Risk taker

Dan Rosen

R2 Financial Technologies

RiskLab Madrid, May 2011

1

© 2006-2011 R2 Financial Technologies

CVA, Basel III and

Wrong-Way Risk

Dan Rosen


[email protected]

© 2006-2011 R2 Financial Technologies 2

Regulatory Capital and CVA

“Mark-to-market losses due to credit valuation

adjustments (CVA) were not directly

capitalised. Roughly two–thirds of CCR

losses were due to CVA losses and only one-

third were due to actual defaults.”

Basel Committee on Banking Supervision (2009)

Dan Rosen



2


Outline

� Introduction

� CCR, CVA, management of CVA

� CCR capital and Basel III

� Wrong-way risk (WWR)

� Computing CVA and CVA VaR

� Wrong-way risk methodology

� Examples

� Concluding remarks


Counterparty Credit Risk Evolution

Counterparty exposures and limits

Economic capital

Default risk

• Basel II (IRB)

• EPE and alpha

CCR valuation: CVA

• Fundamental vs. Market values (CDS spreads)

• Unilateral �� bilateral

Hedging CCR

JtD risk and CVA

Economic capital

Credit + market risk (CVA)

• Basel III...

CVA is now an integral

part of current accounting

rules for P&L, and of the

new proposal for banking

regulation (“Basel III”

rules)

Dan Rosen



3


Pricing CCR: Credit Value Adjustment (CVA)

� CVA is the market value of counterparty credit risk

CVA = Risk-free portfolio value – true portfolio value accounting

for counterparty’s default

� CVA is an integral component of the value of derivatives

� Now an integral part of accounting rules, and Basel III

� Prior to mid-2007, CVA was either ignored by dealers, or too small to be noticed

by customers

� CVA is measured at the counterparty level

� Ideally, it should be part of the trade valuation but calculated separately because

of portfolio effects

� In addition to credit spreads (and competition) the CVA charged on a particular

trade is affected by:

� Bank’s existing portfolio of trades and the credit mitigation used in the deal

� Methodology used to determine exposures

© 2006-2011 R2 Financial Technologies 14©2009 IACPM14

CVA and Risk Management

� Some banks started to price and hedge CVA in the mid 1990s

� More recently, more banks started to price and actively hedge CVA

� Banks currently calculate and manage CVA according to different

business models and subject different accounting regimes

� Various large banks already manage CVA risks as part of their Trading

Books: daily MtM, active hedging, enforced market risk limits and intent to

transfer out the CVA risks

� Some banks have opted for central CVA desk

� Others have opted for CVA desks deployed in their main business units

� CVA desks sell full counterparty credit insurance to the derivatives

trading desks

� Manage the risks of the CVA after inception of the trades

� Subject to risk limits and usually do not have a revenue generation budget

Dan Rosen



4


Some Definitions

� Counterparty exposure: economic loss incurred on all outstanding

transactions if counterparty defaults

� Cost of replacing or hedging the contracts at the time of default

� Accounts for netting and collateral, but is generally not adjusted by possible

recoveries

� More generally, exposures can also be defined as potential losses on credit

migration events such as downgrades (e.g. in CreditMetrics)

� Potential future exposure (PFE): current exposure plus the potential future

changes in exposures during the contracts’ lives

� Accounts for the aging of the portfolio and underlying market factor movements

which directly affect contract values at a future times

� Example: a pay-fix IRS with negative MtM has current exposure = 0.

� If future rates rise, the contract can have a positive value � potential

exposure to holder


Computing CVA

� Value of the CP portfolio at t

� Gross CP-level exposure (netting not allowed)

� Netted CP-level exposure (single agreement)

� CP-level (margined)

� Instantaneous collateral

� Lagged collateral

� CP portfolios with multiple netting agreements and trades outside of the

agreement can be modeled by a combination of these equations

{ }( ) max ( ) ( ), 0E t V t C t= −

1

( ) ( )N

i

i

V t V t=

=∑

( ) { }1

max 0, ( )N

i

i

E t V t=

= ∑ { }( ) max ( ), 0E t V t=

{ }( ) max ( ) ,0C t V t H= −

{ }( ) max ( ) ,0C t V t t Hδ= − −0

5

10

15

20

25

30

35

0 365

730

10

95

14

60

18

25

21

90

25

55

29

20

32

85

36

50

40

15

43

80

47

45

51

10

54

75

Expo

sure

(€M

illio

n)

Time (days)

Counterparty PFE

Mean Exposure

95 Percentile

Cond. EPE

Dan Rosen



5


Exposures

DefaultMigration

Recovery

t

0 t

CCR Credit Risk Model Components


PFE (P, S, t)

CounterpartiesCounterparties

Mark-to-FutureValues

Sce

na

rio

sS

ce

na

rios

V (p, S, t)

InstrumentsInstruments

Time

Time

1. Risk Factor Scenario

Generation

Simulation

(Valuation)

3. CP aggregation,

mitigation

(netting, collateral)

4. PFE

Statistics

PFE (P, S, t)

Counterparties

PFE (P, S, t)Mark-to-FutureValues

Sce

na

rio

s

V (p, S, t)

Assets

Time


V (p, S, t)

1.Risk factors

scenariosgeneration

2. Pricing

3. Exposure generation

(netting, collateral...)

4. Exposuresstatistics

PFE (P, S, t)

CounterpartiesCounterparties


Sce

na

rio

sS

ce

na

rios

V (p, S, t)

InstrumentsInstruments

Time

Time

1. Risk Factor Scenario

Generation

Simulation

(Valuation)

3. CP aggregation,

mitigation

(netting, collateral)

4. PFE

Statistics

PFE (P, S, t)

Counterparties


Sce

na

rio

s

PFE (P, S, t)

Counterparties


Sce

na

rio

s

V (p, S, t)

Assets

Time


V (p, S, t)

1.Risk factors

scenariosgeneration

2. Pricing

3. Exposure generation

(netting, collateral...)

