Counterparty Credit Risk:
Quantifying Economic Capital
Martin Goldberg
martin@validationquant.com
September 18, 2007
Risk Training on Economic Capital
The Usual Caveat
All opinions and views expressed in this presentation
are my own personal opinion, and do not necessarily
reflect the views of my employer, any of its clients, nor
any other person or group.
Questions and comments are welcome. My e-mail
address is on the cover page.
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 2 of 38
Martin Goldberg
Outline
What is Economic Capital
What is Counterparty Credit Risk
How does it differ from Issuer Credit Risk
How is it quantified
Default Only
Loan equivalent and 
Loss of Economic Value
How is it managed in ordinary times
Economic Capital for Counterparty Risk
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 3 of 38
Martin Goldberg
Outline
What is Economic Capital
What is Counterparty Credit Risk
How does it differ from Issuer Credit Risk
How is it quantified
Default Only
Loan equivalent and 
Loss of Economic Value
How is it managed in ordinary times
Economic Capital for Counterparty Risk
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 4 of 38
Martin Goldberg
Regulatory and Economic Capital
Capital is a “Rainy Day Fund” to ensure your institution does not go bankrupt in a
bad period
Potential unexpected loss, over a specified time horizon, at a specified confidence
level.
Market Risk Regulatory Capital = VaR - 99% ten day
 Worst 2 weeks of 4 years
Basel 2 Economic Capital - 99.9% one year
 Worst year of the millennium - somewhat hard to backtest
Basel 2 PD Floor (~ AA rating) Economic Capital - 99.97% one year
 Based on the .03% transition probability from AA-> D
 Third worst year in 10,000
 Very hard to calibrate or backtest with actual historical data
 What was the effect on your bank of the invention of agriculture? Of writing?
 How many of your swap counterparties defaulted when Rome was sacked?
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
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Martin Goldberg
A Reminder: EC And Capital Horizon
EC measures risk from an insolvency or debt holders perspective (potential
loss of value) rather than from an equity investment perspective
(undiversified volatility of returns).
Insolvency risk is calculated by comparing EC to the Available Financial
Resources
(i.e. AFR = book capital – goodwill + fair market
adjustment).
Here is an example of EC for Issuer Credit Risk of a large portfolio
Economic capital
Probability Distribution of Potential Credit Loss
for a Portfolio of Many Obligors
Probability of Credit Loss
3.0%
= Unexpected Loss
2.5%
= Loss at very high CL
– Expected loss.
2.0%
1.5%
1.0%
Loss at
very high
CL
Economic Capital
0.5%
0.0%
-160
-140
Expected
Loss
-120
-100
-80
-60
-40
-20
Potential Credit Loss ($mm)
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Expected loss should be
covered by reserves and/or
pricing.
0
Page 6 of 38
Martin Goldberg
Extrapolating to EC level of risk
Since we do not have 1000 years of data, let alone 10,000, what
can we do instead?
The only derivative contract with a long history is the Japanese rice
futures which has only a 400 year history, and most OTC derivatives
trading started in the 20th century but did not exist in the 19th.
Quick and dirty - pretend everything is normally or lognormally
distributed and scale up accordingly.
Better - fit a fat-tailed distribution to the data you have and scale using
that distribution. I recommend the Tukey g--h distribution[2], where h
controls the fatness of the tail, and the quantiles are known.
X gXh ( Z )  A  B
September 18, 2007
Counterparty Credit Risk
e
1
e
g
gZ
Risk Training on
Economic Capital
hZ 2
2
Page 7 of 38
Martin Goldberg
Extreme Value Theory and EC
Estimates of large percentiles, which correspond to rare events, are both
difficult and possibly misleading.
Extreme value theory has some techniques for extrapolation but these are
fraught with difficulties in practice[3].
In a portfolio context, such as any of your firms, there is the added
complication of contagion - correlations in normal times are usually
irrelevant in a crisis. The relevant measure is tail dependence[4], which is
hard to estimate since by definition you have very few data points, or more
likely none.
