Download PowerPoint ******

글로벌 금융위기 이후 파생상품
Valuation의 변화 및 시사점
김주철
연세대학교 상경대학 경제학부
2015년 10월 20일
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
• In Basel II,
𝐸 𝐿 = 𝐸𝐴𝐷 ⋅ 𝑃𝐷 ⋅ 𝐿𝐺𝐷
• For loans, the initial cash flow is the full or partial drawdown
of the amount lent, creating an immediate credit risk for the
lender.
• This credit risk exists for the life of the loan and can increase
as additional amounts are drawn-down by the borrower and
reduce as principal is paid off.
• The credit risk exposure is predominately in one direction
(unilateral) with the lender being exposed to the borrower.
Credit Valuation Adjustment (CVA)
• 𝐶𝑉𝐴 = 𝐿𝐺𝐷
𝑇
𝑖=1 𝐸𝑃𝐸
𝑡𝑖 𝑃𝐷(𝑡𝑖−1 , 𝑡𝑖 )
• The variability in the lenders credit risk exposure to the
borrower over the life of the loan depends on various factors:
– The Expected Positive Exposure (EPE) which is usually equivalent to
the principal or drawdown plus unused firm commitments, as listed
under the contractual terms of the loan, discounted to current date.
– The likelihood of the borrower not being able to repay amounts
required by the contract is the Probability of Default (PD).
– In the event that a borrower fails to repay their debt, the sum that is
not recovered by the creditor as a percentage of the loan amount is
the Loss Given Default (LGD).
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
• The credit risk exposure can switch between counterparties
over the life of the derivative, that is, no one party is
necessarily the borrower or the lender of the instrument,
• The potential variability of cash flows can be much greater
than those of a loan as derivative cash flows are usually linked
to a much larger notional and are referenced to an underlying
which can be volatile.
CVA with Derivative
• 𝐶𝑉𝐴 = 𝐿𝐺𝐷
𝑇
𝑃𝐷𝑡
0
𝐸𝑃𝐸𝑡 [IV13]
– Expected Positive Exposure(EPE) : The discounted receipts and
unrealized gains an entity forecasts to receive from the counterparty.
• Risky value = risk-free value – CVA [Gr12]
• 𝐶𝑉𝐴 = 𝐿𝐺𝐷
𝑇
𝑖=1 𝐷𝐹
𝑡𝑖 𝐸𝐸 𝑡𝑖 𝑃𝐷 𝑡𝑖−1 , 𝑡𝑖 [Gr12]
– Institutions themselves cannot default. (related to DVA)
– Risk-free valuation is straightforward. (related to FVA)
– The credit exposure and default probability are independent. (related
to Wrong Way Risk (WWR) )
CVA Example
• Payer interest rate swap, USD, 5-year, “Payer IRS USD 5Y”.
• 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 5Y”.
• CVA of IRS for different shape of credit curve. The 5-year
credit spread is 500bps 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
• In addition to the default risk capital requirements for
counterparty credit risk determined based on the
standardized or internal ratings-based (IRB) approaches for
credit risk, a bank must add a capital charge to cover the risk
of mark-to-market losses on the expected counterparty risk
(such losses being known as credit value adjustments, CVA) to
OTC derivatives.
• 𝐶𝑉𝐴 = 𝐿𝐺𝐷𝑀𝐾𝑇
𝑇
𝑖=1 𝑀𝑎𝑥
0, 𝑒𝑥𝑝
𝑆𝑖−1 𝑡𝑖−1
−
𝐿𝐺𝐷𝑀𝐾𝑇
−
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
• BCVA means that an institution would consider a CVA
calculated under the assumption that they, as well as their
counterparty, may default.
• The definition of BCVA follows directly from that of unilateral
CVA, with the assumption that the institution concerned can
also default.
• 𝐵𝐶𝑉𝐴 = 𝐿𝐺𝐷𝑐
+ 𝐿𝐺𝐷𝐼
• 𝐶𝑉𝐴 = 𝐿𝐺𝐷
𝑇
𝑖=1 𝐸𝐸
𝑇
𝑖=1 𝑁𝐸𝐸
𝑇
𝑖=1 𝐸𝐸
𝑡𝑖 [1 − 𝑃𝐷𝐼 (0, 𝑡𝑖−1 )] 𝑃𝐷𝑐 (𝑡𝑖−1 , 𝑡𝑖 )
𝑡𝑖 [1 − 𝑃𝐷𝑐 (0, 𝑡𝑖−1 )] 𝑃𝐷𝐼 (𝑡𝑖−1 , 𝑡𝑖 )
𝑡𝑖 𝑃𝐷 𝑡𝑖−1 , 𝑡𝑖
Debt Valuation Adjustment (DVA)
• 𝐵𝐶𝑉𝐴 = 𝐿𝐺𝐷𝑐
+ 𝐿𝐺𝐷𝐼
𝑇
𝑖=1 𝐸𝐸
𝑇
𝑖=1 𝑁𝐸𝐸
𝑡𝑖 [1 − 𝑃𝐷𝐼 (0, 𝑡𝑖−1 )] 𝑃𝐷𝑐 (𝑡𝑖−1 , 𝑡𝑖 )
𝑡𝑖 [1 − 𝑃𝐷𝑐 (0, 𝑡𝑖−1 )] 𝑃𝐷𝐼 (𝑡𝑖−1 , 𝑡𝑖 )
• The second BCVA term is a mirror image of the first term and
represents a negative contribution (since the NEE will be nega
tive), known as DVA.