4. Exposuresstatistics

CCR and Potential Future Exposures (PFEs)

Maximum Peak

Exposure (T)

Peak Exposure (95%)Effective

Expected

Exposure

Effective

EPE (T)

EPE

(T)

Expected

Exposure

Maximum Peak

Exposure (T)

Peak Exposure (95%)Effective

Expected

Exposure

Effective

EPE (T)

EPE

(T)

Expected

Exposure

Source: de Prisco and Rosen (2005)

Dan Rosen



6


Credit Losses and CVA

� Unilateral CP-level CVA – the bank’s discounted loss due to the CP

default (recovers a fraction R of the exposure )

� CVA obtained by discounting losses and applying the expectation

where

is the risk-neutral discounted expected exposure (EE) at t,

conditional on the CPs default at t

(everything is under the risk-neutral measure)

{ }(1 ) ( ) ( )1

TL R E Dτ τ τ≤= −

0

ˆCVA (1 ) ( ) ( )

T

R dP t e t∗= − ∫

[ ]ˆˆ ( ) E ( ) ( ) E ( ) ( )te t D t E t D t E t tτ∗ = ≡ =


Calculating Exposures and CVA by Simulation

� Banks use Monte Carlo simulation in practice to obtain the distribution of

counterparty-level exposures

� The calculation of CVA and CVA contributions can be easily incorporated to the

Monte Carlo simulation of the counterparty-level exposure

� In general, exposures are simulated separately – implicitly assume that they are

independent of counterparties’ credit quality

� Conditional expectations in the CVA formulae can be replaced by the unconditional

ones

� Dependence of exposure on the counterparty’s credit quality can be

incorporated in the CVA calculation, if the trade values and credit quality of the

bank’s counterparties are simulated jointly (both right/wrong-way risk and

exposure-limiting agreements)

� E.g. using a joint process with stochastic intensities, or a copula methodology as in

Garcia cespedes et al

� Need to make model computationally efficientC

Dan Rosen



7


Calculating CVA – Simulation

( ) ( )

1

1( ) ( ) ( )M j j

k k kjMe t D t E t

=

∗ = ∑

1CVA (1 ) ( )[ ( ) ( )]k k kk

R e t P t P t −∗= − −∑

Unilateral CVA – Independent market and credit risk

0

5

10

15

20

25

30

35

0 365

730

109

5

146

0

182

5

219

0

255

5

292

0

328

5

365

0

401

5

438

0

474

5

511

0

547

5

Exp

osu

re (€

Mill

ion)

Time (days)

Counterparty PFE

Mean Exposure

95 Percentile

Cond. EPE


Analytical CVA (Normal Approx.)

� It is useful in practice to estimate EE, CVA

an CVA contributions quickly outside of the simulation system

� Analytical expression s can be derived for EE and CVA contributions,

for the case when trade values are normally distributes

� Independent market and credit: contributions without collateral

( ) ( ) ( )i i i iV t t t Xµ σ= +

( ) ( )( ) ( ) ( )

( ) ( )

t te t t t

t t

µ µµ σ φ

σ σ

= Φ +

( ) ( )( ) ( )

( ) ( )

( ) ( ) ( )( )

( ) ( ) ( )

t t He t t

t t

t t H t Ht H

t t t

µ µµ

σ σ

µ µ µσ φ φ

σ σ σ

−= Φ − Φ

− −+ − + Φ

[ ]ˆˆ ( ) E ( ) ( ) E ( ) ( )te t D t E t D t E t tτ∗ = ≡ =

Dan Rosen



8


CCR and CVA Capital Charges in Basel III

� Basel III introduces a new charge for MtM losses (CVA – spread risk):

associated with a deterioration in the credit worthiness (greater source of

losses than outright defaults)

� The total CCR charges aim to cover default, migration and spread risks

Total CCR capital = CCR (default) capital + CVA risk capital

� Revision of Internal Model Method (IMM) for measuring exposures based

on Effective EPE with stressed parameters – address wrong-way risk

� Default risk capital charge: greater of

� Portfolio capital charge based on Eff EPE using current market data

� Portfolio capital charge based on Eff EPE using stressed calibration


CCR Capital Carge (Basel II)

� Eff EPE = effective EPE (expected positive exposure)

� Alpha: measures the effect of using deterministic exposures (EPE) instead

of stochastic exposures – ratio of

� EC from a joint simulation of market and credit risk factors

� EC when CP exposures are constant and equal to EPE

� Eff EPE and M (maturity) based on bank’s internal model

� Supervisory alpha = 1.4 – allow for own estimate, subject to floor = 1.2

( ) ( ) ( )∑=

−−

⋅

−

−

−⋅⋅=

N

j

jjj

j

jj

jj PDMMFPDNPDN

NEADLGDCapitalBasel1

11

,1

001.0

ρ

ρ

( )( )EPE

T

LEC

LEC=α

Credit losses – deterministic exposures (EPE)

Credit losses – random exposuresα⋅= jj EPEEffEAD

Dan Rosen



9


CVA Risk Capital Charge

� CVA capital charge calculation depends on bank’s approved methods

for CCR and specific interest rate risk

� Historical simulation, Monte Carlos simulation, etc.

� Full repricing, sensitivities to specific tenors, sensitivities to parallel shifts

(CS01), second order sensitivities, etc.

