Introduction Valuation Adjustments CVA Credit Valuation Adjustment Bilateral

발표 순서 • Introduction • Valuation Adjustments – – – CVA (Credit Valuation Adjustment) Bilateral CVA DVA (Debt Valuation Adjustment) Criticism of DVA FVA (Funding Valuation Adjustment) the link between CVA, DVA and FVA • Future Directions

Two Lessons from Global Crisis • One lesson is that big size counterparties and AAA rated entities do default. – such as Lehman Brothers and super-senior CDOs. – This fact makes the credit value adjustment (CVA) more prevalent in derivative pricing and trading. • The second lesson learned is that funding cost embedded in derivative operation is of great importance to the business bottom line. – Liquidity squeeze after Lehman Brother crash made the funding especially difficult and costly for an extended period of time.

Counterparty Risk • Counterparty risk can be divided into two broad areas. – Counterparty risk measurement for capital requirements, following Basel II. – Counterparty risk from a pricing point of view, when updating the price of instruments to account for possible default of the counterparty. – However, the distinction is now fading with the advent of Basel III. • The same basic philosophy for assessing credit risk can be applied to loans and derivatives. – Although there are some key differences established loan practices provide a good starting point for a discussion on derivative CVA and DVA.

Credit Risk in Basel II •

Credit Valuation Adjustment (CVA) •

Differences in Loan vs. Derivative • For derivatives, the upfront cash flow will often be zero or a very small amount in relation to the notional referenced by the derivative. • As a result the credit risk at the inception of a derivative contract will often be very small, particularly compared with that on a loan. • The variability of derivative cash flows will depend on factors similar to a loan such as PD and LGD, however there are two important differences compared with loans:

Major Differences in Loan vs. Derivative •

CVA with Derivative •

CVA Example • Payer interest rate swap, USD, 5 -year, “Payer IRS USD 5 Y”. • CVA of IRS as a function of the credit spread of the counterparty Spread (bps) CVA (USD) 100 20, 915 250 49, 929 500 92, 593 750 129, 004 1000 160, 033 10000 298, 190 25000 224, 440

CVA Example • Payer interest rate swap, USD, 5 -year, “Payer IRS USD 5 Y”. • CVA of IRS for different shape of credit curve. The 5 -year credit spread is 500 bps in all cases. CVA (USD) 500 92, 593 Upward 84, 752 Flat 92, 593 Downward 94, 358 • For a flat curve, default probability is approximately equally spaced whilst for an upwards (downwards)-sloping curve, defaults are back (front) loaded.

CVA in Basel III •

Problems with unilateral CVA • One of the assumptions made in deriving the CVA formula was that the institution themselves was risk-free and could not default. • Surely two banks with similar credit would trade at midmarket with no adjustment for credit quality. However, both banks incur counterparty risk when trading with each other, which should incur a cost, making the net value of the trade negative from both points of view. • In a world where all parties use CVA, how can two counterparties of similar credit quality ever agree to trade?

Bilateral CVA • DVA, which arises from considering bilateral CVA, solves above issues, at the possible risk of causing greater issues. • On the one hand, it will resolve some theoretical problems with CVA and create a world where risky counterparties can more easily trade with one another. On the other hand, the nature of DVA and its implications and potential unintended consequences may trouble some people. • Although the use of bilateral CVA (BCVA) goes back many years, it has become increasingly relevant and popular since the financial crisis began in 2007.

Bilateral CVA •

Debt Valuation Adjustment (DVA) •

DVA •

Some Aspects of BCVA •

BCVA Example • Assume that the counterparty’s CDS curve is flat at 500 bps and the recovery rate is 40%. Also, assume a constant continuously compounded interest rate of 5%. We assume that the institution has a flat CDS curve of 250 bps. CVA Unilateral CVA 257, 905 CVA 237, 077 DVA -245, 868 BCVA -8, 791 • This example illustrates an important effect, which is that BCVA does not just depend on credit quality.

Properties of DVA • A risky derivative can be worth more than a risk-free derivative. – The BCVA can be negative (if the second term is larger in magnitude than the first) unlike CVA, which is always positive. A negative BCVA implies that the risky value of a derivative (or netting set of derivatives) is greater than the risk-free value. • Pricing counterparty risk is a zero-sum game. – If all counterparties in the market agree on the approach and parameters for calculation of BCVA then the total amount of counterparty risk in the market (as represented by the sum of all BCVAs) will be zero. This follows from the symmetry of equation.

