Global Derivatives 2014 - Did Basel put the final nail in the coffin of CSA Discounting ?

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FVA in presence of stochastic funding spreads, Inititial Margins and imperfect collateralisation conditions.

Since the birth of CSA discounting during the GFC, major regulatory changes have been reshaping collateral practices in a way that challenges the fundamental assumptions of the method.

Agenda:
- FVA for economic value & incremental pricing
- FVA via CSA discounting or Exposure simulation
- Funding spreads and exposure co-dependence
- Collateralisation regimes in the New Normal and Initial Margins

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Global Derivatives 2014 - Did Basel put the final nail in the coffin of CSA Discounting ?

  1. 1. Did Basel put the final nail in the coffin of CSA Discounting ? Amsterdam - May 15th, 2014 Alexandre Bon, Murex FVA in presence of imperfect collateralisation, IMs and variable funding spreads
  2. 2. Copyright © 2014 Murex S.A.S. All rights reserved2 Introduction Funding issues & FVA are all over the news  Institutions recently deciding to include FVA in their Financial Statements  Heated debates aroundValuation Adjustments  Funding troubles for Asian Banks on CNYTARFs products sold to corporates 2007-2009 : birth of the CSA discounting argument Since then, major regulatory initiatives have been reshaping OTC derivatives markets:  Mandatory Clearing (Dodd Frank, Emir)  Upcoming regulation of CSAs for “non centrally cleared derivatives”  Higher costs of capital (LCR, NSFR, CVA charge…) and focus on asset optimisation (balancing capital and collateral management needs) As a result, the question is whether pricing approaches that have been implemented after the GFC are still valid, or whether corrective adjustments are required:  Where funding costs matter most: uncollateralised corporate portfolios, one-way CSAs with SSAs, Centrally cleared portfolios  Given “New Normal” market dynamics : e.g. spread volatility and correlation with other factors
  3. 3. Agenda 1. INTRODUCTION : FVA AND COLLATERALISATION 2. CSA-DISCOUNTINGVS. EXPOSURE SIMULATION 3. FUNDING SPREADS VOLATILITY 4. COLLATERALISATION REGIMES & INITIAL MARGINS
  4. 4. Copyright © 2014 Murex S.A.S. All rights reserved4 Cost Accounting vs. Financial Accounting analogy Why compute valuation adjustments?  Initial motivation: incentivize risk takers by valuing all economic costs/benefits to the BU ignored in the theoretical price (credit, funding, capital…).  Later on: recognize that market prices deviate from their theoretical levels (since institutions adjust their quotes for CVA/FVA…) to present an accurate picture of assets values in financial statements. Cost Accounting: aims at presenting detailed costs information to feed in internal managerial decisions and control current operations by optimally allocating resources to the most efficient and profitable business areas. Financial Accounting: produces formalized financial statements (P&L account and Balance Sheet) that are used by external stakeholders to get a “true and fair” picture of transactions, and analyze the results and financial position of the firm on a given date.
  5. 5. Copyright © 2014 Murex S.A.S. All rights reserved5 Cost Accounting vs. Financial Accounting analogy Cost Accounting  Internal reporting, Forward looking  Costs classified as fixed, variable, semi- variable, but also by product, process, BU…  E.g. marginal costing approach:  Cost per unit ascertained only on the basis of variable costs  Fixed costs are excluded from the product cost and charged as period costs to the P&L of the BU cost center.  Stocks are valued at marginal cost of production Financial Accounting:  External reporting, Backward looking  Costs classified by conventional transaction categories  Valuation approach & reporting:  Unit of account vs. unit of valuation  Conventional by definition  Should follow a symmetry principle (i.e. for valuation adjustments one firm’s cost is its counterparty’s benefit) Proposal for this presentation  Management of EconomicValue :  focus on incremental impact of new operations (trades, unwinds, extensions, roll-out of new CSA…)  only include variable costs in the value adjustment at operations level, manage fixed costs as reserves at the BU level and set profitability target to cover those.  Financial reporting: market transfer price based of conventional assumptions (e.g. market funding levels, HTM)
  6. 6. Copyright © 2014 Murex S.A.S. All rights reserved6 CVA & FVA definition CVA & DVA  CVA is the market value of counterparty credit risk for OTC derivatives (or the difference between the risk-free price and the mid-market price of the portfolio).  Expectation over time of discounted future exposures weighted by default probabilities and recoveries. FVA  Similarly FVA aims to capture the funding costs (FCA) and benefits (FBA) incurred on derivatives transactions due to timing mismatches between inflows and outflows that would be financed at unsecured rates.  Integral over time of Funded Amounts weighted by the corresponding Funding Spreads.  As funding spreads contain a credit risk element and funded amounts can correspond (not always) to discounted exposure, there are definite overlaps between bilateral CVA and FVA (esp. FBA and DVA).
  7. 7. Copyright © 2014 Murex S.A.S. All rights reserved7 Justification for a funding adjustment Case of an unsecured derivatives transaction  Future cash flow assets (liabilities) are term-funded by investing (borrowing) in a “risk-free” money market account that will pay back the required amount.  Since there is no derivatives repo market, the amount to be invested in the cash account needs to be borrowed (lent) on an unsecured basis.This is done theoretically through Treasury by issuing (buying back) zero-coupon bonds maturing on the cash flows value dates.  Since derivatives cash-flows are stochastic the position in the zero-coupon bond (i.e. CFs’ NPV) is re-balanced continuously.  i.e. the value of this derivative can be obtained by :  Discounting future cash-flows on our own unsecured funding curve (term-funding), as established by the Treasury unit.  Equivalently, by taking the integral of future MtMs discounted with our unsecured funding spread over the money market reference we get valuation adjustment that can be subtracted from the “risk-free” price to derive our economic value for this transaction  In this second case splitting MtMs into Expected Exposures and Expected Liabilities let us define a funding benefit (FBA) and funding cost (FCA) components (giving us the option to apply differentiated rates for lending & borrowing).