� Advanced CVA capital charge

� Impact of changes in the counterparties’ credit spreads on the CVAs of all

OTC derivative counterparties, together with eligible CVA hedges

� Using the bank’s VaR model for bonds – restricted to changes in credit

spreads, and does not model the sensitivity of CVA to other factors

� CVA capital charge includes general and specific credit spread risk

� Includes stressed VaR but excludes IRC

� VaR = non-stressed VaR + stressed VaR


CVA VaR: Market Risk Capital and VaR

� From a market risk perspective, CVA is just essentially another price risk

� Standard techniques to measure market VaR

� Full simulation

� Sensitivities

� Very expensive re-pricing

� Simple approximations sought

� Regulatory Basel III focuses only

on spread risk0.00

0.02

0.04

0.06

0.08

0.10

0.12

-140 -100 -60 -20 21 61 101 141

Size of Loss (thousands USD)

Pro

bability

Empirical

Normal

10-day 99% VaR

� Portfolio loss distribution

0

ˆCVA (1 ) ( ) ( )

T

R dP t e t∗= − ∫ [ ]ˆˆ ( ) E ( ) ( ) E ( ) ( )te t D t E t D t E t tτ∗ = ≡ = 0

5

10

15

20

25

30

35

0 365

730

109

5

146

0

182

5

219

0

255

5

292

0

328

5

365

0

401

5

438

0

474

5

511

0

547

5

Expo

sur

e (€

Mill

ion)

Time (days)

Counterparty PFE

Mean Exposure

95 Percentile

Cond. EPE

Dan Rosen



10


CVA Calculation and Basel III Formula

� Regulatory CVA formula

( ) ( ) ( ) ( )[ ]∑ −∗ −⋅⋅−=

k kkkWWR tPtPteRCVA 1ˆ1

� Calibration

� Spreads

� For individual CPs where available, otherwise proxy by rating, industry,

region

� For stressed VaR using the most severe one-year period in the

exposure stressed calibration

� EE

� Non-stressed VaR – EE with current parameter calibration of exposures

� Stressed VaR – EE according to stressed exposure calibration


CVA Risk Capital Charge

� Standardized CVA capital charge

� h = 1 (one-year horizon)

� Bi and Bind denote the hedging positions in

single-name and indices

The level and reasonableness of the standardised CVA risk capital charge, including a

comparison to the advanced approach, is subject to a final impact assessment targeted

for completion in the first quarter of 2011.

Dan Rosen



11


Wrong-Way Risk in Basel III

� Banks must identify exposures that give rise to general WWR

� Stress testing and scenario analyses to identify risk factors positively

correlated with credit worthiness – including severe shocks occurring when

relationships between risk factors have changed

� Monitor general wrong way risk by product, by region, by industry, etc.

� Reports provided to senior management and Board on a regular basis

� Explicit Pillar I charge for identified specific WWR – higher EAD

� Explicit procedure for identifying, monitoring and controlling specific WWR

� Instruments for which there is a legal connection between CP and

underlying issuer and for which specific WWR has been identified are to be

taken out of netting set with other transactions

� CDSs: use expected loss assuming underlying in liquidation (LGD for

swap = 100%)

� Equity, bond, securities financing: EAD = value of transaction under JtD


Analytical CVA and Contributions (Normal Approx.)

Analytical expressions

� Contributions – including wrong-way risk

� Need to modify the approach to obtain the contributions

to the CP EE conditional on the CP defaulting

� For this purpose, we define a Normal copula

� Same results – but instead of the unconditional expectations, standard

deviations and correlations of the trade values, we now use the

conditional ones

( ) ( ) ( )i i i iV t t t Xµ σ= +

1[ ( )]Y P τ−= Φ

2 ˆ1i i i iX bY b X= + −

[ ]1ˆ ( ) E[ ( ) | ] ( ) ( ) ( )i i i i it V t t t t b P tµ τ µ σ −≡ = = + Φ

2ˆ ( ) StDev[ ( ) | ] ( ) 1i i i it V t t t bσ τ σ≡ = = −

2 2

( ) ( )ˆ ( )

(1 )[1 ( )]

i ii

i

t b tt

b t

ρ βρ

β

−=

− −

Dan Rosen



12


CCR Capital and Alpha Methodology (Garcia et al)

� Framework defined by two key components:

� Non-parametric sampling of exposures from pre-computed PFEs (unconditional)

� Direct modelling of codependence of and exposures and systematic credit factors

(non-parametric exposures sampling also from joint market-credit factor scenarios)

� Computationally efficient – fully leverages pre-computed PFE profiles

� Minimizes work during the most computationally intensive step

� Multiple capital calculations – model validation, sensitivities, stress testing

� Model can be applied within general integrated market-credit risk models

� Stress testing

� Wrong-way risk and transparency of counterparty concentrations and factors driving

exposures

� Market-credit correlations – contrast to industry studies, conservative assumptions, or

from a previously estimated market-credit risk model


Wrong-Way Risk – Correlated Market-Credit

General market-credit codependence framework

CP exposures

(Simulated from market factors)

Capital

Copula

Correlation parameters: ρ

Credit factors � defaults

Dan Rosen



13


Copula (X, Z)

Codependence of exposures and credit events

Exposures (market

scenarios)

Syst. factor

X

Credit events

Syst. factor

Z

Idiosyncratic CP factors

WWR Model at the Portfolio Level

ii ZY ερρ −+= 1

( ) ( )

−

−=

−

ρ

ρ

1

1zPDN

NZPD( )XfEi =

Integrated market and

credit portfolio model

Simulated jointly for entire

portfolio


Calculating CVA with Wrong-Way Risk

CVA with WWR

� Analytical formula for EPE | default

� Explicit formula for the joint probability... But very expensive

(large number of bi-Normal distributions)

� Requires numerical evaluation

� Depends on the joint market-credit model and the

correlation parameters 0

5

10

15

20

25

30

35

0 36

5

73

0

10

95

14

60

18

25

21

90

25

55

29

20

32

85

36

50

40

15

43

80

47

45

51

10

54

75

Exp

osure

(€M

illio

n)

Time (days)

Counterparty PFE

Mean Exposure

95 Percentile

Cond. EPE

( ) ( ) ( ) ( )kkjk

j

k k

M

j

j

WWR ttPtEtDRCVA <<⋅⋅⋅−= −∑ ∑ τω 1,1

( ) ( ) ( ) ( )[ ]∑ −∗ −⋅⋅−=

k kkkWWR tPtPteRCVA 1ˆ1

( ) ( ) ( )( )

( ) ( )11,

ˆ−

−∗

−

<<⋅⋅=∑

kk

kkj

k

j

k

M

j

j

ktPtP

ttPtEtDte

τωExpected exposure

conditional on default

Dan Rosen



14


Methods for Calculating CVA with WWR

� Conditioning on the default interval is computationally infeasible.