• It corresponds to the fact that in cases where the institution
defaults (before their counterparty), they will make a “gain” if
the value is negative (a “negative exposure”).
DVA
• BCVA = CVA + DVA
• 𝐵𝐶𝑉𝐴 = 𝐿𝐺𝐷𝑐
+ 𝐿𝐺𝐷𝐼
𝑇
𝑖=1 𝐸𝐸
𝑇
𝑖=1 𝑁𝐸𝐸
𝑡𝑖 [1 − 𝑃𝐷𝐼 (0, 𝑡𝑖−1 )] 𝑃𝐷𝑐 (𝑡𝑖−1 , 𝑡𝑖 )
𝑡𝑖 [1 − 𝑃𝐷𝑐 (0, 𝑡𝑖−1 )] 𝑃𝐷𝐼 (𝑡𝑖−1 , 𝑡𝑖 )
• A gain in this context might seem unusual but it is, strictly
speaking, correct since the institution, in the event of their
own default, pays the counterparty only a fraction (recovery)
of what they owe.
• The negative expected exposure is the opposite of the EE. This
is also the EE from the counterparty’s point of view.
Some Aspects of BCVA
• 𝐵𝐶𝑉𝐴 = 𝐿𝐺𝐷𝑐
+ 𝐿𝐺𝐷𝐼
𝑇
𝑖=1 𝐸𝐸
𝑇
𝑖=1 𝑁𝐸𝐸
𝑡𝑖 [1 − 𝑃𝐷𝐼 (0, 𝑡𝑖−1 )] 𝑃𝐷𝑐 (𝑡𝑖−1 , 𝑡𝑖 )
𝑡𝑖 [1 − 𝑃𝐷𝑐 (0, 𝑡𝑖−1 )] 𝑃𝐷𝐼 (𝑡𝑖−1 , 𝑡𝑖 )
• CVA will always be less than or equal to the unilateral CVA
since it includes multiplication by survival probabilities that
must be no greater than unity.
• In turn, BCVA will always be less than the CVA since the
institution is pricing a “gain” from their future default.
• In general, BCVA is expected to be positive if the counterparty
is more risky than the institution (their credit spread is
greater) and negative otherwise.
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
before
after
Assets
1000
950
1000
950
Liabilities
(800)
(800)
(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
before
after
Assets
1000
950
1000
950
Liabilities
(800)
(800)
(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
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).
• “Sfr1.8 billion DVA gain nearly cancelled out the Sfr1.9 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)
• Although it is quantifying something quite different, FVA is
related to CVA and DVA and will have a rather similar formula.
In a sense, FVA will complete the full picture of all possible
outcomes.
• CVA => 𝑃𝐷𝑐 1 − 𝑃𝐷𝐼
• DVA => 𝑃𝐷𝐼 1 − 𝑃𝐷𝐶
• FVA => 1 − 𝑃𝐷𝑐 1 − 𝑃𝐷𝐼
• FVA is the final missing scenario from CVA/DVA framework.
FVA formula
𝑛
𝐹𝑉𝐴 =
𝑗=1
𝑛
+
𝑗=1
𝐸𝐸(𝑡𝑗 ) 1 − 𝑃𝐷𝑐 (0, 𝑡𝑗−1 ) 1 − 𝑃𝐷𝐼 (0, 𝑡𝑗−1 )
× 𝐹𝑆𝑏 𝑡𝑗−1 , 𝑡𝑗 𝑡𝑗−1 − 𝑡𝑗
𝑁𝐸𝐸(𝑡𝑗 ) 1 − 𝑃𝐷𝑐 (0, 𝑡𝑗−1 ) 1 − 𝑃𝐷𝐼 (0, 𝑡𝑗−1 )
× 𝐹𝑆𝑙 𝑡𝑗−1 , 𝑡𝑗 𝑡𝑗−1 − 𝑡𝑗
• FVA = FCA(Funding Cost Adj.) + FBA(Funding Benefit Adj.)
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 monetizati
on of DVA (as purely a self-default component) is problema
tic.
• 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
• [LJ11] Lu, D., and Juan, F., “Credit Value Adjustment and Funding Value
Adjustment All Together”, 2011. Available at
http://ssrn.com/abstract=1803823.
• [Br12] Brigo, D., "Counterparty Risk FAQ: Credit VaR, 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.
• [IV13] International Valuation Standards Council, “Credit and Debit
Valuation Adjustments”, Exposure draft, 2013.
• [Gr12] Gregory, J., “Wiley Finance Series: Counterparty Credit Risk and
Credit Value Adjustment : A Continuing Challenge for Global Financial
Markets”, 2nd Edition, John Wiley & Sons, 2012.