  8. 8. Copyright © 2014 Murex S.A.S. All rights reserved8 Justification for a funding adjustment Case of an unsecured derivatives transaction (continued)  So, assuming that:  our unsecured cost of funds is directly derived the price our Bond,  there is no CDS-Bond basis,  and that all transactions are done with a single counterparty, under one close-out netting agreement but no collateral agreement, we have DVA = FBA (so this rarely is exactly the case in practice). Other argument : the unsecured derivatives is hedged by a collateralized one  Some may argue that the funding requirement on day-one is not “real” as there are no flows yet  but if the transaction is hedged back-to-back with a counterparty with whom we have a perfect CSA, posting (receiving) collateral covering the outstanding MtM will generate the same funding requirement to source the collateral asset.  As we will see later, using this definition to define what the economic FVA of a trade should be, might raise questions when the market standard collateralisation mechanics deviate from the ideal case.
  9. 9. Copyright © 2014 Murex S.A.S. All rights reserved9 Justification for a funding adjustment Case of a collateralised derivative position When the value of the position 𝑉(𝑡) is positive we effectively borrow the collateral amount 𝐶(𝑡) at the collateral rate 𝑟𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 + 𝑆𝑐𝑜𝑙𝑙𝑎𝑡 and fund the remaining shortfall excess 𝑉 𝑡 − 𝐶 𝑡 at our cost of funds (and vice versa). The collateral rate is the interest rate specified in the agreement, when exchanging cash collateral (potentially in a different currency than the position’s), the funding cost/benefit is thus the combination of:  𝑉 𝑡 − 𝐶 𝑡 + at the unsecured borrowing spread 𝑆 𝑏𝑜𝑟𝑟𝑜𝑤  𝐶 𝑡 − 𝑉 𝑡 − at the unsecured lending spread 𝑆𝑙𝑒𝑛𝑑  𝐶(𝑡) at the collateral spread 𝑆𝑐𝑜𝑙𝑙𝑎𝑡 Assuming continuous collateralisation 𝑉 𝑡 = 𝐶(𝑡) : cash flows can be discounted on the collateral rate Usually the collateral rate is an OIS index which is also the benchmark for repos and our “risk-free” money market account. Under these ideal hypotheses : FVA = 0
  10. 10. Copyright © 2014 Murex S.A.S. All rights reserved10 Justification for a funding adjustment Case of a collateralised derivative position (continued) When posting securities as collateral: with Rehypothecation allowed:  we pay the agreed collateral rate on C(t), but effectively receive 𝐶(𝑡) 1−𝐶𝑆𝐴 𝐻𝑎𝑖𝑟𝑐𝑢𝑡 that can be repo-ed out for 𝐶 𝑡 1−𝑅𝑒𝑝𝑜 𝐻𝑎𝑖𝑟𝑐𝑢𝑡 1 −𝐶𝑆𝐴 𝐻𝑎𝑖𝑟𝑐𝑢𝑡 to earn the market repo rate: 𝑟𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 + 𝑆 𝑟𝑒𝑝𝑜  giving rise to a funding benefit / cost as soon as 𝑅𝑒𝑝𝑜 𝐻𝑎𝑖𝑟𝑐𝑢𝑡 ≠ 𝐶𝑆𝐴 𝐻𝑎𝑖𝑟𝑐𝑢𝑡 or 𝑆𝑟𝑒𝑝𝑜 ≠ 𝑆𝑐𝑜𝑙𝑙𝑎𝑡 without Rehypothecation rights:  When posting collateral we still receive 𝑆𝑐𝑜𝑙𝑙𝑎𝑡 on 𝐶(𝑡)  When receiving 𝑋% of the collateral balance in securities we still need to fund 𝑉 𝑡 − 𝐶 𝑡 . (1 − 𝑋%) + at our funding cost 𝑆 𝑏𝑜𝑟𝑟𝑜𝑤 generating a funding cost. Similarly, one-way CSAs, large thresholds & MTAs, lower margining frequencies … will give rise to funding costs / benefits.
  11. 11. Agenda 1. INTRODUCTION : FVA AND COLLATERALISATION 2. CSA-DISCOUNTINGVS. EXPOSURE SIMULATION 3. FUNDING SPREADS VOLATILITY 4. COLLATERALISATION REGIMES & INITIAL MARGINS
  12. 12. Copyright © 2014 Murex S.A.S. All rights reserved12 ISDA Margin Survey 2014 [17] This year, 66% of participants indicated they were referencing terms contained within their underlying CSAs when pricing derivatives transactions for collateral margining (CSA discounting). Also:  91% of all OTC derivatives trades (cleared and non-cleared) were subject to a collateral agreements at the end of 2013.  90% of non-cleared OTC derivatives trades were subject to collateral agreements at the end of 2013.  87% of non-cleared OTC derivatives collateral agreements relate to portfolios of less than 100 trades.
