cheaper bybuying a call option that gets activated afteran OTM barrier level (or rather two or three).This is still right-way, right?Very limited downside, nice upside, coveredwith collateral, in some instances back-to-back : how bad can it get? Copyright ® 2011 Murex S.A.S. All rights reserved 15
  16. 16. A Familiar Horror StoryCopyright ® 2011 Murex S.A.S. All rights reserved 16
  17. 17. A Familiar Horror Story 520 companies holding for over US$ 10b of KIKOs Average hedge ratio to annual export between 35% and 40% 68 SMEs with an average hedge ratio of 194% Class-Action suit for mis-selling Déjà vu - and though, firms in HK, India, Indonesia, Taiwan, Brazil, Mexico, Poland posted at least $30 billion losses on FXD in 2008.Copyright ® 2011 Murex S.A.S. All rights reserved 17
  18. 18. A Familiar Horror Story: The Gremlin TradeFrom right-way to wrong- Collateralization questions:way – Did CVA desks spot these CCR concentrations?– Trade size vs. turnover : an – Many of those contracts were extremely large exposure will collateralized on favorable terms trigger a default to the banks, but with large– Crowded trade remargining periods and with KRW bonds.Credit risk – Incidentally, an interesting– Counterparty risk stress-test case for regional CCPs and aspiring clearing– Assimilation / Model risk brokers (cf. IM calculation– Reputation risk methods)– Legal risk Some practical IT fixes– Systemic risk Copyright ® 2011 Murex S.A.S. All rights reserved 18
  19. 19. From Credit to Funding Discounting Credit risk Calibration ValuationCopyright ® 2011 Murex S.A.S. All rights reserved 19
  20. 20. Funding un-collateralized tradesIn any derivatives contract future cash-flow exchanges need tobe “funded”.A bilateral position with an open negative MtM can be seen as anovernight loan granted by the counterparty : logically this fundingbenefit is financed at our cost of funds.A positive MtM represents a funding cost : by unwinding the tradeand investing this amount with my treasury (or buying back myown bond issue) I could get the same rate.Hence an uncollateralized transaction’s Cash Flows should bediscounted at my senior unsecured cost of debt.Neglecting the CDS-Bond basis, my senior unsecured cost of fundsis in line with the assumptions PDs and Recovery of the CVAcalculation. Hence at a single contract level (i.e. single deal ornetting set): DVA = Funding Benefit. Copyright ® 2011 Murex S.A.S. All rights reserved 20
  21. 21. Funding cost: the (non-)effect of netting 2 parties A & B have two exactly offsetting trades but no netting agreements between them: – Both parties will have non-zero CVA & DVA terms (and bilateral CVA) – They both have 0 funding cost as CFs will offset. In practice whether a set of transactions is covered by a close-out netting provision (ISDA) or not, has no implication on their funding cost (and thus the discounting curve to be used) For non-fully netted portfolios the Funding Benefit is not equal to DVA! – No close-out netting agreement – Multiple netting sets Copyright ® 2011 Murex S.A.S. All rights reserved 21
  22. 22. Funding collateralized tradesIf a CSA is in place, the “lender” typically receives a collateralfor a value ~ equal to the MtM of the position, either as: – a Cash amount, which can be re-invested (overnight) and on which a pre- specified interest is paid back to the poster (typically compounded OIS index). – a Security. If the CSA agreement allows for re-hypothecation, that collateral can be repo-ed to another party to fund at a much lower rate than an unsecured funding rate. – Simplifying assumptions: 0 Thresholds & MTAs, daily remargining, one currency, no haircuts on securities, no dispute…Hence CSA-covered positions can be funded by using an OISdiscount curveNon CSA-covered positions are funded using the internal costof funds (senior unsecured debt) Copyright ® 2011 Murex S.A.S. All rights reserved 22
  23. 23. The Ideal CSA HypothesesBilateral AgreementContinuous MarginingInstantaneous settlement of margin calls0 Threshold and Minimum Transfer AmountNo Independent AmountsNo haircutsCash (or equivalent instrument) collateral, independent from exposureNo valuation differencesNo disputesNetting set = Margining setNo Initial MarginCCR : – No rehypothecation / segregation of collateral accounts – No Initial Margin with risky entities – No settlement risk on margin flowsFunding : – Rehypothecation / no segregation of collateral accounts – No Initial Margin – Single risk-free collateral asset (e.g. no currency basis arbitrage) Copyright ® 2011 Murex S.A.S. All rights reserved 23
