Counterparty risk – definitions Counterparty risk – derivatives market Counterparty risk metrics Wrong Way Risk Exposure profile
Credit Risk
Lesson 6 – Counterparty risk, CVA, DVA
Vivien BRUNEL
École Nationale des Ponts et Chaussées
Dṕartement Ingénieurie Mathématique et Informatique (IMI) – Master II
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1 Counterparty risk – definitions
2 Counterparty risk – derivatives market
3 Counterparty risk metrics
4 Wrong Way Risk
5 Exposure profiles
6 Counterparty Risk Mitigation
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Counterparty Risk – Definition
Counterparty risk – Definition
The counterparty credit risk is defined as the risk that the counterparty to a
transaction could default before the final settlement of the transaction’s cash flows.
An economic loss would occur if the transactions or portfolio of transactions with the
counterparty has a positive economic value at the time of default. [Basel II, Annex 4,
2/A]
Counterparty risk – A bilateral risk
Unlike a firm’s exposure to credit risk through a loan, where the exposure to credit risk
is unilateral and only the lending bank faces the risk of loss, the counterparty credit
risk creates a bilateral risk of loss: the market value of the transaction can be positive
or negative to either counterparty to the transaction. [Basel II, Annex 4, 2/A]
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Counterparty Risk – Definition
Counterparty risk – A systemic risk
I Derivatives create credit risk between the counterparties
I Derivatives increase the connectedness of the financial system
Counterparty risk – A systemic risk
The 2008 financial crisis showed that counterparty-related losses (e.g. changes in the
credit spreads of the counterparties and changes in the market prices that drive the
underlying derivative exposures) have been much larger than default losses.
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Counterparty Risk – Definition
Counterparty risk is affected by:
I
the OTC contract’s market value risk drivers
I
the counterparty credit spread
I
the correlation between the underlying and default of the
counterparty
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Counterparty Risk – Definition
Difference between the lending business and the derivatives
business:
I
Loans: exposure at any future date is the outstanding
balance, which is certain (without considering prepayments).
Credit risk is unilateral
I
Derivatives: exposure at any future date is determined by the
market value at that date and is uncertain.
Counterparty risk can be:
I
unilateral: one party (the investor) is considered default-free
and only the exposure to the counterparty matters
I
bilateral: both parties are considered risky and face exposures
depending on the value of the positions they hold against each
other
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Counterparty Risk – Derivatives market
OTC derivatives are efficient and effective tools to transfer
financial risks between market participants. As a byproduct of such
transfer:
I
they create credit risk between the counterparties
I
they increase the connectedness of the financial system
The 2008 financial crisis showed that counterparty-related losses
(e.g. changes in the credit spreads of the counterparties and
changes in the market prices that drive the underlying derivative
exposures) have been much larger than default losses.
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Counterparty Risk – Derivatives market
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Counterparty Risk – Derivatives market
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Counterparty Risk – Counterparty risk metrics
Two approaches to counterparty risk:
I
counterparty risk management: for internal purposes and for
regulatory capital requirements, following Basel II
I
counterparty risk from a pricing point of view: Credit
Valuation Adjustment (CVA), when updating the price of
instruments to account for possible default of the counterparty
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Future exposures
Counterparty exposure at any given future time
E (t) = V (t)+
Exposure at Default (EAD) is defined in terms of the exposure
valued at the (random future) default time of the counterparty
(see EEPE)
Potential future exposure (PFE)
PFEq (t) = PE−1
(t) (q)
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Future exposures
Expected exposure (EE) is the average exposure on a future date.
The curve of EE in time, as the future date varies, provides the
expected exposure profile.
EE (t) = E P [E (t)]
Effective Positive Exposure (EPE) is the average EE in time up to
a given future date.
Z
1 T
EE (t) dt
EPE (t) =
T 0
Expected Effective positive exposure (EEPE) the time average of
the running maximum of EPE:
Z
1 T
EEPE =
dt max EE (s)
s≤t
T 0
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CVA definition
CVA is defined as:
I
the difference between the risk-free value and the risky value
of one or more trades or, alternatively,
I
the expected loss arising from a future counterparty default.
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CVA – Unilateral CVA
Riskless price:
PSR = E Q
Z
T
CFt e −rt dt
0
Replacement cost:
LτC = (1 − R)11{τC ≤T } E (τC )
Risky price:
PR = E
Q
Z
0
T
CFt − LτC · 11{τC =t} e
−rt
dt
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CVA – Unilateral CVA
CVA equal to the market value of the expected loss:
CVA = E Q [LτC e −r τC ] = (1 − R)E Q 11{τC ≤T } E (τC ) e −r τC
In the case of independence between the default date and the
exposure:
Z T
CVA = (1 − R)
E Q [E (t)] dQC (t)
0
where
st
QC (t) = 1 − e − 1−R t
Discretization:
s
n
st
X
ti
i+1
E Q [E (ti )] + E Q [E (ti+1 )]
− 1−R
ti
− 1−R
ti+1
CVA ∼ (1−R)
e
−e
2
i=0
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DVA and bilateral CVA
CVAB = CVAU − DVA
CVAU = (1 − R)E Q 11{τC ≤min(T ,τB )} E (τC ) e −r τC
DVA = (1 − R)E Q 11{τB ≤min(T ,τC )} Ē (τB ) e −r τB
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Wrong Way Risk
WWR is defined as the risk that occurs when “exposure to a
counterparty is adversely correlated with the credit quality of that
counterparty”. It arises when default risk and credit exposure
increase together.