Requires approximations:

� Fixed expected exposure at default (can be shown to be conservative)

� Linear Approximation:

� When simulating new PD scenarios, calculate CVA using a linear

approximation (in PD) to the REP formula:

CVANew =CVAOld + PDNew − PDOld( )⋅ ∂CVA

∂PDPDOld( )


Calculating CVA with WWR

� Based on explicit computations of the derivatives, the linear

approximation algorithm is quite fast

� One can show that (from the analytical formulas for the derivatives)

that fixing the expected exposure at default will be conservative

(aggressive) in the presence of wrong-way risk (right-way risk).

PD

CVA

Dan Rosen



15


Methods for Calculating CVA with WWR

� Conditioning on the default interval is computationally infeasible

� Conditioning directly on default exactly at time tk is faster :

� Avoids computation of cumulative bivariate normal distributions.

� Still requires significant computation (inverse normal distributions for

each time, counterparty and simulation scenario)

� Accuracy could be a consideration if the time points are far apart

� Example: trapezoid Rule (conditioning on exact default time):

CVA ≈ (1− Ri)ˆ e *(tk ) + ˆ e

*(tk−1)

2⋅

k=1

K

∑ P(tk) − P(tk−1)( )

ˆ e *(tk ) = D j (tk ) ⋅ Ej (tk ) ⋅ P(ω j | τ i = tk)j

∑

CVA i = (1− Ri) ⋅ ˆ e *(t)dPi0

T

∫ (t)

ˆ e *(t) = E[D(t)E (t) | τ = t]


Copula (X, Z)

Codependence of exposures and credit events

Exposures

Syst. factor

X

Credit events

Syst. factor

Z

Idiosyncratic CP factors

Remarks on WWR at the Portfolio Level

� Integrated market and credit portfolio model

� While the CVA is the sum of CP CVAs,

we must use the same model and

correlation parameters to compute

CVA at the portfolio level

� Under a given model (market factor

and correlation levels) not all CPs will

simultaneously have WWR

� Stress testing of individual CPs can

be done with different set of parameters

ii ZY ερρ −+= 1( )XfEi =

( ) ( )

−

−=

−

ρ

ρ

1

1 zPDNNZPD

Dan Rosen



16


Run of April, 2008 (26/06/2008)

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Alpha Total (LTS/LTD)

Single Step 0.91 0.89 0.92 0.97 1.04 1.12 1.21 1.30 1.42

Multi-Steps 12 TS - MS / MS 0.94 0.92 0.95 0.99 1.07 1.15 1.22 1.29 1.39

MS / SS 0.97 0.95 0.97 1.02 1.10 1.18 1.25 1.33 1.43


MS / SS 0.99 0.97 0.99 1.03 1.09 1.16 1.24 1.33 1.42

Alpha Systematic (LSS/LSD)

Single Step 1.06 0.93 0.93 0.96 1.01 1.08 1.18 1.30 1.42


MS / SS 1.10 0.99 0.98 1.00 1.06 1.14 1.23 1.32 1.45


MS / SS 1.09 0.97 0.98 1.01 1.06 1.13 1.21 1.31 1.40

Client Confidential Copyright R2 Financial Technologies 2008

Correlation

Alpha (99.9%): Comparison Single vs Multiple Steps

Alpha (99.9%) as a function of market-credit correlation

Alpha - Total (99.9%)

0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Correlation

Alp

ha

Single Step Multi-Steps 12 TS - MS / MS

Multi-Steps 59 TS - MS / MS Multi-Steps 12 TS - MS / SS

Multi-Steps 59 TS - MS / SS

Alpha - Systematic (99.9%)

0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Correlation

Alp

ha




Case Study

� Sample portfolio: 70 counterparties

� Transactions: FI, FX, equity and credit derivatives (multiple currencies)

� PFE profiles - simulated over 30 years using 2,000 market scenarios and 21

time steps (MtF)

� Calibrated using historical data

– mean reversion for relevant parameters

Run of April, 2008 (26/06/2008)

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1


Base Case 0.91 0.89 0.92 0.97 1.04 1.12 1.21 1.30 1.42

Stressed Exposures 1.00 0.97 0.97 0.99 1.06 1.13 1.26 1.41 1.63


Base Case 1.06 0.93 0.93 0.96 1.01 1.08 1.18 1.30 1.42



Correlation

Alpha (99.9%): Base Case vs. Stressed Exposures



0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Correlation

Alp

ha

Base Case

Stress Exposures


0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Correlation

Alp

ha

Base Case

Stress ExposuresAverage % Vol: 17.71% Average Mean / Vol: 5.65

Total Exposure: 2,176,463 Exposure > No of CP No of Eff CP HI

No Counterparties: 70 1 € 70 32 0.031

Counterparty Mean 95th Percentile 5th Percentile Sigma No CP Exp Zero or Neg: - 100,000 € 69 31 0.032