  24. 24. New FO and Risk systems needsFront-Office systems require flexible curve allocationmechanisms:– Collateral documentation is pricing data!– Rule-based dynamic allocation of curves based on both the leg currency and underlying collateral currencyProper allocation of risk and sensitivities– E.g. Uncollateralised CMS swap (CMS rate derived from collateralised instruments)Need a multiple curve calibration engine: – Able to detect the dependencies – Wider selection of curve building instruments – Simultaneous bootstrapping of all involved curves with accuracy and speed. Copyright ® 2011 Murex S.A.S. All rights reserved 24
  25. 25. Pricing exampleUncollateralized USD CSA In-the-money XCCY swap EUR/USD with 5Y outstanding maturity P&L impact of 36bp Forward MtM, vs. Expected Exposure & Expected Liability evolution. Copyright ® 2011 Murex S.A.S. All rights reserved 25
  26. 26. Pricing in a Multiple Curve EnvironmentForwarding curves are derived from collateralized quotes – Joint bootstrapping of discounting and forwarding curves – E.g. EONIA and EURIBOR 3M, then EURIBOR 6M vs. 3M… – Triangular calibration with XCCY basis curves or markets with varying liquid swap tenors depending on the horizon.Different discounting curves depending on the CSA clauses. – EURIBOR swap collateralized in EUR is discounted on an EONIA curve – EURIBOR swap collateralized in USD is discounted on a EUR/USD XCCY basis curve built upon a USD Feds Funds curve. Copyright ® 2011 Murex S.A.S. All rights reserved 26
  27. 27. Pricing in a Multiple Curve EnvironmentThe new funding paradigm requires multi-curveevolutions for derivatives pricing and CVAestimation. – Current standard market practice: deterministic basis spreads curves on top of a risk-free OIS curve – Currently testing a HJM 2F stochastic basis spread model, calibrated to historical data (results to be presented soon).Another difficult question pertains tocorrelations(OIS-LIBOR spread vs. rates, bond-CDS basis vs. LIBOR basis andcredit…) Copyright ® 2011 Murex S.A.S. All rights reserved 27
  28. 28. Main issue: the CSA is not perfectWhen exposure is in-between thresholds, we fund atLIBOR + spread and not at OIS flatNon-cash asset: haircuts and rehypothecation rights?Choice of collateral currency: – Steep XCCY basis spreads with the current USD squeeze – Apparently comparable to a contingent Bermudan XCCY swaption on the portfolio (hint at American Monte Carlo pricing) – In practice varying implementation approaches – However, uncertain execution / enforceability • Different legal interpretations (US vs. UK law – do we require the consent of the receiving party? Is full substitution always possible when there is no margin call?...) • Will the collateral management team deliver the adequate collateral? – Will the issue disappear with the Standard CSA?Does the local market even have a liquid OIS instrument?One-way CSA case is another tricky case of fundingasymmetry (one threshold pushed to infinity) Copyright ® 2011 Murex S.A.S. All rights reserved 28
  29. 29. One-Way Collateral Agreements Part II Funding cost at OIS flat Funding benefit at unsecured debt level Double hit: CVA & FVA Usually SSAs will have much lower credit spreads than the institution so the Funding risk effect would dominate the Credit risk one. Difficult to value in the simple discount switch setting, however actual quoted price is unlikely to be the “fair-one”. Borrow at LIBOR + spread Receive funding at OIS flat Copyright ® 2011 Murex S.A.S. All rights reserved 29
  30. 30. Introducing the Standard CSANew collateral support annex protocol promoted byISDAAim to standardize valuation practices– Specify OIS discounting– Remove the collateral switch optionality– Align CSA to the margining mechanics of CCPs0 Threshold, no MTA, daily marginingCash collateral only for variation marginPhased implementation in 2012 : transactions canbe moved from legacy CSA to S-CSATransactions pooled in 5 Designated CollateralCurrency buckets Copyright ® 2011 Murex S.A.S. All rights reserved 30
  31. 31. Introducing the Standard CSA Phase I Discounting on USD Local currency OIS discounting Feds Funds & corresponding (EONIA, SONIA…) FX basis curves CCS and CHF trades EUR trades GBP trades JPY trades other currencies CHF EUR GBP JPY USD collateral collateral collateral collateral collateral balance balance balance balance balance MarginCalls / Deliveries Counterparty Herstatt Risk! Copyright ® 2011 Murex S.A.S. All rights reserved 31
  32. 32. Introducing the Standard CSA Phase II CCS and CHF trades EUR trades GBP trades JPY trades other currencies CHF EUR GBP JPY USD collateral collateral collateral collateral collateral balance balance balance balance balance MarginCalls / Deliveries Safe settlement: PvP platform operated by ISDA Swap margins to USD (ISA method) Counterparty Copyright ® 2011 Murex S.A.S. All rights reserved 32