  13. 13. Copyright © 2014 Murex S.A.S. All rights reserved13 CSA-discounting Uncollateralised trades are priced by discounting Cash Flows on a curve representing our cost of fund (usually Libor + spread). Collateralised trades are priced by discounting Cash Flows on a curve representing the collateral rate (usually OIS rate of a specified currency). For instance:  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. Implicitly assumes that for each 𝑡 there is a single funded amount 𝑉(𝑡) and a single funding rate 𝑆 𝑏𝑜𝑟𝑟𝑜𝑤 or 𝑆𝑐𝑜𝑙𝑙𝑎𝑡 Transactions are held to maturity and term-funded
  14. 14. Copyright © 2014 Murex S.A.S. All rights reserved14 CSA-discounting assumptions In practice, this hypothesis implies that we postulate: strong “ideal CSA” assumptions  Bilateral (2-way CSA) with continuous margining  Cash equivalent collateral  0-thresholds, MTAs, Rounding, IAs  No IMs  Full substitution and re-hypothecation rights and that funding spreads are  symmetrical (lending/borrowing)  fixed (and obviously independent from exposure drivers) usual consensus that, so far, the “ideal CSA” assumption has worked for the bulk of interbank portfolios on “classical” CSAs and for uncollateralised positions as well.
  15. 15. Copyright © 2014 Murex S.A.S. All rights reserved15 CSA-discounting in practice Relatively simple implementation in FO systems:  May lead to maintaining very large number of collateral funding curves (CF currency vs. Collateral currency vs. Collateral rate) and large curve routing tables  Data management investments required (linking FO pricers with Collateral data)  Multi-curve set-up (joint calibration of multiple curves, etc.) The devil is in the details  Careful attention is required to properly handle pricing and risk analysis of some corner cases – often needing additional work (systems configuration or updates to pricing libraries) :  Uncollateralised CMS cap (CMS rate derived from collateralised instruments)  EUR collateralised AUD swaption with delivery settlement (and upfront premium)  Uncollateralised swap with mandatory mutual break (risk free close-out)  Collateral currency switch “option” Hedging uncollateralised positions with collateralised derivatives:  Hedge ratios need to be adjusted  Basis risk remains with originating desk
  16. 16. Copyright © 2014 Murex S.A.S. All rights reserved16 FVA via Exposure Simulation Another approach consists in extending the existing CVA simulation framework: All trades are discounted on their relevant “risk-free” OIS benchmark for pricing, regardless of the collateral agreement details Exposures and Collateral balances are simulated explicitly taking into account the full details of the collateral agreement (coverage, thresholds, collateral currency, haircuts, IMs, etc.) FVA is measured by taking the integral of discounted exposures/liabilities weighted by the appropriate funding spreads (if desired, different rates can be applied for the lending & borrowing cases).
  17. 17. Copyright © 2014 Murex S.A.S. All rights reserved17 FVA via Exposure Simulation Funding spreads are measured between the effective Collateral rate and the chosen reference risk-free funding rate  Similar to the CSA discounting case, with the option of also evolving spreads as a stochastic risk factor Behavioural assumptions can be made regarding the :  Counterparty's choice of collateral assets (currency switch option, cash/securities mix).  Assumed funding lifetime of the positions  Effective rehypothecation ratio / repo haircuts of illiquid securities (RMBS, corporate / municipal bonds, etc.) and counterparty’s own bonds on stressed scenarios. FVA can be simply split into sub-components:  FBA vs. FVA  FVA, LVA, CollVA, MVA… (e.g. separating CDS-Bond basis liquidity spread from the credit spread, or isolating the funding component due to collateral excesses/shortfalls).  P&L attribution elements
  18. 18. Copyright © 2014 Murex S.A.S. All rights reserved18 Exposure simulation : FVA vs. CVA/DVA One may choose to apply different funding curves to Exposures and Liabilities (akin to CVA & DVA), or take a view that theTrading desk is structurally net short/long funding and that the funding unit /Treasury will charge an average rate. From a funding perspective Cash Flows always net, regardless of Close-Out netting agreements Funding costs/benefits occur as long as the institution operates as a going concern:  Some Wrong Way Risk adjustments may thus differ between DVA and FVA (JTD scenarios, Recovery correlated with exposure factors).  First intuition is that Exposures should be weighted by the survival probabilities of both parties when computing FVA (similar to first-to-default CVA)  Nevertheless this can be disputed as different results can be derived depending on business assumptions (risk-free vs. risky close-out, set-off strategies, credit-contingent pay-offs and CSAs…)  Usually a minor effect.  Credit-focused “Margin Period of Risk” assumptions should not be applied to FVA, only the re- margining frequency should be considered since interests are computed from the value date of the margin call.
  19. 19. Copyright © 2014 Murex S.A.S. All rights reserved19 Exposure simulation : FVA vs. CVA/DVA Simulation dateTi Collateral Balance (CVA/DVA) Margin Period of Risk (e.g. 10d) Ti - MPR margining frequency Ti - MF Collateral Balance (FVA) Collateral Funding close-out grace period dispute fail margining frequency  Credit-focused “Margin Period of Risk” assumptions should not be applied to FVA.
