cva, basel iii and wrong-way · pdf filecva, basel iii and wrong-way risk dan rosen...
TRANSCRIPT
Dan Rosen
R2 Financial Technologies
RiskLab Madrid, May 2011
1
© 2006-2011 R2 Financial Technologies
CVA, Basel III and
Wrong-Way Risk
Dan Rosen
R2 Financial Technologies
© 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
R2 Financial Technologies
RiskLab Madrid, May 2011
2
© 2006-2011 R2 Financial Technologies 9
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
© 2006-2011 R2 Financial Technologies 12
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
R2 Financial Technologies
RiskLab Madrid, May 2011
3
© 2006-2011 R2 Financial Technologies 13
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
R2 Financial Technologies
RiskLab Madrid, May 2011
4
© 2006-2011 R2 Financial Technologies 17
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
© 2006-2011 R2 Financial Technologies 18
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
R2 Financial Technologies
RiskLab Madrid, May 2011
5
© 2006-2011 R2 Financial Technologies 19
Exposures
DefaultMigration
Recovery
t
0 t
CCR Credit Risk Model Components
© 2006-2011 R2 Financial Technologies 20
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
Mark-to-FutureValues
V (p, S, t)
1.Risk factors
scenariosgeneration
2. Pricing
3. Exposure generation
(netting, collateral...)
4. Exposuresstatistics
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
PFE (P, S, t)
Counterparties
PFE (P, S, t)Mark-to-FutureValues
Sce
na
rio
s
V (p, S, t)
Assets
Time
Mark-to-FutureValues
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
R2 Financial Technologies
RiskLab Madrid, May 2011
6
© 2006-2011 R2 Financial Technologies 21
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∗ = ≡ =
© 2006-2011 R2 Financial Technologies 22
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
R2 Financial Technologies
RiskLab Madrid, May 2011
7
© 2006-2011 R2 Financial Technologies 23
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
© 2006-2011 R2 Financial Technologies 24
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
R2 Financial Technologies
RiskLab Madrid, May 2011
8
© 2006-2011 R2 Financial Technologies 28
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
© 2006-2011 R2 Financial Technologies 32
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
R2 Financial Technologies
RiskLab Madrid, May 2011
9
© 2006-2011 R2 Financial Technologies 33
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
© 2006-2011 R2 Financial Technologies 34
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
R2 Financial Technologies
RiskLab Madrid, May 2011
10
© 2006-2011 R2 Financial Technologies 35
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
© 2006-2011 R2 Financial Technologies 36
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
R2 Financial Technologies
RiskLab Madrid, May 2011
11
© 2006-2011 R2 Financial Technologies 38
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
© 2006-2011 R2 Financial Technologies 39
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
R2 Financial Technologies
RiskLab Madrid, May 2011
12
© 2006-2011 R2 Financial Technologies 40
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
© 2006-2011 R2 Financial Technologies 41
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
R2 Financial Technologies
RiskLab Madrid, May 2011
13
© 2006-2011 R2 Financial Technologies 42
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
© 2006-2011 R2 Financial Technologies 45
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
R2 Financial Technologies
RiskLab Madrid, May 2011
14
© 2006-2011 R2 Financial Technologies 46
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( )
© 2006-2011 R2 Financial Technologies 47
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
R2 Financial Technologies
RiskLab Madrid, May 2011
15
© 2006-2011 R2 Financial Technologies 48
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]
© 2006-2011 R2 Financial Technologies 49
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
R2 Financial Technologies
RiskLab Madrid, May 2011
16
© 2006-2011 R2 Financial Technologies 51
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
Multi-Steps 59 TS - MS / MS 0.96 0.94 0.96 1.00 1.06 1.13 1.21 1.29 1.38
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
Multi-Steps 12 TS - MS / MS 1.03 0.94 0.93 0.94 1.00 1.08 1.16 1.24 1.37
MS / SS 1.10 0.99 0.98 1.00 1.06 1.14 1.23 1.32 1.45
Multi-Steps 59 TS - MS / MS 1.04 0.93 0.94 0.96 1.01 1.08 1.16 1.26 1.34
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
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
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
Alpha Total (LTS/LTD)
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
Alpha Systematic (LSS/LSD)
Base Case 1.06 0.93 0.93 0.96 1.01 1.08 1.18 1.30 1.42
Stressed Exposures 1.05 1.00 0.96 0.97 1.02 1.11 1.25 1.44 1.74
Client Confidential Copyright R2 Financial Technologies 2008
Correlation
Alpha (99.9%): Base Case vs. Stressed Exposures
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
1.60
1.70
-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1
Correlation
Alp
ha
Base Case
Stress Exposures
Alpha - Systematic (99.9%)
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
Client Confidential Copyright R2 Financial Technologies 2007
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
© 2006-2011 R2 Financial Technologies 52
Portfolio – Exposures
Average % 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%
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
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%
50%
100%
150%
200%
250%
300%
% 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
1
2
3
4
5
6
7
8
9
10
Dan Rosen
R2 Financial Technologies
RiskLab Madrid, May 2011
17