  33. 33. Moving to S-CSA: system implicationStraight-forwardadaptation of theCVA Monte Carlo Margining Counterparties Netting Nodes NodesEngine thanks todynamicconstruction of the CSA – EURnetting andmargining sets(rule-based) … ISDA - ABCIn practice, need CSA – USD*to follow closelymigration of trade Bank ABCblocks (by Legacy CSAproducts, entities) …from legacy CSA toSCSA margining. No collateral Copyright ® 2011 Murex S.A.S. All rights reserved 33
  34. 34. S-CSA implementation challengesISDA : “Regardless of approach, firms will need to undertake considerable internaltechnology and process re-engineering work to implement the SCSA.” Collateral systems impact: – Electronic messaging – Exposure pooling and collateral accounts by currency buckets & flexible mechanism to migrate positions off legacy CSA – Mandatory OIS discounting – Implementation of ISA & PvP processes Front-office: – Availability of collateral eligibility criteria at point of pricing – Discount curve allocation mechanism based on CSA / SCSA mappings – For a period of time maintain local OIS curves and Basis OIS curves CVA / FVA units – Consistent mapping of the positions to currency buckets – Multiple margining sets per netting set – Value margin conversion via ISA-type method and capture FX risk over MPR Copyright ® 2011 Murex S.A.S. All rights reserved 34
  35. 35. FVA - Collateral ModelingAn alternative approach to the Discount Method consists inlooking at the question from a portfolio level by representing thefunding cost as another valuation adjustment(the OIS curve providing a proxy for the risk-free rate).Evolve market rates and explicitly model the collateral balancesand a funding strategy. E.g. – Collateral balance : funded at OIS flat – Portfolio value – balance : shortfall funded at own cost of fundsExtend existing CVA simulation framework since this will provide: – A consistent pricing framework for CVA and FVA (calibration, deal aging and termination events) – The CVA engine already has all required business logic (margining set mapping, curve and spreads evolution) – A validated & controlled infrastructure : inter-system data flows, interfaces, reconciliation processes – A low & managed TCO, as one can leverage existing infrastructure (e.g. grid, GPU farm) : running FVA calculations on top of a CVA simulation is computationally efficient (provided i. consistent modeling assumptions and ii. that collateralized positions are already included) Copyright ® 2011 Murex S.A.S. All rights reserved 35
  36. 36. FVA - Collateral ModelingRates curves areevolved jointly Margining Counterparties Netting Nodes NodesCollateralBalances areobtained at the CSA – EURmargining nodelevel … ISDA - ABCCollateral assetsare funded at the CSA – USD*Agreement’s Bank ABCspecified ratesource Legacy CSA …Collateralshortfalls funded No collateralon funding curve Copyright ® 2011 Murex S.A.S. All rights reserved 36
  37. 37. FVA - Collateral Modeling Practical simulation implementation : DVA is not the FVA benefit (MPR vs. Settlement lag). Margin Period of Risk Settlement Lag Collateral Funding Collateral Balance (FVA) Collateral Balance (CVA)Simulation Simulation Ti - MPR Ti - SL date Ti-1 date Ti Copyright ® 2011 Murex S.A.S. All rights reserved 37
  38. 38. FVA - Collateral Modeling Reducing the MPR (10 days) to the Settlement lag (3 days) halves the DVA estimate. Final FVA impact would be stronger on portfolios with imbalanced EPE/ENE profiles or asymmetric collateral terms (thresholds, IAs, one- way CSA).Copyright ® 2011 Murex S.A.S. All rights reserved 38
  39. 39. What about FVA for CCP-cleared products?Margin requirement broadly split in IM and VMIM typically much larger and aimed at covering gap risk over theauctioning period (so as to preserve default funds contributions)IM models are typically VaR-based (adjusted with credit andliquidity factors)The IM funding requirement will then depend on the“directionality” of the cleared portfolio!Should this additional cost be modeled on an incremental basis(consistent with CVA and OTC FVA), or handled as a post tradeoperational cost? Incentives may differ vastly depending on theinstitution.Extending the CVA/FVA model to provide estimation of forwardInitial Margin requirements would require a forward approximationof the margining sets VaR. Computationally, the issue is similar tothe estimation of the incremental RWA cost of capital. Copyright ® 2011 Murex S.A.S. All rights reserved 39
  40. 40. Variation Margin and Initial Margin FVA for cleared products should, in theory, account for the incremental cost of funding the Initial Margin 5 days to close the auctioning process High C.L. VaR Initial MarginVariation Margin Position at Ti-1 Position at T Copyright ® 2011 Murex S.A.S. All rights reserved 40
  41. 41. An open questionShould we look at aligning the industry’s modeling of MPR and close-out gap risk for CVA/PFE with the CCPs’ I.M. estimation models?– Standard I.M. models implemented at CCPs– Volatility vs. time-acceleration– Directionality of underlying netting sets exposures– Adjustments for systematically important financial institutions. Initial Margin– Contingent funding stress vs. WWR models Position at T Copyright ® 2011 Murex S.A.S. All rights reserved 41