  20. 20. Copyright © 2014 Murex S.A.S. All rights reserved20 Imperfect Collateralisation modelling challenges CSA-Discounting vs. FVA via exposure simulation
  21. 21. Copyright © 2014 Murex S.A.S. All rights reserved21 Imperfect Collateralisation modelling challenges The question is whether a CSA discounting approach alone can be used to price incrementally without the risk of providing distorted incentives:  Depends on the portfolio in place (transactions and agreements) and magnitude of the impacts. E.g. if clearing of a given product can happen only on a single CCP.  Option to fix some of the CSA-discounting shortfalls by fiddling with the pricing and curve libraries.  Strong intuition that aggregation-dependent effects (VaR-based IMs, one-way CSAs) should be modeled upfront  Whether the volatility of spreads and their correlation with exposure factors can have a material impact is less clear (apart from obvious pathological cases)
  22. 22. Agenda 1. INTRODUCTION : FVA AND COLLATERALISATION 2. CSA-DISCOUNTINGVS. EXPOSURE SIMULATION 3. FUNDING SPREADS VOLATILITY 4. COLLATERALISATION REGIMES & INITIAL MARGINS
  23. 23. Copyright © 2014 Murex S.A.S. All rights reserved23 Funding spread decisions Which funding curve?  Own CDS – liquidity basis  OIS-LIBOR + spread  Blended curves  Different curves for legal entities Symmetric funding curve ? Different choices depending on the valuation context:  FairValue accounting : what is a reasonable proxy for the average market funding spread?  Is “own funding cost” a justifiable option?  CDX/Itraxx Financials ; LIBOR + spread …  EconomicValue : own cost of funds, as charged by FVA desk / Treasury
  24. 24. Copyright © 2014 Murex S.A.S. All rights reserved24 One possible FVA operational model All trades are priced with OIS discounting and FVA adjustment:  Funding costs are priced via FVA adjustment(s), like credit is priced via CVA  FVA fees and positions are transferred to a FVA desk (can be part of Treasury or CVA desk), leaving limited IR basis risks in the trading portfolio. Hedge ratios are identical for collateralised / uncollateralised positions in the trader’s book.  A dedicated desk, reports and manages the Funding P&L (analysis, hedging / reserving for basis effects, etc.) As a default rule, assume that all trades are held to maturity (i.e. full lifetime term-funding)  Some exceptions can be granted for specific counterparties (hedge funds) in order to price competitively, they are managed through ad hoc processes.  Transaction extensions / roll-overs (or cash settled swaptions, exercised in delivery mode) incur an incremental FVA charge – consistent with CVA.  Conversely early-terminations/unwinds can get back a FVA benefit fee.
  25. 25. Copyright © 2014 Murex S.A.S. All rights reserved25 One possible FVA operational model Regarding the funding curve, an arrangement can be made with the FVA/Treasury desk:  Treasury agrees to apply a single FTP/funding rate (lend & borrow) based for a year on an industry benchmark (e.g. Libor + Xbp) - cf. Smirnov [9]  This rate is guaranteed for as long as the trading desk maintains positions within pre-agreed limits (gaps, CF ladders, PV01s…). Otherwise punitive rates are applied.  A reserve is passed at the BU level to cover for the risk of higher reset of the funding at year end (period cost) Additional costs  Contribution to Liquidity buffer is not included in transaction prices as Treasury/ALM takes the responsibility to optimize the funding strategy (this premium is already included in the internal funding rate)  LCR/NSFR contributions can be incorporated in a KVA adjustment The CVA/FVA desk,Treasury and the Collateral Management function need to collaborate closely  Continuous alignment of pricing assumptions with Collateral Management practices (substitutions,re- hypothecation…)  Securities assets optimization (collateral & regulator capital)  Data management, implementation of new CSAs…
  26. 26. Copyright © 2014 Murex S.A.S. All rights reserved26 Historical analysis : LIBOR-OIS spreads 0 20 40 60 80 100 120 140 160 180 200 EUR Libor - EONIA spread (in bps) Spread 0 20 40 60 80 100 120 140 160 180 200 EURIBOR - EONIA Spread Itraxx Senior Financial (Normalised) EUR EONIA spreads Vs Credit spreads 0 50 100 150 200 250 300 350 400 450 500 USD Libor - FF spread (in bps) Spread 0 50 100 150 200 250 300 350 400 450 500 USD Libor - FF spread CDX Financial 5Y (Normalised) USD Libor - FF spread (in bps)
  27. 27. Copyright © 2014 Murex S.A.S. All rights reserved27 0 50 100 150 200 250 300 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 195 205 215 225 235 255 270 280 290 300 310 325 345 390 420 450 Historical spread distribution 2007-2014 Numberofoccurences Spread level 0 50 100 150 200 250 300 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 80 Historical spread distribution 2010-2014 LIBOR-OIS spreads distributions
  28. 28. Copyright © 2014 Murex S.A.S. All rights reserved28 From August 2007, clear de-correlation patterns are observed between EONIA and EURIBOR 6M swap rates.  De-correlation is stronger on longer maturities.  Correlation levels dropped down to 75% on the 10 years maturity.  Following graphs show 6M sliding historical log-return correlations, for 2y and 10y maturities. Subprimes crisis Lehman Brothers Greek crisis Historical analysis : LIBOR vs. OIS swap rates
  29. 29. Copyright © 2014 Murex S.A.S. All rights reserved29 Stochastic basis spreads experiment Use a simple short rate model (Hull & White 1 factor) to evolve jointly the forward estimation and discount curves as correlated processes  Discount curve short rate rt: ∀𝑡 ≥ 0, 𝑟𝑡 = 𝑓 0, 𝑡 + 𝑥𝑡 + 𝜑 𝑡 ; 𝑑𝑥𝑡 = −𝑎𝑥𝑡 𝑑𝑡 + 𝜎 𝑡 𝑑𝑊𝑡 𝑥 ; 𝑥0 = 0  Estimation curve short rate st: ∀𝑡 ≥ 0, 𝑠𝑡 = 𝑔 0, 𝑡 + 𝑦𝑡 + 𝜓 𝑡 ; 𝑑𝑦𝑡 = −𝑏𝑦𝑡 𝑑𝑡 + 𝜂 𝑡 𝑑𝑊𝑡 𝑦 ; 𝑦0 = 0 where : • 𝒇 𝟎, 𝒕 (resp. 𝒈 𝟎, 𝒕 ) is the forward short rate at time 0 for date t observed in the market for the discount curve (resp. estimation curve) • a and b are two mean reversion rates, 𝝈 𝒕 and 𝜼 𝒕 are two piecewise constant volatility functions • (𝑾𝒕 𝒙 ) and (𝑾𝒕 𝒚 ) are two correlated standard Brownian motions, with a constant instantaneous correlation: d 𝑾𝒕 𝒙 , 𝑾𝒕 𝒚 = 𝝆𝒅𝒕 • 𝝋 𝒕 and 𝝍 𝒕 are two deterministic shifts Assess the impact on the FVA of a simple payer swap:  3Y, Pay fix 0.5%, Receive Euribor 6M  CSA Discounting & Exposure simulation FVA match exactly with correlation at 1 (i.e. deterministic spreads)
