The OIS and FVA relationship Ion Mihai, PhD Client Solutions Group
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Agenda 1. Collateral discounting and Risk-Neutral Discounting 2. Credit Support Annex 3. A Primer on Funding Value Adjustment 4. An FVA case study 5. Can you pass on this charge? 6. Regulation 7. Summary and Conclusions
OIS Discounting What precipitated the market adoption of OIS discounting? Longer term LIBOR commanded higher spreads 1. Liquidity preference 2. Credit worthiness of banks Source: Numerix, PRISM Valuations
Clearing / Collateralization - A Critical Element of GFC Response All standardized OTC derivative contracts should be traded on exchanges or electronic trading platforms, where appropriate, and cleared through central counterparties by end-2012 at the latest. OTC derivative contracts should be reported to trade repositories. Noncentrally cleared contracts should be subject to higher capital requirements. - G20, Pittsburgh Summit Declaration
OIS Discounting There was no longer a single curve from which to: 1. Estimate future LIBOR fixings 2. Discount future cashflows What curve do we use to discount? Discounting should be at the risk-free rate The reason for using the risk-free rate as the discount rate is that it is required by the risk-neutral valuation paradigm In our view, the best proxy available for the risk-free rate is the OIS rate. - John Hull and Alan White 1 Discounting is inextricably tied to funding To reduce counterparty credit exposure, collateral is used Market practitioners started realizing how this affected the funding of the derivatives The rate in typical collateral agreements is the OIS rate 1. Risk25 July 2012, pages 83 85 or http://www.rotman.utoronto.ca/~hull/downloadablepublications/fva.pdf
Credit Exposure Collateral Discounting What does discounting have to do with a collateral agreement? To illustrate the connection,consider an example where I buy two cashflows from a counterparty, paid at T 1 and T 2 T 1 T 2 T A collateral account is established in order to hedge the credit exposure, at each point in time, the amount is equal to the amount owed by the counterparty. T 1 T 2 T
Credit Exposure Collateral Discounting T 1 T 2 T Since this is an asset, the counterparty posts collateral to me, and I must pay interest on this amount of money, at the rate determined by the collateral agreement. In order to minimize the amount of collateral the counterparty posts, and correspondingly minimize the amount of interest I need to pay, we agree upon the amount that will exactly cover the cashflows. Therefore the correct way to determine this collateral amount is to discount at the collateral rate. In this way, my counterparty does not need to fund the derivative in the free market, and the correct discounting rate to use for fair value calculations is the collateral amount.
Credit Support Annex / Credit Support Deed Defines the Credit Support Amount for protecting the entity with positive exposure from default of the other Can be one-sided or bilateral Separation into Initial Margin (Independent Amount) and Delivery/Return Amount Defines Eligible Assets and Transfer mechanics: Eligible currencies, Bonds, Haircuts, Thresholds, Minimum Transfer Amounts, Rounding, etc Date Schedules Valuation, Notification, Settlement Treatment of Collateral and Interest/Distributions related to Collateral Ratings based or triggers Dispute resolution Break clauses A large number of embedded options or a VERY exotic derivative!
Credit Support Annex Legal agreement Attached to OTC derivative contracts Terms and rules surrounding collateral posting and transfers Why the scrutiny? Above arguments on collateral funding Impacted the funding, and therefore the profitability of trades Front and middle offices started to scrutinize these legal agreements Collateral Parameters Collateral Threshold Minimum Transfer Amount Posting Frequency Description The amount of exposure below which is not collateralized The minimum change in exposure that is posted to collateral The frequency at which exposure is calculated an collateral is adjusted
(Very!) Simplified Sample CSA Base Currency USD Eligible Currency USD, EUR, GBP Independent Amount 5M Haircuts [Schedule] Threshold 50M Minimum Transfer Amount 500,000 Rounding Nearest 100,000 USD Valuation Agent Party A Valuation Date Daily, New York Business Day Notification Time 2PM, New York Business Day Interest Rate OIS, EONIA, SONIA Daycount Act/360
Types of CSAs in Use Significant amount of CSA customization exists in the market today Unilateral (one-sided CSAs) expected to remain into the future Source: ISDA Margin Survey, 2012
CSA - Too big to ignore Term Sheet CSA Governs Entire Portfolio Long Dated Funding Implications Counterparty Risk Mitigation Critical in Stress Conditions CVA, FVA, Risk Exposure Impact