  42. 42. Questions and practical issuesVanillas are de-facto level-2 derivatives and market prices are nottransparent (difficulty to unwind off-market positions)Broker quotes need to be reinterpreted (e.g. B&S vols)New premium quotation modes (unfortunately not applicable for alltypes of options)Sensitivities and hedge ratios differ between collateralized anduncollateralized casesPerfect hedge can only be achieved under identical collateralizationtermsPricing effects are complex to quantify for imperfectcollateralization cases and embedded optionalitiesDifficult /costly hedging of basis risksConvexity and wrong-way funding effects deemed small (priceimpact smaller than bid-ask) but traders need to be aware of themWhich CSA clauses should be modeled / can be hedged ? Copyright ® 2011 Murex S.A.S. All rights reserved 42
  43. 43. Questions and practical issuesInternal organization challenges: Need to implement consistent pricing of new transactions, unwinds and legacy books Fair pricing of internal positions Ownership of the funding issue and hedging Ensure that the Collateral Management & Treasury functions provide optimal funding (as supposed in the pricing) Integration of data flows and inter-operability : both a processes and systems challenge ! Establish clear-cut transfer pricing and cost management policies Copyright ® 2011 Murex S.A.S. All rights reserved 43
  44. 44. Two modeling and organizational modelsDiscount curves method Global FVA/CVA exposure methodSimpler to implement in a crude way, Requires significant investments (starting withadditional complexity with curves a simulation framework)management and FO assignments Global hybrid pricing consistent across desksTrade pricing compatible with local desk and with CVA.models. Flexible handling of CSA agreements andFail to account for corner cases explicit modeling of the funding strategy – asymmetric funding terms – Reproduces the previous method results under – convexity effects (e.g. spread / rates correlation) specific cases – liquidation value different from risk-free value – Can include funding impact of credit mitigantsNon-explicit link with DVA Isolates clearly funding cost from valuation and CVA/DVADeal-level and easily understood by traders Portfolio-level, cost reallocated to the tradesFunding and convexity risk owned by the (like CVA)traders Funding and convexity risk transferred to aWorks best with smaller decentralized centralized Funding / Treasury deskoperations well collateralized Works best when bringing together Treasury, CVA and Collateral trading operations Open question : what should be the regulatory treatment of the FVA market risk in the second setting? FVA VaR integrated in the IMA model? Copyright ® 2011 Murex S.A.S. All rights reserved 44
  45. 45. Some useful referencesCollateralization & Counterparty Risk: D. Brigo & A. Pallavicini (2011) – Arbitrage-Free Counterparty Risk Valuation under Collateral Margining D. Brigo (2011) – Counterparty Risk FAQ: Credit VaR, PFE, CVA, DVA, Closeout, Netting, Collateral, Re-Hypothecation, WWR, Basel, Funding, CCDS and Margin Lending. J. Gregory (2009) – Being two-faced over counterparty risk J. Hull & A. White (2011) – CVA and Wrong Way Risk. ISDA (2011) – Overview of ISDA Standard Credit Support Annex (SCSA). M. Pykhtin (2010) – Collateralised credit exposure, in Counterparty Credit Risk, edited by E. Canabarro, Risk Books. M. Pykhtin & D. Rosen (2010) – Pricing Counterparty Risk at the Trade Level and CVA Allocations.Books: J. Gregory – Counterparty credit risk – The new challenge for global financial markets. Wiley Finance. G. Cesari & al. – Modelling, Pricing, and Hedging Counterparty Credit Exposure. Copyright ® 2011 Murex S.A.S. All rights reserved 45
  46. 46. Some useful referencesCollateralization & Funding: C. Fries (2010) – Discounting Revisited: Valuation Under, Funding, Counterparty Risk and Collateralisation. M. Fuji, Y. Shimada & A. Takahashi (2010) – Collateral Posting and Choice of Collateral Currency. A. Green (2011) – Engineering a CVA and FVA solution, talk given at the WBS Discounting and Funding conference , November. M. Morini & A. Prampolini (2010) – Risky funding: a unified framework for counterparty and liquidity charges. V. Piterbarg (2010) – Funding beyond discounting: collateral agreements and derivatives pricing, Risk Magazine, February issue. Risk Magazine (2011) – The evolution of swap pricing. Nick Sawyer, March issue. M. Singh & J. Aitken (2010) – The (sizable) Role of Rehypothecation in the Shadow Banking System.Blogs: Deus ex Macchiatto ( FT Alphaville ( Copyright ® 2011 Murex S.A.S. All rights reserved 46
  47. 47. THANK YOU 47