Financial institutions which apply for an IMM waiver under Basel III need to fullfill a broad set of requirements. We present the quantitative, organizational and operational implications and provide some hand-on guidance how to fulfill the regulatory requirements.
1. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Counterparty Credit Risk and CVA under Basel III
Patrick H¨aner
H¨aner Consulting Berlin
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2. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Outline
1 Credit Risk Measures
2 Credit Risk Mitigation
3 Model Implementation
4 Back Testing
5 Regulatory Requirements and Basel III
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3. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Motivation
Definition (Credit Risk)
Risk to incur a loss due to counterparty’s default or loss of
creditworthiness.
Credit risk measures are introduced to
Quantify the credit risk
Help Mitigating that risk
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4. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Motivation
Risk measures are estimated by Credit Risk Models
Impact of Credit Risk Model
Trading activity limits set by PE
Capital charges regularity capital dependent of EEPE
P&L EE enters CVA/DVA
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5. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Motivation
Challenges
Measure Asking the right question
Model Picking right model to estimate measure
Act Make descisions based on measurements
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6. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Overview
1 Credit Risk Measures
2 Credit Risk Mitigation
3 Model Implementation
4 Back Testing
5 Regulatory Requirements and Basel III
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7. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Likeliness vs Severity of Credit Events
Categories
Which dimensions to consider?
Severity How much will we lose?
Likeliness What’s the chance that we lose?
Granularity What does the measure refer to?
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8. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Granularity of Measure
Based on Defaults
All Counterparties
Single Counterparty
Other Aggregations
Global/macro economic
Sector, country
Trade
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9. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Exposure and Recovery
How to measure severity? Need to value trade:
Definition (Exposure at Default)
EAD(t) = max 0, p(t)|τ = t
τ : time at which CP defaults
Definition (Loss Given Default)
Loss at time t = LGD(t)EAD(t)
Definition (Recovery)
R(t) = 1 − LGD(t)
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10. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Severity
Valuation Approaches
Accrual Banking book; rarely adjust; illiquid assets
Mark to market Trading book; frequently adjusted; traded assets
Mark to model Trading book; frequently adjusted; complex
structures
Example
CreditRiskMeasures.xlsx
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11. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Severity
Accrual
Loan to Acme Ltd
value is face value
maximal loss is notional of loan
Mark to market
Buy bond of Acme Ltd; assume liquid market
value is mark to market of bond
value lower than in risk-free valuation
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12. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Severity
Mark to model
Exotic interest rate swap with Acme Ltd. What is the value
risk free: assuming Acme may never default
risky: Acme may default
risky with own risk: Acme and we may default
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13. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Forward Looking Measures
Assess exposure in future → model how state of the world evolves
Deterministic Evolution Scenario Analysis, Stress testing
Stochastic Evolution Model for risk factors
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14. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Scenario Analysis/Stress Test
Meanings of Stress
change model parameters →
pick a single path → degenerate measure (Dirac measure)
Unified handling by Measure Transforms
Stochstic Process
(Langevin Equation)
Dual Model Representations
Probabiliy Measure
(Path Integrals)
: t ! x(t) Path
µ( ) ⇠ e S( )
S( ) ⌘
Z ⌧
0
L(x, ˙x) Action
L(x, ˙x) : Lagrangian
˙x = f(x) + ⇠
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15. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Types of Stress Tests
Approaches
give economic scenario
given loss (inverse stress)
Inverse stresses
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16. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Statistical Measures
Single Netting Set
Definition (Potential Future Exposure)
PFE(t) = max 0, p(t)|τ = t
τ : time at which CP defaults
Definition (Expected Exposure (EE))
EE(t) = E[PFE]
Definition (Expected Positive Exposure)
EPE(T) =
1
T
T
0
EE(t) dt
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17. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Regulatory Measures
Definition (Effective Expected Exposure (EEE))
Maximum of EPE and past EEE: never decreasing.
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18. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Statistical Measures
Multiple Netting Set
Definition (Losses across Netting Sets)
L(t) =
a
χτa≤tLGDa max 0, pa(τa)
a : Identifier of netting set
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19. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Portfolio Measures
Meaningful risk measures for portfolios
Definition (Coherent Risk Measure)
Risk measure ρ: for portolio X:
Normalization ρ(∅) = 0 empty portfolio has no risk
Monotonicity X1 ≤ X2 → ρ(X1) ≥ ρ(X2)
Sub-additivity ρ(X1 + X2) ≤ ρ(X1) + ρ(X2) diversification/netting
Homogeneity ρ(αX) = αρ(X) α > 0
Translation invariance ρ(X + a) = ρ(X) − a adding cash a reduces
risk
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20. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Portfolio Measures
Quantile
q% quantile: value, for which q% of outcomes are smaller/larger.
Quantiles are not coherent measures.
Expected Shortfall
Expected loss conditioned on the loss being larget than X. The
Expected Shortfall (Mean Excess Loss) is a coherent measure.
Example
PortfolioMeasure.xlsx
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21. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Likeliness of Default
Example
LikelihoodExperiment.xlsx
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22. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
What does probability mean?