  30. 30. Copyright © 2014 Murex S.A.S. All rights reserved30 Stochastic basis spreads experiment FVA increases as correlation decreases (spread volatilities increases) Realised spread distributions at 3Y for different correlation values Obviously not the ideal model for OIS/LIBOR spreads with significant de-correlation. 0,2 0,3 0,4 0,5 0,6 0,7 0,68 0,78 0,88 0,98 EURIBOR / EONIA correlation FVA in Bps 0 200 400 600 800 1000 0 5 10 15 20 25 30 35 40 45 50 55 60 0 20 40 60 80 100 -425 -315 -265 -215 -165 -115 -65 -15 35 85 135 185 235 285 335 400 0 20 40 60 80 -525 -370 -310 -250 -190 -130 -70 -10 50 110 170 230 290 350 410 470 0.95 0.8 0.7
  31. 31. Copyright © 2014 Murex S.A.S. All rights reserved31 Spreads vs. exposure factors co-dependence (WWR) Intuition that Credit Risk represent a significant portion of Funding Spreads (cf. historical analysis) Funding costs can be “correlated” with factor(s) driving as well the Funded Amount (e.g. interest rates, credit spreads or FX levels) Use a portfolio WWR risk model like Hull & White 2011 [7]  Express default intensities / spreads as a parametric function of an underlying observable variable (e.g. FX or ZC rate, MV of the bank trading portfolio, but also a stochastic OIS-LIBOR spread factor or a function of observables…)  Hull & White propose two functional forms :
  32. 32. Copyright © 2014 Murex S.A.S. All rights reserved32 Form Std deviation 3bp Std deviation 15bp Std deviation 25bp 1 2 Increasing B Spreads vs. exposure factors co-dependence (WWR) Example  Calibrate a(t) to match LIBOR spread expectations (from rate curve)  B is computed to match historical standard deviation (e.g. OIS-LIBOR : 12bp for 2010-14, 55 for 2007-14)
  33. 33. Copyright © 2014 Murex S.A.S. All rights reserved33 FX & Cross Currency swap RWR example e.g. expect a funding costs increase if EUR depreciates  4Y, Pay EUR EONIA 6M, Receive USD LIBOR 6M  Funding spread = OIS-Libor + 40bp  X set as FX, MV or EE pathwise  FVA switches from a benefit to a cost.
  34. 34. Copyright © 2014 Murex S.A.S. All rights reserved34 Real-life examples SSAs hedging bonds issuances:  Long-Term IRD positions with One-way CSAs  Alternatively the Counterparty posts their Own Bond as Collateral : no reduction of CVA. Recover funding benefit in normal market conditions, but funding benefit may vanish in stressed market (inability to repo large positions, rising haircuts…) Selling structured products hedges to Corporates  Local bank selling structure back-to-back : uncollateralised with corporate, collateralised with hedge counterparty (e.g.TARFS,TARNS,Accumulators, PRDCs…)  Hedging products, hence often believed to carry no CVA WWR, or even be Right Way positions  Often packaged as 0-premium notes:  Attractive rate for customer (e.g; carry trade, ITM options),but with limited upside (target redemption or KO)  Reverse position for the bank knocking in at OTM level, often with gearing  Competitive markets (very popular products can turn into crowded trades)  Very asymmetric pay-offs : potential for high funding requirements, and specific WWR (gearing and one-way market)  Local banks funding spreads can be strongly correlated to large moves in the underlying asset price
  35. 35. Copyright © 2014 Murex S.A.S. All rights reserved35 CNYTarget Redemption Forward example CNY/USD rate – Source: Bloomberg Hugely popular structure in Asia  Anticipated constant appreciation of the CNY  Typically monthly strips of FX options (vanillas and KI barriers), with redemption clause and gearing.  Feb 18, PBoC starts fixing the USD/CNY higher and doubles the authorised daily variation range
  36. 36. Copyright © 2014 Murex S.A.S. All rights reserved36 CNYTarget Redemption Forward example Average KI strikes in the market for outstanding transactions in the 6.15 – 6.20 range.  Morgan Stanley estimates USD 150bn of outstanding notional.  Estimate that above 6.2 corporates will lose USD 200m a month per 0.1 move (contracts are 24months…) Taiwanese banks in the spotlight after they asked their corporates to post collateral  FSC taking actions against four banks  In parallel skyrocketing funding costs forTaiwanese banks (collateralised in USD),TAIFX (interbank USD/TWD funding) has risen to 1.53% in April from ~0.85% from Jun to Nov 2013. In summary, for the issuing bank : - CVA: General RWR + Specific WRW - FVA : WWR A taste of déjà vu (cf. 2008 Korea, Brazil, Indonesia, Poland…) cf. R. Dodd [2] and [10b]
  37. 37. Copyright © 2014 Murex S.A.S. All rights reserved37 TARF/KIKOToy Example Payoff function (from the BANK perspective): FX Tarf USD/THB: Maturity 2y, N=1M USD, Monthly payment. Forward 2y at 36 (Spot 35.29) Funding at 20bp (fix) over interbank funding spread (variable) Ignoring all WRW effects: USD/THB 0 33 36,4 41 Payoff Gearing Factor 2.0 Monthly TARF payoff function PFE, PFL & MTM EE, EL & MTM
  38. 38. Copyright © 2014 Murex S.A.S. All rights reserved38 TARF/KIKOToy Example  Funding at 20bp (fix) over interbank funding spread (variable)  WWR on FX spot, the following B values generate the following distributions for the interbank funding spread portion:
  39. 39. Copyright © 2014 Murex S.A.S. All rights reserved39 TARF/KIKOToy Example Taking the funding B(FX) as 0.1, we get a 65% increase in FVA Adding similar dynamics for CVA :  General RWR on FX (the corporate is hedging against THB appreciation)  Specific WWR on the structure’s MtM (due to gearing, default probabilities rise sharply once the MtM rises beyond certain levels) We get the following results with a 78% XVA increase due to combinedWWR effects on funding costs and credit risk.