I
Specific WWR arises due to counterparty specific factors: a
rating downgrade, poor earnings or litigation.
I
General WWR occurs when the trade position is affected by
macroeconomic factors: interest rates, inflation, political
tension in a particular region, etc...
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Wrong Way Risk – examples
Monoline insurers (e.g. Ambac and MBIA)
During the subprime crisis, the monolines specialized in guaranteeing mortgage
backed securities (MBS); when the mortgage market collapsed, the monolines
saw their creditworthiness deteriorate and found themselves unable to pay all of
the insurance claims. Almost all exposure mitigation from monoline insurance
fell short due to the guarantors’ increased probability of default under exactly
the same conditions when insurance was most needed.
Collateralized loan
Bank A enters into a collateralized loan with Bank B (the counterparty). The
collateral that Bank B provides to A can be of different nature: bonds issued
by Bank B (specific WWR) bonds issued by a different issuer belonging to a
similar industry, or the same country or geographical region (general WWR).
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Right Way Risk
Right way risk is the opposite of wrong way risk. It is the effect
observed when the exposure decreases as the default probability
increases, i.e. when there is a negative dependency between the
two. The size of credit risk decreases as the counterparty
approaches a potential default. RWR occurs when a company
enters into transactions to partially hedge an existing exposure.
Examples:
I
An airline usually protects itself against a rise in fuel prices by
entering into long oil derivative contracts.
I
A company would normally issue calls and not puts on its
stock. WWR and RWR are together referred to as DWR
(directional way risk).
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Regulatory treatment
Basel II deals with wrong-way risk using the so-called α multiplier
to increase the exposure, in the version of the model in which
exposure and counterparty creditworthiness are assumed to be
independent. The effect is to increase EE by the α multiplier. The
Basel II rules set α equal to 1.4 or allows banks to use their own
models, with a floor for α of 1.2, i.e.
I
if a bank uses its own model, at minimum, the EE has to be
20% higher than that given by the model where default and
exposure are independent
I
if a bank does not have its own model for wrong way risk it
has to be 40% higher.
Estimates of α reported by banks range from 1.07 to 1.10.
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Exposure profile
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Exposure profile
Let’s consider the exposure on a CDS protection contract:
V (t) = (st − s0 ).DV (t, T )
We assume that the spread process is normal:
st = s0 + σWt
√
EE (t) = E P [V (t)+ ] ∼ E P [(st −s0 )+ ].DVF (t, T ) ∝ σ t.DVF (t, T )
√ EE (t) = E P [V (t)+ ] ∝ σ t e −(r +λ)t − e −(r +λ)T
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Netting
In presence of multiple trades with a counterparty, netting
agreements allow, in the event of default of one of the
counterparties, to aggregate the transactions before settling claims.
I
In the absence of netting, the exposure is:
X
X
E (t) =
Ei (t) =
Vi (t)+
i
I
i
A netting agreement is a legally binding contract between two
counterparties based on which, in the event of default, the
exposure results in:
!+
X
E (t) =
Vi (t)
i
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Netting
Assumptions
Two counterparties, a bank B and a counterparty C, such that:
I
C holds a currency option written by B with a market value of
50
I
B has an IRS with C, having a marked to market value in
favor of B of 80
Exposures
I
The exposure of the bank B to the counterparty C is 80
I
The exposure of the counterparty C to the bank B is 50
I
The exposure of the bank B to the counterparty C, with
netting, is 30
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Collateral
Consider the bank B and the counterparty C. Let C (t) be the
(cash) collateral amount posted by C to B, at time t. B has no
exposure to the contract up to the collateral amount, while its
losses are reduced by the collateral amount whenever the exposure
exceeds it. The collateralized exposure EC (t) is defined as:
EC (t) = (E (t) − C (t))+
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Collateral
I
Posting threshold H > 0: below the threshold no collateral is
posted.
I
Margin period δ: the interval at which margin is monitored
and called for:
C (t) = [E (t − δ) − H]+
I
Minimum transfer amount MTA: the amount below which no
margin transfer is made.
C (t) = [E (t − δ) − H] + 1{E (t−δ)−H>MTA}
I
Downgrade triggers: post more collateral to its counterparty,
if it is downgraded below a certain level
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