Issues in Counterparty Credit Risk
David Lynch
Federal Reserve Board
Presentation to Quant Congress USA
2008
The views expressed in this presentation are those of the presenter and do not
represent the views of the Board of Governors of the Federal Reserve System
Background and Outline

Background

In 2005 the BCBS adopted changes to Basel II capital
requirements for counterparty credit risk that allowed firms
to use expected positive exposure as the basis for
regulatory capital requirements


Expected positive exposure is the average over time of the
forecast of the mean exposure to a counterparty at various
horizons over the next year
Outline





Explanation of IMM Capital Charge.
EPE vs EEPE
Rollover then aggregate
Risk neutral or historical distributions to calculate EE.
CDS to cover counterparty credit risk
An Explanation of the Counterparty Credit Risk
Charge Using the Internal Models Method.

In Basel II IRB formula for credit risk use:


EAD =1.4 x EEPE (“Effective Expected Positive
Exposure”)
Theory: Developed by Canabarro, Picoult,
and Wilde in a series of papers and
documented in ISDA-LIBA-TBMA
compendium of Papers (2004).

EPE (“Expected positive exposure”) is the loan
equivalent (deterministic) amount to use for
stochastic exposures in a portfolio credit risk
model.
Expected positive exposure

Expected positive exposure (EPE) is the basis for calculating EAD in Basel II (actually
uses effective EPE). Steps to find EPE:

Find the Distribution of Market Values for trades with a counterparty

For many future dates find the probability distribution of net market values of
transactions within a netting set for some future date given the realized
market value of those transactions up to the present time.

Find the Distribution of Exposures

Adjust the probability distribution of market values for each of those future
dates by setting cases of negative net market values equal to zero within the
distribution (this takes account of the fact that, when the bank owes the
counterparty money, the bank does not have an exposure to the
counterparty).

Find the Expected Exposure

For each date find the mean (average) of the distribution of exposures at any
particular future date before the longest-maturity transaction in the netting set
matures. An expected exposure value is typically generated for many future
dates up until the longest maturity date of transactions in the netting set.

Find Expected Positive Exposure (EPE)

Take the weighted average over time of expected exposures where the
weights are the proportion that an individual expected exposure represents of
the entire time interval. When calculating the minimum capital requirement,
the average is taken over the first year or over the time period of the longestmaturity contract in the netting set.
EEPE vs. EPE

CCR for an amortizing loan
$151,000
exposure
$150,000

$150,000
$149,170
Under Basel II, loans in the
banking book use the remaining
unpaid balance for the exposure
at default in determining capital.
The theory is that Counterparty
Credit Risk exposures use
Expected Positive Exposure for
exposure at default.
The Chart shows the exposure
values for an amortizing loan of
$150,000 that cannot be prepaid.

$149,000


$148,000
$147,000
1
2
3
4
5
6
7
8
9
m onth
expected exposure
EPE
10
11
12
13
Unpaid balance is $150,000
Expected Positive Exposure is
$149,170
To reconcile the loan exposure
and CCR exposure (by
accounting for rollover in the
CCR charge) use Effective EPE
which is the average over time of
effective expected exposure
(EEEt);

EEEt = Max (EEEt-1, EEt)

Use of EEPE adjustment
reconciles Loan and CCR
capital charges
Unpaid balance= EEPE=
$150,000

Rollover then Aggregate?

Industry has raised the issue of whether banks
should aggregate exposures across netting sets
(add EEt’s of netting sets) before rollover (EEEt =
max(EEEt-1, EEt)) or account for rollover before
aggregating netting sets


BCBS documents specify rollover then aggregating netting
sets
BCBS is considering the issue but has formed no
conclusion
Graphical depiction of rollover before netting
issue
EEPE at the Netting set
level
Netting
Set A
EEPE at the counterparty
Level
EEEA
EEA
Netting
Set B
EEA
EEB = EEEB
EEB
EEEA+EEEB
EEPE
Combined
Netting Sets
EPE
EPE=EEPE
Risk Neutral vs. “Real World” modeling of EPE
Real World EPE model based on historic diffusion:
•Current exposure (CE) does not always equal
modeled current exposure (EE0) since pricing is
done with historic volatility
•Modeled drift is same as actual drift
$
Risk Neutral EPE model based on risk neutral model:
•Current exposure is the same as modeled current
exposure
•Risk neutral drift is different than real world drift
$
EE
Real world EE
EE
Risk Neutral EE
EE0
EE0=CE
C
ECE
C
E
Time
Time
Basel Committee does not specify which to use, nor does US implementation, The Choice is left to the firm.
Regardless of choice, the firm should know “CE”, what a counterparty would owe the bank if it defaulted today
CDS to cover counterparty credit risk

CDS may be used to hedge counterparty risk



Other ways to hedge CVA have not been addressed
Contingent CDS are CDS that reference a
derivative underlying
How should CDS be incorporated into Counterparty
credit risk metrics?

Substitution approach – subtract the underlying reference
obligation of the CDS from the netting set of the reference
entity of the CDS (even if there is not an offsetting
identical transaction) and add the underlying obligation to
the netting set of the protection provider.
CCDS Capital treatment-simple example
Exposure allocated to counterparties under various capital treatments for the case
of a CCDS hedging the counterparty risk of an IRS where the terms of the
IRS and the reference derivative of the CCDS exactly match
Values for comparison
Contract
EPE
EEPE
IRS
.0778
.1055
Capital treatment
IRS EAD
CCDS EAD
Total of EADS
CCDS
.00038
.00052
1. No recognition of
risk mitigation
0.1055
0.0005
0.106
2. No charge for risk
mitigation
0.1055
0
0.1055
3. Substitution of
exposures
0
0.1055
0.1055
4.Independent Double
default through
exposures
0
0.0005
0.0005
•US rules allows substitution of exposures, note that there is an additional benefit
If CCDS protection provider has a lower PD than the original counterparty
Modeling multiple forms of collateral


Explicit modeling of collateral agreements in a counterparty
credit risk model is envisioned by Basel rules. This is
straightforward when collateral is in the form of cash
It is much more difficult to model collateral agreements when
the counterparty can deliver other forms of collateral
What kind of collateral is delivered at this
time when the collateral threshold is met?
exposure
Collateral
threshold
time