  40. 40. Copyright © 2014 Murex S.A.S. All rights reserved40 TARF/KIKOToy Example Counterparty’s credit spreads distributions at 2Y points for varying B(FX) and B(MtM):
  41. 41. Copyright © 2014 Murex S.A.S. All rights reserved41 TARF/KIKOToy Example 0 100 200 300 400 500 600 0,02 0,05 0,1 0,3 FVAVariation in % as a function of b(FX) -200 -150 -100 -50 0 50 100 150 200 250 300 1 2 3 CVA WWR MV CVA RWR FX CVA variation in % (for increasing b values) RWR WWR CVA Specific WWR General RWR
  42. 42. Agenda 1. INTRODUCTION : FVA AND COLLATERALISATION 2. CSA-DISCOUNTINGVS. EXPOSURE SIMULATION 3. FUNDING SPREADS VOLATILITY 4. COLLATERALISATION REGIMES & INITIAL MARGINS
  43. 43. Copyright © 2014 Murex S.A.S. All rights reserved43 Centrally Cleared Portfolios Practically no CVA (quasi default-free entity) and no DVA (the CCP is over- collateralized). Collateral balance is split inVM & IM:  VM:Variation Margin (covers current MtM)  IM: Initial Margin (covers the collateral gap risk over the liquidation period, e.g. 5 open days)  Multipliers : Credit, Liquidity, Concentration… CCP pays back an OIS rate minus a spread on Cash Collateral received, not necessarily on Securities.
  44. 44. Copyright © 2014 Murex S.A.S. All rights reserved44 Centrally Cleared Portfolios On-going clearing costs for DCMs: Unsecured funding of excess collateral balance :  Function of the trade specifics w.r.t the legacy portfolio and the CCP methodology, as well as effective collateral rate  Proposal : should be handled as a trade-level variable cost and measured a priori. Default fund contribution :  Monthly charge function of the relative volume transacted with the CCP vs. other participants. Can only be measured a posteriori  Proposal : handled as a business unit level period cost (that can be reserved for) since the impact of a single trade is unclear and this component should not drive the decision to make an incremental transaction. Other Costs:  Clearing Fees (semi-variable: fixed+volume based), Settlement & CSD charges, Bank Charges, Operating costs  Can be allocated as trade variable costs, can be difficult to analyse but require no complex modelling
  45. 45. Copyright © 2014 Murex S.A.S. All rights reserved45 Centrally Cleared Portfolios Proposed setup for Economic value FVA : Model cost of funding IMs as part of FVA adjustment at trade-level Allocate Default Funds & Liquidity Buffer costs as BUs fixed costs (monthly reserves and profitability targets) Incorporate other trade-volume based operational expenses as variable costs, if deemed sufficiently material
  46. 46. Copyright © 2014 Murex S.A.S. All rights reserved46 Centrally Cleared Portfolios : computation of IMs Different CCPs can apply different methodogies Listed products usually SPAN-based methods OTC derivatives usuallyVaR-based: 10 years historical series with EWMA decay (e.g. LCH SwapClear) or EWMA vol re- scaling (cf. Hull &White [6]). 5d/10d risk factor shocks are applied (with overlapping sampling) High percentileVaR or Expected Shortfall (e.g. 99.7%) CCP-specific pricing conventions (e.g. OIS discounting) Credit & Liquidity Multipliers: Can be material too Can show some cliff effects
  47. 47. Copyright © 2014 Murex S.A.S. All rights reserved47 The new CSAs New regulation aiming at “reducing systemic risk and promoting central clearing”  BCBS-IOSCO “Margin requirements for non-centrally cleared derivatives”, bcbs 261, Sep 2013 [14]  ESMA-EBA “Draft RTS on risk-mitigation techniques for OTC-derivative contracts not cleared by a CCP”, Apr 2014 , on-going consultation [15]  Applicable to Financial Institutions (interbank) with over €8bn notional of non-centrally cleared derivatives - gradual roll-out from Dec 2015 to Dec 2019 Key provisions in a FVA context  Mandatory exchange of “two-way initial margins”  Margin segregations and no re-hypothecation / re-use rights  Internal models or Standardised schedule methods for determining IMs and collateral haircuts  FX mismatch haircut  Group-level threshold (max €50m) across legal entities and netting agreements De facto killed the S-CSA initiative  Dec 2013 : ISDA SIMM proposal for an internal model Initial [16]  Expected May 2014 : proposals for an S-SCSA II
  48. 48. Copyright © 2014 Murex S.A.S. All rights reserved48 New CSA : zoom on IM requirements FX cash products exempted, as well as final Notional exchange in CCS Standardised IM schedule  Very simple to implement, ideal for dispute resolution  Too conservative for most firms (40/60 NGR rule)  BCBS footnote 17 [14] : can we hope to see a move to the more sensible SA-CCR method (with a rescaling of the Margin add-on to 99% PFE)? Internal Models  Complex, require regulatory approval  Firm-specific models are impossible to manage for disputes  Need to converge to market standard (e.g. ISDA SIMM, or 3rd party provider)  Consistent with 99% PFE (1%VaR)  Calibration period of at least 3Y and with at least 25% of stressed data  Minimum liquidity horizon of 10d  Positions split in 4 asset classes : (1) IRD, FX & Gold, (2) Equities, (3) Credit, (4) Commodities & Others. No offsets allowed across asset classes.