The usual cheat scheme is to assume ergodicity - pretend that one year’s data
on 1000 counterparties is a good proxy for any one firm followed for a
millennium. Also one can assume stationarity - the nature of the market will
be about the same in the near future as it has been in the recent past. This
worked poorly for, say, Russian debt issued in 1915.
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 8 of 38
Martin Goldberg
Outline
What is Economic Capital
What is Counterparty Credit Risk
How does it differ from Issuer Credit Risk
How is it quantified
Default Only
Loan equivalent and 
Loss of Economic Value
How is it managed in ordinary times
Economic Capital for Counterparty Risk
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 9 of 38
Martin Goldberg
Counterparty Credit Risk Defined
Counterparty Credit Risk is the risk of loss to your firm due to a
counterparty’s default on money owed you in a derivatives transaction.
The derivatives could be any OTC swap, forward, option, repo lending, or
securities lending.
The market value of the derivative does not explicitly depend on the counterparty
There is no default-free exchange involved - the exchanges are assumed to have
no risk of default and thus futures and listed options have no counterparty risk.
Basel 2 has a few ways of calculating the regulatory measure of counterparty
risk - I will not address the more approximate measures but only the
Advanced IRB approach.
The implementation of Basel 2 differs from one country to the next, and
when in doubt ask your national regulator. For multinationals there may be a
turf war or requirements for multiple incompatible calculations.
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
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Martin Goldberg
Default-Only vs. Loss-of-Market-Value
Counterparty risk can be measured in two incompatible ways
The banking book (accrual) view is that there is no loss until bankruptcy
is declared or a permanent impairment is recognized.
The trading book (mark-to-market) view is that there is a loss in value if
the counterparty becomes less creditworthy and a gain in value if the
counterparty gets further from default. This value is measured as a Credit
Valuation Adjustment (CVA) which ideally would move in tandem with
the counterparty’s CDS spreads.
There is a legal distinction between two different kinds of counterparty:
Bilateral - a legally enforceable netting arrangement exists.
Unilateral - No netting; each contract stands alone. If at default you owe them
$100 on some swaps and they owe you $100 on others, you pay them $100 and go
to court to try to collect some of the $100 they owe you.
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Risk Training on
Economic Capital
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Martin Goldberg
Always adds a layer of optionality
If you owe them money when they default, you have not incurred any loss.
If they owe you money when they default, you are in line with everyone else
they owe money to.
The payoff for counterparty risk on one contract is max(0,contract value)
which is an option struck at zero. If the contract is linear, this is an option.
If the contract is an option, this is a compound option. If the contract is an
exotic, this is even more exotic.
For bilateral, this is an option on a portfolio.
The one exception is Extinguishers - derivatives where it says in the contract
that the derivative vanishes with no payments in the event of default of either
counterparty. These are not very common, but I have seen them, in FX
especially.
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 12 of 38
Martin Goldberg
Outline
What is Economic Capital
What is Counterparty Credit Risk
How does it differ from Issuer Credit Risk
How is it quantified
Default Only
Loan equivalent and 
Loss of Economic Value
How is it managed in ordinary times
Economic Capital for Counterparty Risk
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 13 of 38
Martin Goldberg
Comparison to Debt
Debt
Counterparty Exposures
Exposure to obligor depends on
obligor’s actions
Exposure depends on market
movements
Cannot issue negative debt
Can go long or short OTC
derivatives
Usually cross-default provisions, so
exposures add
Diversification across obligors
reduces risk
Mainly simple Discounted Cash
Flows
September 18, 2007
Counterparty Credit Risk
Exposures net if bilateral, might be
allowed to net OTC derivatives and
repo’s
Diversification not as effective in a
market meltdown
Option valuation - usually requires
Monte Carlo simulation
Risk Training on
Economic Capital
Page 14 of 38
Martin Goldberg
Outline
What is Economic Capital
What is Counterparty Credit Risk
How does it differ from Issuer Credit Risk
How is it quantified
Default Only
Loan equivalent and 
Loss of Economic Value
How is it managed in ordinary times
Economic Capital for Counterparty Risk
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 15 of 38
Martin Goldberg
Calculating Counterparty Risk 1
First Step - What are your exposures? Can you aggregate all OTC
derivatives, repo, Sec Lending, etc. by counterparty? Often these are housed
in incompatible systems that do not communicate.