Credit Support Annex Embedded Optionality 1. Choice of currency to post 2. Choice of instrument to post Utopian CSA Collateral accounts for 100% of the funding of the derivative Threshold 0 MTA 0 Utopian CSA Real World CSA Posting Frequency Instantaneous Daily/weekly Optionality None Collateral Instruments Cash Hedge Credit Exposures 100% <100% Collateral Funding 100% <100% 100,000-10,000,000 Depends on cpty Typically a fraction of the Threshold Choice of collateral currency Cash/Treasuries
Changes proposed in ISDA Standard CSA Elimination of currency switch options Standardization on OIS Better alignment with CCPs Implied Swap Adjustment (ISA) method in the near term to eliminate Herstatt Risk Institutions can move from CSA to SCSA but not viceversa Not mandatory Phased rollout, economics as the driver of adoption
Tradeoff between Counterparty Risk and Funding Risk/Costs Greater collateralization reduces counterparty risk but increases funding costs Strains the limited high quality collateral assets due to increased need for such assets. Estimates of collateral required range from $700 Billion to $3000 Billion or more. Penalizes derivative end-users who may not have natural funding flows aligned with collateral needs Potential destabilizing pro-cyclical effects (for e.g. a drop in Credit standing might trigger a margin call and further Credit shocks) Source: Jon Gregory, Counterparty credit risk and credit value adjustment
Real World CSA Why does the CSA not hedge 100% of Credit Exposure? Value of trade changes Faster than collateral frequency Less than the Minimum Transfer Amount Overall exposure less than threshold Cashflow events take place Movements in the value of the collateral itself Implies trade cannot be 100% funded with collateral
Funding Value Adjustment An institution s cost, above the risk-free price, to fund the trade in the presence of a real world CSA. Real World CSA Utopian CSA FVA( t) PV PV The cost of the institution to fund the trade above that of the risk-free price. Including Funding Costs RiskNeutral FVA( t) PV PV Why is this at the forefront? Collateral was introduced to mitigate CVA success If the collateral affects funding the trade, it affects profitability There is no argument that this charge is real, and is passed on to traders by the funding desks Ongoing debate How to calculate? Pass this cost on to counterparties? Build this into MtM price/unrealized P&L? Report this number? What do regulators have to say?
FVA calculation - basics: modern theory The market prior to the GFC assumed a single risk-free discounting rate The modern market has multiple rates
FVA calculation - basics: classic theory The classical theory postulates the existence of a single rate r(t): all tradable assets grow on average with this rate (under risk-neutral measure) By the standard replication argument the portfolio value v(t) satisfies the standard PDE where is the evolution operator. The solution is given by
FVA calculation - basics: modern theory The collateral C(t) is a function of portfolio value V(t), e.g. C(t) = MAX(V(t) H,0) Again by a replication argument the portfolio value V(t) satisfies the non-linear PDE The solution is given by
FVA calculation - basics: modern theory Multi-curve portfolio price This can also be written
FVA calculation - Special cases Non-collateralized deal (C=0) Fully collateralized deal (C=V)
How to calculate FVA for the portfolio? The calculation workflow can be summarized as follows: 1. Compute future values (exposures) for each instrument in the portfolio using the single-curve model. 1 2. Aggregate the instrument future values at the portfolio (netting set) level and compute the FVA with the following approximate formula: Future exposure Effective Funding Discount factor Effective Funding Spread over OIS rate 1 A. Antonov, S. Issakov, and S. Mechkov - Algorithmic exposure and CVA for exotic derivatives. SSRN elibrary, April 2012
Continuation value vs. future value 1 A. Antonov, S. Issakov, and S. Mechkov - Algorithmic exposure and CVA for exotic derivatives. SSRN elibrary, April 2012
FVA - Effective rate
FVA Effective Rate Effective Funding Rate Two limiting cases 100% collateral 100% funding 1 0 Collateral (OIS) rate Fraction of trade value with credit exposure Fraction of trade value in the collateral account Funding rate CSA Utopian None
Effective Funding Rate As Threshold Increases
Effective Funding Rate As Threshold Increases
Effective Funding Rate As Threshold Increases
Effective Funding Rate As Threshold Increases
Effective Funding Rate As Threshold Increases
Effective Funding Rate As Threshold Increases
Effective Funding Rate As Threshold Increases
Effective Funding Rate As Threshold Increases
Why do we need to compute FVA? Isn t it enough to establish lower and upper bounds? From the two limiting cases: 100% collateral ( Utopian CSA): discount using OIS 0% collateral (no CSA): discount using the funding rate The price including the funding-cost in somewhere in the middle. Not always true!