A48010615 158,032 199,954 120,191 15.19% 1 M € 69 31 0.032

6EAD4TE 154,454 238,365 83,296 30.75% Mean: 31,092

284500046 127,155 152,864 102,277 12.23% Median: 15,947.26

9CRUPAR 98,508 116,262 79,307 11.26% STD: 33,411

90000001 95,401 110,398 80,209 9.58% Kurtosis*: 4.53

Y18500690 94,691 140,345 51,071 28.68% Skew*: 2.21

10048092 84,931 91,878 78,495 4.72% Maximum : 158,032

280580040 79,592 90,347 70,976 7.41% Largest(10): 59,223

6KHBNYC 78,014 82,675 73,494 3.58% Smallest(10): 8,505.34

P40010019 59,223 74,456 44,392 15.45% Minimum: 8,053.13


Statistics for CP Exposure > 1 Euro

Portfolio Size Statistics

Portfolio Exposure Summary: Regulatory Capital

One-Year Equivalent Exposures One-Year Equivalent Mean Exposures

Top 10 Exposures ('000 Euros)

Mean Exposure Statistics ('000s)

0%

100%

200%

300%

400%

500%

600%

700%

800%

% M

ean e

xposure

Counterparty (Top 70 mean exposures)

95% Percentile %5 Percentile Mean exp

0

1

2

3

4

5

6

Fre

quency

Exposure ('000s)

0

10

20

30

40

No o

f Eff

CP

No of CPs

Effective Counterparty Number


Portfolio – Exposures

Average % Vol: 17.71% Average Mean / Vol: 5.65




A48010615 158,032 199,954 120,191 15.19%

6EAD4TE 154,454 238,365 83,296 30.75% Mean: 31,092

284500046 127,155 152,864 102,277 12.23% Median: 15,947.26

9CRUPAR 98,508 116,262 79,307 11.26% STD: 33,411

90000001 95,401 110,398 80,209 9.58% Kurtosis*: 4.53

Y18500690 94,691 140,345 51,071 28.68% Skew*: 2.21

10048092 84,931 91,878 78,495 4.72% Maximum : 158,032

280580040 79,592 90,347 70,976 7.41% Largest(10): 59,223

6KHBNYC 78,014 82,675 73,494 3.58% Smallest(10): 8,505.34

P40010019 59,223 74,456 44,392 15.45% Minimum: 8,053.13

Client Conf idential Copyright R2 Financial Technologies 2010







0%

50%

100%

150%

200%

250%

300%

% M

ean e

xposure


95% Percentile

%5 Percentile

Mean exp

0

1

2

3

4

5

6

Fre

quency

Exposure ('000s)

0

10

20

30

40

No o

f Eff

CP

No of CPs


1

2

3

4

5

6

7

8

9

10

Dan Rosen



17


Counterparty Level Exposures

Run of December, 2009 (18/10/2010 CP level)

A48010615

111

FINANCIALS

BBB+

0.1367%

0.40

0.024

0.0500

0.2149

Actual Exposure 304.64

EPE 158.03

Effective EPE 305.84

Effective Maturity* 1.57

Total Capital 8.51

Market-Credit Corr. 0.25

CVA Unilateral 3.13

CVA Bilateral

CVA Uncorrelated 3.06

Correlation -1 -0.75 -0.50 -0.25 1 0.25 0.50 0.75 1

CVA 2.80 2.87 2.93 3.00 3.06 3.13 3.20 3.26 3.33

Copyright R2 Financial Technologies 2010

Counterparty

Counterparty Report: Exposure and CVA

Counterparty Info

Statistics (€ million)

Sector

No of Instruments

CVA - WWR Stress Test (€ million)

Exposure

CVA

Asset Correlation

PD

Rating

LGD

Hazard Rate

HR Volatility

0

50

100

150

200

250

300

350

400

0 36

5

73

0

10

95

14

60

18

25

21

90

25

55

29

20

32

85

36

50

40

15

43

80

47

45

51

10

54

75

Ex

po

sure

(€

Mil

lio

n)

Time in Days

Exposure

Mean Exposure

Cond. Mean Exposure

95 Percentile

2.60

2.70

2.80

2.90

3.00

3.10

3.20

3.30

3.40

-1 -0.75 -0.50 -0.25 1 0.25 0.50 0.75 1

CV

A (€

Million)

Correlation

CVA Stress Testing6MPEBTQ

11

INDUSTRIALS

BBB-

0.3059%

0.40

0.024

0.0500

0.2149


EPE 35.50

Effective EPE 59.35


Total Capital 3.44

Mkt- Credit Corr. 0.25

CVA Unilateral 1.36

CVA Bilateral



Counterparty Info

Counterparty

No of Instruments

Sector

Rating

Exposure

CVA

PD

LGD

Hazard Rate

HR Volatility

Asset Correlation


0

20

40

60

80

100

120

0 36

5

73

0

10

95

14

60

18

25

21

90

25

55

29

20

32

85

36

50

40

15

43

80

47

45

51

10

54

75

(€M

illi

on

)

Time in Days

Exposure

Mean Exposure

Cond Mean Exposure

95 Percentile


CCR Capital (Independent Market-Credit)

(Simulation: 1M systematic scenarios)

(Numbers in Million) Run of December, 2009 (18/10/2010)

EL Capital Sigma VaR 90% VaR 95% VaR 99% VaR 99.5% VaR 99.9% ES 99.9%

Det - SA 4.42 111.81 11.68 14.91 23.99 59.85 71.54 116.23 150.70

Systematic 4.42 58.59 6.26 10.07 14.87 30.27 38.72 63.01 82.42

Percent 100% 52% 54% 68% 62% 51% 54% 54% 55%

Stoch - SA* 4.42 118.33 12.04 14.59 24.21 57.90 76.62 122.74 157.30

Systematic 4.42 59.18 6.30 10.11 14.93 30.42 38.83 63.60 82.95

Percent 100% 50% 52% 69% 62% 53% 51% 52% 53%

* Correlation = 0 Client Confidential Copyright R2 Financial Technologies 2010

CCR Losses and EC Report

CCR Losses and EC Total (Stochastic) Loss Histogram

OTC Derivatives Credit Capital

-

10

20

30

40

50

60

70

80

90

100

110

120

130

VaR 90% VaR 95% VaR 99% VaR 99.5% VaR 99.9%

VaR

Quantile

Deterministic Deterministic - Syst

Stochastic Stochastic - Sys

0

200

400

600

800

1000

1200

1400

1600

1800

Fre

quency (Thousands)