Second - Real-world measure simulation of the entire market for many years
Must include fat-tail effects - Basel requires it
Must backtest well and be calibrated to historical experience
Probably should include contagion
Interest rates are mean-reverting in the long run, so need to include that
 Early attempts at this include the Alan Beilis / Jan Dash Macro-Micro
Model [ 7 ]
There is no really good solution yet for this that I know of, but many are trying to
solve it
September 18, 2007
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Risk Training on
Economic Capital
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Martin Goldberg
Calculating Counterparty Risk 2
Third Step - For each simulation path, calculate the risk-free market value of
each contract at each time step
If the contract is too time-consuming to price, use a proxy that can be priced
faster, preferably a closed-form solution.
This gets far messier if you want to assume market values are correlated with
default likelihood. They are - many of the recent sub-prime defaults were
arguably triggered by margin calls on repo exposures.
Fourth - Calculate the potential exposure for each path
Aggregation by counterparty
Include risk mitigants such as margining, and do unilateral differently from
bilateral.
Assume no additional transactions
Fifth - Collect into an Exposure Profile of potential exposure at different
times and confidence levels.
Page 17 of 38
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Martin Goldberg
Exposure Profile of an Interest Rate Swap
This is a typical exposure profile of a typical 5-year swap at a high
confidence level. The sharp drops are coupon dates.
Average Exposure
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 18 of 38
Martin Goldberg
Outline
What is Economic Capital
What is Counterparty Credit Risk
How does it differ from Issuer Credit Risk
How is it quantified
Default Only
Loan equivalent and 
Loss of Economic Value
How is it managed in ordinary times
Economic Capital for Counterparty Risk
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 19 of 38
Martin Goldberg
Default-only calculation
Messiest technique - assume everything is correlated, and each simulated
path includes a draw from the probability of default distribution, the recovery
distribution, and also all the market factors. If you assume that default is not
just correlated by a Pearson correlation with the market, but requires a more
complicated copula to correctly describe the dependence, it gets even worse.
This is closer to reality - firms can handle small changes in market conditions
but there is often a trigger level past which they run out of alternatives and
declare bankruptcy. If you are doing this whole exercise just for regulatory
compliance, none of this is relevant.
Basel-compliant technique Simulate the market factors and derive exposure profiles
Calculate Expected Positive Exposure profiles as [Exposure Profile]+
Average to get a single number EPE for each counterparty
Simulate default and recovery
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 20 of 38
Martin Goldberg
Outline
What is Economic Capital
What is Counterparty Credit Risk
How does it differ from Issuer Credit Risk
How is it quantified
Default Only
Loan equivalent and 
Loss of Economic Value
How is it managed in ordinary times
Economic Capital for Counterparty Risk
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 21 of 38
Martin Goldberg
Basel 2 Rules for AIRB
In the Basel 2 AIRB framework, counterparty credit risk is treated as if it
were a corporate exposure. Thus the regulatory capital charge C is
C = EAD  K (PD, LGD)  MA(PD,M’)
where the effective remaining maturity M’ = Min(5 years,Max(1 year, tenor))
Probability of Default PD = max(.03%, counterparty’s default likelihood)
Loss Given Default LGD = 1 - Recovery Rate (not same as for loans or bonds)
K is the “default-only capital factor” given by a messy formula
MA is a maturity adjustment that is intended to capture migration risk, also a
messy formula
Exposure At Default EAD is the loan-equivalent net expected positive exposure to
a counterparty (“netting set”) if bilateral, and sum of expected positive exposures
to each contract if unilateral.
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 22 of 38
Martin Goldberg
Loan Equivalent and 
Basel is a one-size-fits-all methodology, so naturally it wants to see all credit
risk as loans. This requires a Loan Equivalent for counterparty risk to fit into
the Basel 2 EAD slot.