  49. 49. Copyright © 2014 Murex S.A.S. All rights reserved49 Should IMs be considered in trade-level FVAs? Conceptually, valuing the incremental IMs funding impact is meaningful when pricing new operations:  A variable cost relevant at the trade level (e.g. will the trade hedge or diversify the existing Margining Node portfolio?)  Directly linked to practical business decisions such as the choice of CCP / Counterparty for execution (function of IM methodology and legacy portfolio) However, are IMs material enough ?  Obviously extremely variable and a function of the leverage and directionality of the portfolio being cleared/collateralised  Simplistic example :  Assume a portfolio’s value is normally distributed (IID)  Compare the daily IMs with the portfolio average MtM, depending on the average “age” of the positions  IM replication benchmark runs (IRD portfolios)
  50. 50. Copyright © 2014 Murex S.A.S. All rights reserved50 Should IMs be considered in trade-level FVAs? Are IMs material enough ?  Simplistic example :  Margin replication benchmark exercise on IRD portfolios:
  51. 51. Copyright © 2014 Murex S.A.S. All rights reserved51 ModellingVaR-based IMs for FVA
  52. 52. Copyright © 2014 Murex S.A.S. All rights reserved52 VM balance IM+ (e.g.VaR 1%) IM- (e.g.VaR 99%) ModellingVaR-based IMs for FVA Liquidation horizon
  53. 53. Copyright © 2014 Murex S.A.S. All rights reserved53 ModellingVaR-based IMs for FVA VM balance Collateral posted by Counterparty Collateral posted by us
  54. 54. Copyright © 2014 Murex S.A.S. All rights reserved54 Measuring IMs contributions to FVA Main question : is the co-dependence between spread and IM exposure drivers a second order effect that can be neglected? Various methods are being implemented, for instance: Crude approximation #1: forwardVaR contributions  Typically when the institution does not have a full-fledged incremental CVA/FVA pricing framework  Run HsVaR IM calculation on the Margining Node portfolio  Ignores as well asymmetry in volatility profiles over future time-points , path-dependent effects (e.g. delivery settled swaptions, exotics…), VM-IM funding offset option…  Usually incorrect ageing of portfolio (usuallyVaR systems do not “age” the deals), implicitly assuming a “constant-state” portfolio except for maturing deals which are dropped  Consider then pricing all trades with OIS discounting and charge all FVA costs a posteriori only?
  55. 55. Copyright © 2014 Murex S.A.S. All rights reserved55 Measuring IMs contributions to FVA Crude approximation #2: within the CVA/FVA exposure simulation  At each future time point sample the distribution of Margin Node portfolio value  Extract the required local VaR / volatility estimate, scale it to the required liquidity horizon and apply required multipliers  Apply the collateral balance functions as per the normal case (cash/securities mix, appropriate funding spreads) to derive FVA / MVA  Ignores as well asymmetry in forward volatility profiles, assumes independence of spreads with exposure factors, etc.
  56. 56. Copyright © 2014 Murex S.A.S. All rights reserved56 Measuring IMs contributions to FVA More accurate approaches typically leverage an existing CVA simulation framework (or AMC for exotics pricing).  Option 1 : Taylor-VaR  Output first-order sensitivities by scenario path and time step (possibly using a reduced set of scenarios). AAD or sensitivities approximated by regression are possible options  ApplyVaR scenario and revalue the portfolio via aTaylor-Expansion – Note that this corresponds to the proposed ISDA SIMM approach.  Option 2 : LSMC regression  View each Margin Node portfolio as an exotic trade pay-off  Oversample the initial Monte Carlo draw to have enough observations for extreme quantiles (e.g. 99%VaR on the 99% PFE scenario point). Efficient implementation with GPUs.  Select a limited number of basis functions relevant to the portfolio (e.g. pre-defined for clearing pools or estimate sensitivities on forward path central scenario…), then regress the portfolio’s “continuation value” against the basis functions in backward induction pass.  Apply theVaR scenarios on the resulting portfolio pricing function. Forward pass can use only a subset of the initial scenarios.  Option 3 : Resampling of AMC simulation values  Based on chosen observables work-out transition probability kernel from scenario i at point t, to all scenarios j at date t+1  Approximate HistVaR by local conditional distribution function (MC on MC)
  57. 57. Copyright © 2014 Murex S.A.S. All rights reserved57 Local regression for LSMC-based IM simulation In low dimensions (e.g. clearing), local regression methods (LOWESS) can be an interesting alternative to the usual parametric forms (e.g. polynomials).  Significant accuracy improvement on high “PFE” quantiles for exotic pay-offs  LSMC PFE accuracy w.r.t closed-form pricing (cf. Morali [12]) Parametric regression Local regression