Criticism of DVA • Should an institution measure its liabilities including the possibility of its own financial failure? • Accountancy standards have generally evolved to a point where “own credit risk” can be incorporated in the valuation of liabilities. • Why do accounting rules view an institution’s own credit risk as being an important component of fair value measurement? – The answer to this is that the fair value of an institution’s bonds is considered to be the price other entities are willing to pay for them. – Another reason is that the failure to account for own credit risk could lead to an accounting mismatch.

Accounting Example Method 1 Method 2 before after Assets 1000 950 Liabilities (800) (760) Equity (200) (150) (200) (190) • Consider two simple accounting approaches. Method 1 values an institution’s liabilities at their face value, which is a fixed amount while Method 2 values them using the current market valuation. • An institution typically has assets and liabilities that are affected by similar market forces (e. g. , they hold bonds and have issued their own debt). Suppose that a change in interest rates reduces the value of the assets by 5% (1000 to 950).

Accounting Example Method 1 Method 2 before after Assets 1000 950 Liabilities (800) (760) Equity (200) (150) (200) (190) • Under Method 1, this creates a distorted view seen as an apparent loss of 50 from the equity of the company. Method 2 appears better because the liabilities also lose (800 – 760 = 40), which balances much of the apparent equity loss leading to an adjustment of only 10. • Suppose that the change in value of the assets above is caused by a change in credit spreads. Method 2 now corresponds to incorporating “own credit” to create a loss on the liabilities.

Accounting Example before after Assets 1000 Liabilities (800) (760) Equity (200) (240) • Consider that the credit spread of the institution widens whilst all other variables (including other credit spreads) are held fixed. Now the institution reports a profit of 40 due to an increase in the value of their equity, which is driven by their own declining credit quality (as measured by their credit spread trading in the market). • “Sfr 1. 8 billion DVA gain nearly cancelled out the Sfr 1. 9 billion it lost in an alleged rogue trading incident”. – UBS case.

Criticism of DVA • An institution booking profits from their own declining credit quality, either due to the debt held on their books or with respect to derivatives via a bilateral counterparty risk adjustment, is a subject that has been fiercely debated. • The criticism of DVA stems mainly from the fact that it is not easily realizable, just as an individual cannot realize gains on their own life insurance policy. Whilst an institution may buy and sell assets on a daily basis, liabilities sometimes cannot be transferred without permission. Hence, it could be argued that the accounting treatment of liabilities should not necessarily mirror that of assets.

Monetizing DVA • • • File for bankruptcy Unwinding and novation Closeout Hedging To hedge CVA => Shorting bonds/Buying CDS protection To hedge DVA => Buying back their own bonds or Selling CDS protection (impossible)

Funding Value Adjustment (FVA) •

FVA formula •

FVA and DVA BCVA = CVA + DVA FVA = FCA + FBA DVA = FBA (? ) Symmetric funding and CVA (CVA + FCA + FBA) – This would ignore DVA benefit on the basis that monetization of DVA (as purely a self-default component) is problematic. • Asymmetric funding and BCVA (CVA + DVA + FCA) – This includes DVA as a funding benefit and considers a funding cost only. • •

Future Directions • While not all details for valuing collateralized derivatives have been resolved, the general principle of collateral discounting is now well defined in literature and adopted as common practice or market convention. The differences among dealers for similar collateralized transactions are generally small. • However, different opinions continue to exist around valuation of derivatives under uncollateralized situations, which is the focus of FVA discussions, or debates. • Wrong Way Risk

Concluding Remarks • Despite the increased use of collateral, a significant portion of OTC derivatives remain uncollateralized. This arises mainly due to the nature of the counterparties involved, such as corporates and sovereigns, without the liquidity and operational capacity to adhere to daily collateral calls. In such cases, an institution must consider the full impact of counterparty risk and funding of the transactions in question.

References • [LJ 11] Lu, D. , and Juan, F. , “Credit Value Adjustment and Funding Value Adjustment All Together”, 2011. Available at http: //ssrn. com/abstract=1803823. • [Br 12] Brigo, D. , "Counterparty Risk FAQ: Credit Va. R, PFE, CVA, DVA, Closeout, Netting, Collateral, Re-hypothecation, WWR, Basel, Funding, CCDS and Margin Lending“, revised Jun 2012, Available at http: //arxiv. org/pdf/1111. 1331. • [IV 13] International Valuation Standards Council, “Credit and Debit Valuation Adjustments”, Exposure draft, 2013. • [Gr 12] Gregory, J. , “Wiley Finance Series: Counterparty Credit Risk and Credit Value Adjustment : A Continuing Challenge for Global Financial Markets”, 2 nd Edition, John Wiley & Sons, 2012.