“By using EPE, transactions with CCR are given the same standing as loans with the goal of
reducing the capital treatment’s influence on a firm’s decision to extend an on-balance sheet
loan rather than engage in an economically equivalent transaction that involves exposure to
CCR. Consistent with this determination, the internal model and standardised methods to
estimating EAD employ the concept of EPE.”
Evan Picoult of Citigroup figured out how to do this, worked out the details
with Eduardo Canabarro (then at GS), and Tom Wilde (then at CSFB) and
Basel adopted this methodology [6].
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
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Martin Goldberg
Verbatim Quote from Basel 2
September 18, 2007
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Risk Training on
Economic Capital
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Martin Goldberg
The mysterious multiplier 
 is defined as the ratio of Economic Capital computed with a full
simulation of all defaults and all underlying factors in the real world measure
divided by the EC computed with the fixed EPE required by Basel. Tom
Wilde did some experiments and found a range of 1.02 - 1.43, with an
average of about 1.1.
Basel mandated  = 1.4 at first, but now allows internal calculations subject
to the floor  = Max( you calculate, 1.2).
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 25 of 38
Martin Goldberg
Outline
What is Economic Capital
What is Counterparty Credit Risk
How does it differ from Issuer Credit Risk
How is it quantified
Default Only
Loan equivalent and 
Loss of Economic Value
How is it managed in ordinary times
Economic Capital for Counterparty Risk
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 26 of 38
Martin Goldberg
Credit Value Adjustments
Bonds and loans are cash flows discounted at a credit spread above the riskfree rate. By analogy, counterparty exposures should have a credit spread
baked in.
The CVA is the derivative value discounted at the risk-free rate minus the
same derivative discounted at the relevant spread over risk-free.
Complications Whose spread? If we owe them money, is it our spread instead of theirs?
CVA applies to portfolio, not each exposure separately, for bilateral
Unilateral would as usual work differently
Need to introduce “maturity adjustments” to fit the Basel definition of a one-year
horizon
Spread is another variable to simulate
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 27 of 38
Martin Goldberg
Advantage of CVA over Default-Only
Since CVA varies with creditworthiness and market conditions, you can
hedge counterparty risk as measured by CVA (not as much with unilateral).
You can’t do that with a default-only view.
Hedge the loan-equivalent exposure to each counterparty, netted across all
markets, with default swaps or with the counterparty’s debt securities.
Hedge the market exposure to each market factor, aggregating across all
counterparties.
Still exposed to the cross-gamma of changes in market inducing changes in
credit spread - not easy to hedge.
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 28 of 38
Martin Goldberg
Outline
What is Economic Capital
What is Counterparty Credit Risk
How does it differ from Issuer Credit Risk
How is it quantified
Default Only
Loan equivalent and 
Loss of Economic Value
How is it managed in ordinary times
Economic Capital for Counterparty Risk
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 29 of 38
Martin Goldberg
Ways to Manage Counterparty Risk
There are several ways to manage counterparty credit risk, and most
institutions use most or all of these.
1.
Avoid it - since exchanges are assumed to be free from default risk, the counterparty credit
risk for exchange-traded contracts is zero.
2.
Ameliorate it - margining for OTC counterparties lowers the total amount at risk on any
given day - most financial firms will offer cross-product margining agreements, but most
OTC derivatives are not margined.
3.
Diversify - this is an insurance-style hedge - assumes that defaults are independent or at
least not 100% correlated - may be a bad assumption in the once-per-thousand-years
systemic crisis where the whole banking system goes under.
4.
Delta-hedge with debt or CDS of the counterparty - this may work quite differently if you
do not have a good bilateral netting agreement, or the CDS seller is closely related to the
counterparty - “wrong-way risk” such as buying protection on swaps with a foreign
government from banks in that same country.
5.
Sell it - Contingent Credit Default Swaps transfer counterparty risk and get it off your
books. The regulators will need to agree that this is a true sale, but I expect that to happen.