  58. 58. Copyright © 2014 Murex S.A.S. All rights reserved58 FVA vs.VaR methodology questions IM Calculations : Historical Simulation  Calibration to historical series since wantVaR to use Real-World probability measure  Assume no drift, no mean-reversion  Regulatory IMs require the inclusion of a “period of stress” : another probability measure FVA exposure simulations: Monte Carlo Simulation  Implementations usually use Risk Neutral calibration  Risk factor evolution models (drift, MR, volatilities term-structure) Is FVA estimated in the Risk-Neutral or Real World measure? Approximations will have to be used, esp. for translating VaR scenarios in the forward simulation  Initialization of path-wise calibration time series should be avoided :  Potentially complex (e.g. filtering or vol rescaling)  Undesirable “change of volatility regime” from today onwards, impact of mean-reversion over long-horizons  Can we assume equivalence between:  Historical and Monte CarloVaR?  Risk Neutral – Real World equivalence by a change of measure and use RN calibration for VaR  For regulatory IM, apply a change of measure or a simple volatilities scale-up (Stressed Measure for Real-World Measure)?  Handling ofVaR scenarios on risk factors not captured in the FVA simulation / Margining node pricing function
  59. 59. Copyright © 2014 Murex S.A.S. All rights reserved59 Challenges in measuring CVA/FVA InteDelta / Murex - May 2014 : “CVA & Counterparty Risk Management survey” Top 4 challenges highlighted [13] : http://survey.murex.com/content/Intedelta_CVA_and_Counterparty_Risk_Survey
  60. 60. Copyright © 2014 Murex S.A.S. All rights reserved60 How did regulation impact collateral funding ? Dodd Frank / EMIR - Centrally cleared derivatives:  CCPs IMs requirements generate a significant additional funding cost  Effective collateral rate is not OIS (fees, handling of securities assets) BCBS 261 - New CSA’s impacts on effective collateral funding spread:  Margin Segregation  Re-hypothecation now effectively disallowed BCBS 261 - New CSA’s impacts on the collateral balance and funded amounts:  FX mismatch haircuts  The group level EUR 50M threshold (somewhat increases complexity : how should allocate corresponding Collateral shortfalls across entities & netting sets).  Regulatory haircuts (Schedule or IMM) calibrated for systemic shocks  Two-way posting of Initial Margins
  61. 61. Copyright © 2014 Murex S.A.S. All rights reserved61 Conclusion Computing FVA for EconomicValue assessment or FairValue Accounting purpose may warrant using different modelling approaches, both in terms of methodology and inputs (e.g. choice of funding curves) In the near future, the bulk of OTC derivatives positions will be split across:  Centrally cleared position (largest portion), where IMs, multipliers and default fund contributions generate additional funding requirements  New style CSAs (with two-ways IMs, re-hypothecation and haircuts)  Some old-style CSAs with buy-side institutions, corporates & SSAs – sometimes with the usual twists (one-way, thresholds…)  Exotics and uncollateralised transactions with corporates, SSAs (often structured trns), that can be quite sensitive to stochastic funding spreads and WWR effects. In order to price incremental operations in a way that recognizes the economic benefits/costs of funding, a plain CSA discounting valuation approach will not suffice anymore.  It may even provide distorted incentives by missing some important effects.  Current CSA discounting implementations, will need to be complemented by additional computations (e.g. MVA) or replaced by comprehensive exposure simulations.
  62. 62. Copyright © 2014 Murex S.A.S. All rights reserved62 Acknowledgments Sincere thanks to Murex colleagues, and in particular:  Guillaume Juge  Thibault Phlipponneau  AdrienTaÿ-Pamart
  63. 63. Copyright © 2014 Murex S.A.S. All rights reserved63 References Industry papers  [1] G. Cesari & a. - 2009 « Modelling, Pricing, and Hedging Counterparty Credit Exposure.ATechnical Guide »  [2] R. Dodd, IMF paper – July 2009 « Exotic Derivatives Losses in Emerging Markets: Questions of Suitability, Concerns for Stability »  [3]C. Fries – February 2011 « Funded replication:Valuing with stochastic funding »  [4] A. Green, C. Kenyon,and C. R. Dennis – February 2014 « KVA: CapitalValuation Adjustment »  [5] J. Gregory – 2009 « Counterparty credit risk –The new challenge for global financial markets. »  [6] J. Hull & A.White – March 1998 « Incorporating volatility updating into the historical simulation for value at risk »  [7] J. Hull & A.White – June 2011 « CVA & WrongWay Risk »  [8] M. Morini,WBS Fixed income conference – October 2012 « Model risk in today’s approaches to funding and collateral »  [9] I. Smirnov,WBS Fixed income conference – October 2013 « Liquidity & Capital in derivatives pricing »
  64. 64. Copyright © 2014 Murex S.A.S. All rights reserved64 References Murex documents  [10] A. Bon,WBS CVA conference – March 2012 « OTC Collateralisation : Implementation Issues in CVA & FVA frameworks »  [10b] A. Bon – September 2010 « Specific WWR examples – case 3 : from right way to wrong way »  [11] D. Loiseau, MathFinance conference, March 2012 « Introducing Stochastic Spreads in a Multi-Curves Framework »  [12] A. Morali, HPCFinance Conference – May 2013 « American Monte Carlo for Portfolio CVA & PFE »  [13] InteDelta & Murex – May 2014 « CVA & Counterparty Risk Management : a survey of management, measurement and systems » http://survey.murex.com/content/Intedelta_CVA_and_Counterparty_Risk_Survey Regulation & institutional documents  [14] BCBS-IOSCO – September 2013 « Margin requirements for non-centrally cleared derivatives »  [15] ESMA-EBA – April 2014 « Draft RTS on risk-mitigation techniques for OTC-derivative contracts not cleared by a CCP »  [16] ISDA – December 2013 « Standard Initial Margin Model for Non-Cleared Derivatives »  [17] ISDA – April 2014 « Margin Survey 2014 »
  65. 65. THANKYOU

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