Dan Rosen



18


CCR Capital WWR – Correlated Market-Credit

� Alpha <1.2� correlations ~ 75% (Basel II)

� Negative correlations � “right-way exposures” (alpha < 1.0)

� Systematic alpha more sensitive to market-credit correlation (no idiosyncratic risk)

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1


VaR Based 0.89 0.92 0.97 1.01 1.06 1.11 1.16 1.22 1.28

Capital Based 0.89 0.92 0.97 1.01 1.06 1.12 1.16 1.22 1.29


VaR Based 0.81 0.85 0.90 0.95 1.01 1.07 1.14 1.22 1.32

Capital Based 0.81 0.84 0.89 0.95 1.01 1.07 1.15 1.23 1.34


Correlation

Wrong-Way Risk CCR Capital Stress Test: Alpha (99.9%)

Alpha Multiplier by Correlation level at 99.9% (Between Exposures and Credit Events)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Alp

ha

Correlation


VaR Based

Capital Based

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Alp

ha

Correlation


VaR Based

Capital Based


CCR Capital WWR – Correlated Market-Credit

“Market factor” correlated to defaults

� Important to understand “why?”

� Portfolio may have right-way or

wrong-way exposures? – may change

over time

� In practice, can find “smile effect” –

some CPs are positively correlated

and some negatively correlated

� Exposure factors include PCs, EL

Total exposure

(TE is generally the most

conservative)

Run of December, 2009 (18/10/2010)

No Scenarios: 2,000 PC Explained Variation

Maximum*: 1,144.17 First 69.60%

Mean*: 885.37 Second 14.95%

Median*: 880.52 Third 5.75%

STD*: 53.41

Minimum*: 752.61

* million Client Conf idential Copyright R2 Financial Technologies 2010

Exposures and Ordered Scenarios

Ordered Scenarios based on Total Exposure

Scenario Statistics Principal Components

700

720

740

760

780

800

820

840

860

880

900

1 151 301 451 601 751 901

Exposure

(m

illions)

Ordered Scenario (First PC)

Total Exposure Moving Avg. Trendline

Dan Rosen



19


CCR Regulatory Capital – Internal Model


Example 2: Stressed Exposures

Run of April, 2008 (26/06/2008)

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1


Base Case 0.91 0.89 0.92 0.97 1.04 1.12 1.21 1.30 1.42



Base Case 1.06 0.93 0.93 0.96 1.01 1.08 1.18 1.30 1.42



Correlation




0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Correlation

Alp

ha

Base Case

Stress Exposures


0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Correlation

Alp

ha

Base Case

Stress Exposures

Dan Rosen



20


Empirical Market-Credit Correlations

Historical time series: market index, implied credit driver and default rates (S&P data)

Correlation between all ratings and

investment only

Default rates = 78%

Implied Credit factors = 70%

Historical Default Rates (1981-2007)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1981 1986 1991 1996 2001 2006

Def Rate ALL (%)

Def Rate INV (%) X 10

EQ Index vs. ALL Grades

-2.000

-1.000

0.000

1.000

2.000

3.000

4.000

1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

Equity Index

Systematic Credit factor

Default Rate (%)

EQ Index vs. Investment Grade

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

1981 1986 1991 1996 2001 2006

Equity Index

Systematic Credit factor

default rate (%) X 10

Correlation between credit factor and

market index

All ratings = 23%

Investment grade = 29% *


� For simplicity, use same exposures as for CCR capital (not risk-neutral)

� Credit model

� Constant risk-neutral HR – per rating (real PDs also per rating and higher

than we have used in the past at BBVA)

� LGDs from spread pricing

� Asset correlation – Basel II

� Base market-credit correlation =25%

� Market risk factors – hazard rates

(and not the spreads)

� Daily volatility returns 3-5%

� Flat market factor correlations 40%

� Stand-alone VaR computed analytically, and simulation for portfolio VaR

Run of April, 2008 (26/06/2008)

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1


Single Step 0.91 0.89 0.92 0.97 1.04 1.12 1.21 1.30 1.42


MS / SS 0.97 0.95 0.97 1.02 1.10 1.18 1.25 1.33 1.43


MS / SS 0.99 0.97 0.99 1.03 1.09 1.16 1.24 1.33 1.42


Single Step 1.06 0.93 0.93 0.96 1.01 1.08 1.18 1.30 1.42


MS / SS 1.10 0.99 0.98 1.00 1.06 1.14 1.23 1.32 1.45


MS / SS 1.09 0.97 0.98 1.01 1.06 1.13 1.21 1.31 1.40


Correlation

Alpha (99.9%): Comparison Single vs Multiple Steps



0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Correlation

Alp

ha





0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Correlation

Alp

ha




CVA – Some Assumptions for CVA

Run of April, 2008 (26/06/2008)