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
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Martin Goldberg
Margining
A margin agreement reduces the exposure at default. A margin account is
set up at one of the two counterparty’s institutions, or at a third-party
margining manager. These work differently for bilateral than for unilateral
counterparties.
Both counterparties (X and Y) agree to their threshold margin limit, which is
usually based on credit quality. If the total exposure of X to Y (add up all
positive exposures for unilateral, net all exposures of either sign for bilateral)
exceeds the limit, based on the (usually daily) mark-to-market (mark-tomodel of the agreed calculation agent if necessary), then Y must deposit
funds, either cash or acceptable securities, into the margin account by the end
of a prespecified “cure period” to bring the exposure back to the limit. X’s
total loss if Y defaults is at most the limit, plus the excess triggering the
margin call, plus or minus the change in value during the cure period. Same
for Y exposure to X.
Does default on a margin call trigger cross-default on all debts? Ask your
lawyer.
Page 31 of 38
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Martin Goldberg
What is Margined? Ref [5]
September 18, 2007
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Risk Training on
Economic Capital
Page 32 of 38
Martin Goldberg
Cross-Product Netting
Some margin accounts have a VaR-like limit, where the limit for a portfolio
of many different exposures is calculated to be the (usually one-day, 99th
percentile) potential exposure tomorrow. This is a more objective way of
setting limits, and responds appropriately to changes in the mix of exposure
types.
You can buy off-the-shelf calculators for this - called Cross-Product Netting
(CPN) or Cross-Product Margining (CPM).
One of my former employers used an exact copy of the corporate VaR
engine to calculate CPM.
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 33 of 38
Martin Goldberg
Contingent Credit Default Swaps
Also called C-CDS
Liquid market for some names
Only for a handful of vanilla derivatives underlyers
Some basis risk remains if you are actually protecting an exotic
Not yet available on a portfolio of diverse underlying types, but the vanilla can
have a complicated but non-stochastic amortization / accretion schedule
Bloomberg page ICVA
Bilateral flavor can be modeled as two unilaterals in opposite directions
Counterparty risk causes a correlation between credit and market risk
CCDS extinguish the credit risk part, and transform it into market risk, plus
some counterparty risk to the issuer of the CCDS
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 34 of 38
Martin Goldberg
Outline
What is Economic Capital
What is Counterparty Credit Risk
How does it differ from Issuer Credit Risk
How is it quantified
Default Only
Loan equivalent and 
Loss of Economic Value
How is it managed in ordinary times
Economic Capital for Counterparty Risk
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
Page 35 of 38
Martin Goldberg
Basel 2 Capital vs. Economic Capital
As mentioned before, Basel assumes no contagion or systemic risk in their
AIRB calculation guidelines. In reality, the once-per-thousand-year worst
case will certainly sink your firm.
Show of hands - How many people in the audience work for firms founded
before the year 1007?
September 18, 2007
Counterparty Credit Risk
Risk Training on
Economic Capital
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Martin Goldberg
Conclusion
Economic Capital for Counterparty risk, as defined in Basel 2 rules, is a
useful measure of credit risk exposure separate from issuer credit risk.
If you want to hedge the exposures, it can be done using CVA as a dynamic
measure.
There is lots of interesting work in this area still undone.
Don’t confuse the 99.9% risk levels you measure with true economic risk in
a true systemic credit event.
September 18, 2007
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Risk Training on
Economic Capital
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Martin Goldberg
References
1.
Martin@validationquant.com, 732-742-8977
2.
The Tukey gh distribution is getting quite good press. See
http://www.bos.frb.org/economic/wp/index.htm and the references there
3.
http://www.math.ethz.ch/~baltes/ftp/g-and-h_May07.pdf
4.
http://www.quantlet.com/mdstat/scripts/stf/html/stfhtmlnode17.html
5.
http://www.isda.org/whatsnew/pdf/2001Margin.pdf
6.
http://www.bis.org/publ/bcbs116.pdf
7.
Part VI of Quantitative Finance And Risk Management: A Physicist's
Approach by Jan W. Dash (World Scientific Publishing Co © 2004 )
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Economic Capital
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Martin Goldberg