Why do we need to compute FVA? This holds if the trade s value is always positive (of negative) Consider the case of an Equity Call: Maturity 5Y Strike 100% ATM (spot) Notional 10000
Equity Call FVA as Threshold increases
Equity Call Premium Forward Same Equity Call with Forward Premium Maturity 5Y Strike 100% ATM (spot) Notional 10000 The FVA curve is humped The two bounds are both 0!
FVA Equity Call Premium Forward vs. Threshold
Swap: Equity Call vs. Cash More generally, consider a swap Leg1: same Equity Call Maturity 5Y Strike 100% ATM (spot) Notional 10000 vs. Leg2: some cash amount
Equity Call swap vs. Threshold
Can FVA be split?
Effective Funding Rate As Threshold Increases Threshold = 1000
Effective Funding Rate As Threshold Increases Threshold = 2000
FVA Charge Law of One Price? If a corporate (price-taker) gets bids from a number of banks, will certainly get different quotes Can be up to 100bps difference FVA is a Real Charge to Traders Reflecting their differing costs of funding Traders are passed this charge from their treasury/funding desk Recent interview with Hull: Traders will respond to the incentives given 1 They will attempt to pass this charge onto the purchaser 1. Upfront fee 2. Running spread over floating rate However This will be difficult in competitive markets The FVA will certainly affect the profitability of the trade All traders must know this charge 1. F. Mercurio, J. Hull, Quant Congress 2013 Interview. http://www.youtube.com/watch?v=pejrcoaz0-g
FVA Charge Does the Executed Value Include the FVA Charge? Not in the Interbank market, where the price is determined by the law of supply and demand Possibly when dealing between sell-side and buy-side Is this currently a Line Item in financial statements? Only four banks reported listing funding valuation in financial statements RBS: 475M Goldman Barclays Lloyds: 143M Lloyds indicated this number will move 14M for every 10bp change in funding cost
Regulation- Should the MtM Value include the FVA Charge? Fair value accounting The value to report for a trade is the value that the free market would pay, in an ordinary transaction, for that derivative today Three ways of thinking about this Unwinding which will incur a cost of executing the opposite trades. The funding rate should be the cost that will be charged to you by your counterparty to unwind Novation having a similar counterparty take over the trade. The funding rate should be an industry average of funding rates Holding the trade to Maturity The funding rate should be your own institutions rate Regulation There is currently no requirement by any accounting body to include this in regulatory accounting Regulators and accountants are on the sidelines for now, waiting for a consensus among practitioners
Conclusions While there is no consensus on reporting, the FVA is a real charge that will affect the profitability of trades Institutions should pass this cost on if they can, but this may be difficult in competitive markets However, it is imperative that they know this cost, so they can make the best decisions for their business The future will bring more clarity on the interrelationship between the three value adjustments, at which point accounting bodies and regulators will synthesize this measure into requirements
Summary 1. OIS is the new standard for discounting a) Proxy for risk-free rate b) Collateral discounting Enshrined by the new SCSA 2. A mismatch between the current exposure and amount in collateral account means funding is not purely OIS 3. A careful accounting of this mismatch produces effective funding rate 4. FVA defined as the price difference taking this effective rate into account, and pure OIS discounting 5. FVA charged to desks, but not always to counterparties 6. No consensus on how to report, or which funding rate to use
References 1. J. Hull and A. White, Risk25 July 2012. http://www.rotman.utoronto.ca/~hull/downloadablepublications/fva.pdf 2. A. Antonov, FVA for General Instruments: Theory and Practice. Available under NDA, please contact a Numerix representative. 3. A. Antonov, M. Bianchetti, Modern Derivatives Pricing Including Funding Value Adjustment. in preparation, 2013. 4. A. Antonov, M. Bianchetti, I. Mihai, FVA for General Financial Instruments: Theory and Practice. In preparation, 2013 5. F. Mercurio, J. Hull, Quant Congress 2013 Interview. http://www.youtube.com/watch?v=pejrcoaz0-g 6. A. Castagna, Funding Valuation Adjustment (FVA) and Theory of the Firm. 7. V. Piterbarg, Funding beyond discounting: collateral agreements and derivatives pricing. 8. A. Pallavicini, D. Perini, D. Brigo, Funding Valuation Adjustment: a consistent framework including CVA, DVA, collateral, netting rules and re-hypothecation 9. L. Carver, Traders close ranks against FVA critics. Risk, September 2012. 10. M. Cameron, Goldman and the OIS gold rush: How fortunes were made from a discounting change. Risk, May 2013.
About Numerix Numerix provides cross-asset analytics software and services for structuring, pre-trade pricing and analysis, trade capture, valuation, and risk management of derivatives and structured products. Visit us online at: www.numerix.com imihai@numerix.com