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1


Base Case 0.91 0.89 0.92 0.97 1.04 1.12 1.21 1.30 1.42



Base Case 1.06 0.93 0.93 0.96 1.01 1.08 1.18 1.30 1.42



Correlation




0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Correlation

Alp

ha

Base Case

Stress Exposures


0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Correlation

Alp

ha

Base Case

Stress Exposures

Average % Vol: 17.71% Average Mean / Vol: 5.65




A48010615 158,032 199,954 120,191 15.19% 1 M € 69 31 0.032

6EAD4TE 154,454 238,365 83,296 30.75% Mean: 31,092

284500046 127,155 152,864 102,277 12.23% Median: 15,947.26

9CRUPAR 98,508 116,262 79,307 11.26% STD: 33,411

90000001 95,401 110,398 80,209 9.58% Kurtosis*: 4.53

Y18500690 94,691 140,345 51,071 28.68% Skew*: 2.21

10048092 84,931 91,878 78,495 4.72% Maximum : 158,032

280580040 79,592 90,347 70,976 7.41% Largest(10): 59,223

6KHBNYC 78,014 82,675 73,494 3.58% Smallest(10): 8,505.34

P40010019 59,223 74,456 44,392 15.45% Minimum: 8,053.13








0%

100%

200%

300%

400%

500%

600%

700%

800%

% M

ean e

xposure


95% Percentile %5 Percentile Mean exp

0

1

2

3

4

5

6

Fre

quency

Exposure ('000s)

0

10

20

30

40

No o

f Eff

CP

No of CPs


Dan Rosen



21


Portfolio CVA

Portfolio CVA Summary

No of CPs 70

Mark-to-Market 2,291

Actual Exposure 3,882

EPE 2,176

Unilateral 75.80

Bilateral

CCR Capital 55.53

CVA VaR 13.44

Portfolio Summary (€ million)

CVA

Capital

Total CVA 75.80

Mkt-Credit Corr. 0.25

Mean 1.08

Median 0.39

STD 2.57

Kurtosis* 41.22

Skew* 5.95

Maximum 19.76

Largest 10 1.46

Smallest 10 0.10

Minimum 0.004

CVA Statistics (€ million)

0

5

10

15

20

25

(€M

illion)

Counterparties

CVAby Counterparty

70.00

71.00

72.00

73.00

74.00

75.00

76.00

77.00

78.00

-1 -0.75 -0.50 -0.25 0 0.25 0.50 0.75 1

(€M

illion)

Correlation

CVA Stress Testing

CVA

-1 -0.75 -0.50 -0.25 0 0.25 0.50 0.75 1

CVA 73.04 73.60 74.13 74.68 75.23 75.80 76.38 76.96 77.54


Correlation

Project

Finance,

22.86

Financials,

39.69

Internationa

l Corporates,

41.18

Central

Bank, 0.34

Large

Domestic

Corporates,

8.48

Other

Corporates,

6.00

CVA Concentration


Counterparty Exposure, CVA, and WWR

Run of December, 2009 (18/10/2010 CP level)

6MPEBTQ

11

INDUSTRIALS

BBB-

0.3059%

0.40

0.024

0.0500

0.2149


EPE 35.50

Effective EPE 59.35


Total Capital 3.44

Mkt- Credit Corr. 0.25

CVA Unilateral 1.36

CVA Bilateral


Correlation -1 -0.75 -0.50 -0.25 1 0.25 0.50 0.75 1

CVA 1.08 1.14 1.20 1.26 1.31 1.36 1.41 1.45 1.48


Counterparty Report: Exposure and CVA

Counterparty Info

Counterparty

No of Instruments

Sector

Rating

Exposure

CVA


PD

LGD

Hazard Rate

HR Volatility

Asset Correlation


0

20

40

60

80

100

120

0 36

5

73

0

10

95

14

60

18

25

21

90

25

55

29

20

32

85

36

50

40

15

43

80

47

45

51

10

54

75

(€M

illi

on

)

Time in Days

Exposure

Mean Exposure

Cond Mean Exposure

95 Percentile

1.00

1.10

1.20

1.30

1.40

1.50

1.60

-1 -0.75 -0.50 -0.25 1 0.25 0.50 0.75 1

(CVA

€M

illion)

Correlation

CVA Stress Testing

Dan Rosen



22


CVA Market VaR


Base Case Results

� Independent market and credit risk.

0.00E+00

1.00E+06

2.00E+06

3.00E+06

4.00E+06

5.00E+06

6.00E+06

7.00E+06

VaR 0.90 VaR0.95 VaR 0.99 VaR 0.995 VaR 0.999 CVaR 0.999

Fixed ExpEAD

Full Internal Model (Trap)

Linear Approximation

Dan Rosen



23


Stress Testing WWR

� 1-Day VaR at 99% confidence level, for various assumed levels of

market-credit correlation.

4.30E+06

4.40E+06

4.50E+06

4.60E+06

4.70E+06

4.80E+06

4.90E+06

5.00E+06

5.10E+06

10.750.50.250-0.25-0.5-0.751

Fixed EDPE Full Internal Model Linear Approximation


Capital Charges

� Standardized Capital Charge: 184.56m

� Internal model charges (millions) for different correlation levels:

Capital = 3 ⋅ 10 ⋅ VaR1 day,0.99 +SVaR1 day,0.99( )Correlation -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Base Case 87.48 88.11 88.76 89.43 90.13 90.85 91.58 92.32 93.08

Stress Case 109.35 110.14 110.95 111.78 112.66 113.56 114.47 115.41 116.35

Base Case : SVaR = VaR

Stress Case : SVaR = 1.5 ×VaR

Dan Rosen



24


Concluding Remarks


CVA and Wrong Way Risk

� CVA must be priced for derivatives portfolios – the crisis showed its

practical role and impact

� Conceptually simple, but complex problem in practice

� Consequences now reflected in accounting and capital rules

� We are just starting to understand its modelling and its financial, regulatory

and management requirementsand impacts

� Wrong-way risk is important

� Portfolio effects may reduce its systematic impacts (general WWR)

� Specific WWR needs to be analyzed with stress testing and individual

counterparty analysis

� Basel III regulation is not yet fully aligned with some of the best

practices, but will likely move there over time

Dan Rosen



25


CVA and Model Risk

� CVA is pricing – do we want to achieve “pricing-level accuracy”

� Marginal contributions, real time, securitization of CVAC

� ButC how accurate can weC. Or will we do it in the near future?