© 2006-2011 R2 Financial Technologies 53
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
Actual Exposure 42.88
EPE 35.50
Effective EPE 59.35
Effective Maturity* 2.81
Total Capital 3.44
Mkt- Credit Corr. 0.25
CVA Unilateral 1.36
CVA Bilateral
CVA Uncorrelated 1.31
Copyright R2 Financial Technologies 2010
Counterparty Info
Counterparty
No of Instruments
Sector
Rating
Exposure
CVA
PD
LGD
Hazard Rate
HR Volatility
Asset Correlation
Statistics (€ million)
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
© 2006-2011 R2 Financial Technologies 54
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
R2 Financial Technologies
RiskLab Madrid, May 2011
18
© 2006-2011 R2 Financial Technologies 55
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
Alpha Total (LTS/LTD)
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
Alpha Systematic (LSS/LSD)
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
Client Confidential Copyright R2 Financial Technologies 2010
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
Alpha - Total (99.9%)
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
Alpha - Systematic (99.9%)
VaR Based
Capital Based
© 2006-2011 R2 Financial Technologies 57
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
R2 Financial Technologies
RiskLab Madrid, May 2011
19
© 2006-2011 R2 Financial Technologies 58
CCR Regulatory Capital – Internal Model
© 2006-2011 R2 Financial Technologies 59
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
Alpha Total (LTS/LTD)
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
Alpha Systematic (LSS/LSD)
Base Case 1.06 0.93 0.93 0.96 1.01 1.08 1.18 1.30 1.42
Stressed Exposures 1.05 1.00 0.96 0.97 1.02 1.11 1.25 1.44 1.74
Client Confidential Copyright R2 Financial Technologies 2008
Correlation
Alpha (99.9%): Base Case vs. Stressed Exposures
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
1.60
1.70
-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1
Correlation
Alp
ha
Base Case
Stress Exposures
Alpha - Systematic (99.9%)
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
R2 Financial Technologies
RiskLab Madrid, May 2011
20
© 2006-2011 R2 Financial Technologies 66
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% *
© 2006-2011 R2 Financial Technologies 72
� 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
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
Multi-Steps 59 TS - MS / MS 0.96 0.94 0.96 1.00 1.06 1.13 1.21 1.29 1.38
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
Multi-Steps 12 TS - MS / MS 1.03 0.94 0.93 0.94 1.00 1.08 1.16 1.24 1.37
MS / SS 1.10 0.99 0.98 1.00 1.06 1.14 1.23 1.32 1.45
Multi-Steps 59 TS - MS / MS 1.04 0.93 0.94 0.96 1.01 1.08 1.16 1.26 1.34
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
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
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
Alpha Total (LTS/LTD)
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
Alpha Systematic (LSS/LSD)
Base Case 1.06 0.93 0.93 0.96 1.01 1.08 1.18 1.30 1.42
Stressed Exposures 1.05 1.00 0.96 0.97 1.02 1.11 1.25 1.44 1.74
Client Confidential Copyright R2 Financial Technologies 2008
Correlation
Alpha (99.9%): Base Case vs. Stressed Exposures
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
1.60
1.70
-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1
Correlation
Alp
ha
Base Case
Stress Exposures
Alpha - Systematic (99.9%)
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
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
Client Confidential Copyright R2 Financial Technologies 2007
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
Dan Rosen
R2 Financial Technologies
RiskLab Madrid, May 2011
21
© 2006-2011 R2 Financial Technologies 73
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
CVA - WWR Stress Test (€ million)
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
© 2006-2011 R2 Financial Technologies 74
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
Actual Exposure 42.88
EPE 35.50
Effective EPE 59.35
Effective Maturity* 2.81
Total Capital 3.44
Mkt- Credit Corr. 0.25
CVA Unilateral 1.36
CVA Bilateral
CVA Uncorrelated 1.31
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
Copyright R2 Financial Technologies 2010
Counterparty Report: Exposure and CVA
Counterparty Info
Counterparty
No of Instruments
Sector
Rating
Exposure
CVA
CVA - WWR Stress Test (€ million)
PD
LGD
Hazard Rate
HR Volatility
Asset Correlation
Statistics (€ million)
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
R2 Financial Technologies
RiskLab Madrid, May 2011
22
© 2006-2011 R2 Financial Technologies 77
CVA Market VaR
© 2006-2011 R2 Financial Technologies 79
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
R2 Financial Technologies
RiskLab Madrid, May 2011
23
© 2006-2011 R2 Financial Technologies 80
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
© 2006-2011 R2 Financial Technologies 81
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
R2 Financial Technologies
RiskLab Madrid, May 2011
24
© 2006-2011 R2 Financial Technologies 83
Concluding Remarks
© 2006-2011 R2 Financial Technologies 84
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
R2 Financial Technologies
RiskLab Madrid, May 2011
25
© 2006-2011 R2 Financial Technologies 85
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.
© 2006-2011 R2 Financial Technologies 90
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
R2 Financial Technologies
RiskLab Madrid, May 2011
26
© 2006-2011 R2 Financial Technologies 93
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.
© 2006-2011 R2 Financial Technologies 94
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
R2 Financial Technologies
RiskLab Madrid, May 2011
27
© 2006-2011 R2 Financial Technologies 95
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