Average observers Implied ensemble Genuine ensemble
Probability and Measurement
Need to define
Ensemble
Measurement process
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23. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Examples
Genuine Ensemble
Mathematics
Physics: Identically prepared experiment
Average observers
Consensus of observers:
Market prices
Betting quota
Implied Ensemble
Equivalence classes:
Names with same rating
Price returns in different time windows
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24. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Measures for Probability of Default
Definition (Survival/Default Probability, Default Intensity)
Let τ be time of default
S(t) = p(τ > t)
S : survival probability
S(t) = e−λ(t)t
λ : term default intensity
D(t) = 1 − S(t)
D : default probability
Note: D is a CDF!
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25. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Forward Intensity
Forward default intensity
Probability d(t) of defaulting between t and dt:
d(t) =
dD(t)
dt
(1)
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26. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Estimating Probability of Default
Estimating λ
Credit Rating Typically using historical data
Market Prices Current credit spreads from bonds or CDS
Implied Default Intensity
Let s(t) be a credit spread
s(t) = (1 − R)λ(t)
R : recovery rate
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27. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Unifiying Severity and Frequency Measures
High Severity/Low Frequency vs. Low Severity High Frequency
How to compare
Single large deal with good counterparty
Set of small deals with bad counterparties
Answer
Pricing including credit risk allows comparing!
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28. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Approaches
Top-down vs Bottom-up
Top-down Pricing from first principles
Bottom-up Calculate price correction from building blocks:
Exposure (EE) and PE, LGD
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29. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Bottom-Up approach
Assumptions
Risk-free prices known
Calculate EE
Estimate PE, LGD
Calculate correction to risk-free price
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30. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Measuring the Corrections
Riskiness of counterparty reduces the price:
Definition (CVA)
Risky price p∗
A as seen from counterparty A with counterparty B:
p∗
= p − CVAB
p : risk-free price
CVAB : Credit Valuation Adjustment for counterparty B
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31. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Measuring the Corrections
Does credit risk of counterparty A also affect price?
Definition (DVA)
Price pA as seen from counterparty A with counterparty B:
p∗ = p − CVAB + DVAA
p : risk-free price
DVAA : Debit Valuation Adjustment for counterparty A
DVA increases the price.
Accounting vs. Regulatory
DVA must be used for P&L but not for regulatory capital.
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32. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Regulatory CVA
BCBS 189, paragraph 89:
Regulatory CVA
Similar to regulatory capital charge for default:
Assumes independence of exposure and default process.
CVA =
T
0
(1 − R)Df (t)EE(t)d(t) dt
where d is the default probability from equation (1),Df discount
factor
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33. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
CVA
Example
CVA.xlsx
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34. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Regulatory CVA
Regulatory vs Trading CVA
Regulatory Historic measure for EE, implied for PD
Trading Both EE and PD in implied measure
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35. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Pricing for Portfolio of Netting Sets
As for single netting sets: pricing combines severity and likeliness.
Requires knowing
prices of individual netting sets at default
probability of default P(χτ1≤t1 , χτ2≤t2 , . . . , χτN ≤tN
)
Additional useful quantity: in terms of total losses:
Definition (Loss distribution)
L(l, t) = P(L(t) ≥ l)
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36. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Types of Measures
Severity
Frequency
Pricing Credit Risk
Granularity of Measure in Regulatory Context
Metrics used for Regulatory Purposes
Focus on measures for individual counterparties. No proper
modelling of collective losses required.
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37. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Overview
1 Credit Risk Measures
2 Credit Risk Mitigation
3 Model Implementation
4 Back Testing
5 Regulatory Requirements and Basel III
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38. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Mitigate
realized losses from default of counterparty
P&L fluctuation from change in credit spreads of counterparty
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39. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Netting Agreement
Definition (Netting Set)
For all trades within a netting set long and short positions may be
netted. The exposure is reduced due to
max
i
pi , 0 ≤
i
max pi , 0
Example
A short and a long position worth 10 Mios with counterparty acme
yield an exposure of 10 Mio w/o netting agreement and 0 with.
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40. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
CSA
ISDA Credit Support Annex (CSA) : collateral that must be
delivered between the parties
Definition
the Secured Party’s Exposure plus
the aggregate of all Independent Amounts applicable to the
Pledgor, minus
all Independent Amounts applicable to the Secured Party, if
any, minus
the Pledgor’s Threshold
The Secured Party is the party that is holding collateral; the
Pledgor is the party that has delivered collateral
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41. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
CSA
MtM
0
IA(A)
IA(B)
T(B)
Collateral held
At default losses offset by collateral
Rebalancing needed
Collateral price may move
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42. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Re-hypothecation
Counterparty may repo the collateral → when defaulting
collateral gone
Forbidding may increase costs
Transferring collateral management to central counterparty
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43. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Gap Risk
Collateral process is discreet, e.g. daily.