� This is probably the Most complex “instrument” we have ever priced!

� Complex risks

� Modelling CCR and CVA requires integrated market-credit models:

� 10s or 100s of market factors driving exposures over very long horizons

� Wrong-way risk

� Credit risk of portfolios of very complex and varied derivatives

� Mitigation: netting, collateral, margin callsC.

� We cant price very well yet synthetic CDOs!

� Simple portfolios, standardized instruments, 125 creditsC.


Final Lessons

Model risk frameworkC

� Acknowledge the “heroic” assumptions in our models and the

limitation of the information which we can reasonably extract from

the market and quoted prices

� Effectively incorporate fundamental credit information, historical data

and expert judgment into the valuation process

� Develop explicit model risk and stress testing approaches which can

help us understand better

� The behaviour of instruments and portfolios,

� “Knightean” uncertainties we could be facing.

Dan Rosen



26


Bio – Dan Rosen

Dan Rosen is the CEO and co-founder of R2 Financial Technologies and an adjunct professor of

Mathematical Finance at the University of Toronto.

Dr. Rosen lectures extensively around the world on financial engineering, enterprise risk and capital

management, credit risk and market risk. He has authored several patents and numerous papers on

quantitative methods in risk management, applied mathematics, operations research, and has coauthored

two books and various chapters in risk management books (including two chapters of PRMIA’s Professional

Risk Manger Handbook). In addition, Dr. Rosen is a member of the Industrial Advisory Boards of the Fields

Institute and the Center for Advanced Financial Studies at the University of Waterloo; the Academic Advisory

Board of Fitch; the Advisory Board of the IAFE; a founder former Regional Director and current steering

committee member of PRMIA in Toronto; and a member of the Oliver Wyman Institute. He is also one of the

founders of RiskLab, an international network of research centers in Financial Engineering and Risk

Management. Dr. Rosen was inducted in 2010 as a fellow of the Fields Institute for Research in Mathematical

Sciences, for his “outstanding contributions to the Fields Institute, its programs, and to the Canadian

mathematical community”.

Prior to co-founding R2 , Dr. Rosen had a successful ten-year career at Algorithmics Inc., where he held

senior management roles in research and financial engineering, strategy and business development, and

product marketing. In these roles, he was responsible for setting strategic direction, new initiatives and

alliances; the design and positioning of credit risk and capital management solutions, market risk tools,

operational risk, and advanced simulation and optimization, as well as their application to industrial settings.

He holds an M.A.Sc. and Ph.D. in Chemical Engineering from the University of Toronto.


Selected Recent Publications

� Rosen D. , 2010, Rethinking Valuations, in Rethinking Risk Measurement (Ed. K. Boecker),

RISK Publications

� Rosen D. and Saunders D. 2011, Structured Finance Valuation and Risk Management with

Implied factor Models, in Advances in Credit Derivatives, Bloomberg Publications

� Nedeljkovic, J., Rosen D. and Saunders D. 2010, Pricing and Hedging CLOs with Implied

Factor Models, Journal of Credit Risk, fall issue

� Rosen D. and Saunders D. 2009, Valuing CDOs of Bespoke Portfolios with Implied Multi-

Factor Models, Journal of Credit Risk, Fall Issue

� Rosen D. and Saunders D. 2011, Wrong-Way CVA and CVA VaR, working paper

� Pykhtin M., Rosen D. 2010, Pricing Counterparty Risk at the Trade Level and CVA

Allocations, Federal Reserve Research Paper Series (Journal of Credit Risk)

� Rosen D. and Saunders D. 2010, Computing and Stress Testing Counterparty Credit Risk

Capital, in Counterparty Credit Risk Modelling, (ed. E. Canabarro), Risk Books

� Garcia Cespedes J. C., de Juan Herrero J. A., Rosen D., Saunders D. 2010, Effective

modelling of Counterparty Credit risk Capital and Alpha, Journal of Risk Model validation

� De Prisco B., Rosen D., 2005, Modelling Stochastic Counterparty Credit Exposures for

Derivatives Portfolios, Counterparty Credit Risk (M. Pykhtin, Editor), Risk Books

Dan Rosen



27


Selected Recent Publications

� Rosen D. and Saunders D. 2010, Economic Capital, in Encyclopedia of Quantitative Finance

� Rosen D. and Saunders D. 2010, Risk Contributions and Economic Credit Capital Allocation,

in Advances in Credit Derivatives, Bloomberg Publications (forthcoming)

� Rosen D. and Saunders D. 2010, Measuring Capital Contributions of Systemic Factors in

Credit Portfolios, Journal of Banking and Finance

� Rosen D. and Saunders D. 2009, Analytical Methods for Hedging Systematic Credit Risk

with Linear Factor Portfolios, Journal of Economic Dynamics and Control

� Mausser H. and Rosen D. 2007, Economic Credit Capital Allocation and Risk Contributions,

in Handbook of Financial Engineering (J. Birge and V. Linetsky Editors)

� Garcia Cespedes J. C., Keinin A., de Juan Herrero J. A. and Rosen D. 2006, A Simple

Multi-Factor “Factor Adjustment” for Credit Capital Diversification, Special issue on Risk

Concentrations in Credit Portofolios (M. gordy, editor) Journal of Credit Risk, Fall 2006

� Rosen D., 2004, Credit Risk Capital Calculation, in Professional Risk Manager (PRM)

Handbook, Chapter III.B5, PRMIA Publications

� Aziz A., Rosen D., 2004, Capital Allocation and RAPM, in Professional Risk Manager (PRM)

Handbook, Chapter III.0, PRMIA Publications

© 2006-2011 R2 Financial Technologies

www.R2-financial.com

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