position value
collateral value
may move
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44. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Central Counterparties
Counterparty to every trade
Multiateral netting → reducing risk
Potentially mutualizing credit losses among participants
Increased transparency
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45. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Spread vs Default Risk
Definition (Default Risk)
Risk of changes in price p induced by hitting default time τ:
t → τ
p → p + ∆τ p
∆τ p = (R − 1)p
Definition (Spread Risk)
Risk of changes in price p induced by changes of counterparty
credit spread s:
s → s + ∆s
p → p + ∆sp
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46. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Spread vs Default Risk
Hedging
Loans
Default Risk Single name CDS or short bond
Spread Risk MtM accounting Single name CDS/bond, index or
proxy
Accrual accounting N/A
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47. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Hedging Instruments and Strategies
Static Hedges
Insurance for replacement of some asset on default:
Bond hedged by Credit Default Swap
Swap, CCYSwap Contingent Credit Default Swap (CCDS)
Netting sets insurance from CVA desk
Dynamic Hedges
Hedging default or spread risk: use instruments with price q. First
order:
Default ∆τ q = −∆τ p
Spread ∆sq = −∆sp
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48. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Cross Counterparty Hedges
Analogy Hedging Credit Risk for Bonds
Granularity Underlying Hedge
Single
Bond CDS
Netting Set CCDS
Portfolio
Bonds CDO
Netting Sest ”CCDO”
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49. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Securitisation
Hedging losses across netting sets:
CDO on CVA
bond↔exposure of netting set
tranches like CDO
Issues
notional of ”bond”s fluctuating
”bond” not transparent
who rates the ”bond”s and the CDO?
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50. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Systemic Risks
In distressed market environment correlations increase → less
diversification.
Macro hedges
Buying insurance won’t work (→ Monolines)
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51. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Limit Monitoring
Limits
Manage size of exposure per
counterparty
industry
region
Limits may typically expressed in terms of
Quantiles E.g. 95% quantile: 5% of losses are larger than that
quantile
Mean Expess Loss E.g. Average of the 5% biggest losses
A term structure of limits may be reflect risk appetite.
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52. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Mutualization
Central Counterparties
Losses distributed among participants → diversification
Systemic risks?
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53. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Internal CVA Desk
Trading CVA
Trading desk within the firm:
Sells default protection to other desks
Hedges counterparty credit spread risk
Costs/Benefits
High build and run costs
⊕ More accurate metrics for credit risk
⊕ Increased transparency on costs
! Hegdges bought from CVA desk yield no regulatory capital
relief
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54. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Internal CVA Desk
Operating Model
Mandate
Depends on rationale for setting up
Risk management or front office function?
Responsibility often changes with sophistication . . .
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55. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Internal CVA Desk
Responsibility
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56. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Internal CVA Desk
Profit Centre vs Service Centre
Approach Advantages Disadvantages
Profit Centre
P&L enable
performance to be
measured
Easy to align
renumeration with
success and design
incentives
Potential conflicts of
iterest
May lead to overactive
position taking
Requires more
infrastructure
Service Centre
Requires less infrastructure
Less market activity
Less internal politics
Qualitative focus can lead
to broader focus
Difficult to measure
performance
Harder to retain and
incentivise appropriate staff
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57. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Internal CVA Desk
Methodology
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58. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Internal CVA Desk
Methodology
Risk vs pricing models: Use same models?
Pricing model Fit market prices
Risk model Predict future outcomes
Bilateral vs unilateral calculation: Include products w/o PFE
(e.g. notes)
Define proxy spreads when no liquid CDS market
Wrong way risk
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59. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Internal CVA Desk
Infrastructure
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60. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Internal CVA Desk
System Requirements
Basic requirements same as Monte Carlo Credit Risk system for
Risk/Regulatory capital
Additional Requirements
Calulation of sensitivities
Include wrong way risk in price
Simulate in risk neutral calibration
Integration with FO infrastructure and processes
Attribution ability
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61. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Netting Agreements
Collateralization
Hedging
Limiting
Internal CVA Desk
Infrastructure
Pre-trade approval/marginal CVA/DVA calculation:
Needs to be fast
Avoid recalculating whole portfolio: add new trades in
scenario-consitent manner
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62. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Overview
1 Credit Risk Measures
2 Credit Risk Mitigation
3 Model Implementation
4 Back Testing
5 Regulatory Requirements and Basel III
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63. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Building Blocks
Model Building Process
Business Analysis Materiality, specification
Model choice Find adequate model
Software implementation Develop and roll out
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64. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Materiality
What to Model?
Which risk factors material for current portfolio?
How can we assess materiality without exposure model in place?
Approach
Simple estimation of exposure assuming
future portfolio prices normally distributed
estimation of first two moments
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65. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Gaussian Approximation
Need to estimate E[p(T)], E[p2(Ti )] at some future times T:
Performing Taylor expansion for price p around expected risk
factor:
p(x(T), T) ≈ p(x0(T), T) +
i
∂p(x0(T), T)
∂xi
∆xi (T)
+
1
2
ij
∂2p(x0(T), T)
∂xi ∂xj
∆xi (T)∆xj (T)
x0(T) ≡ E[x(T)]
∆xi (T) ≡ xi (T) − x0,i (T)
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66. Credit Risk Measures
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Model Implementation
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Analysis
Models
Software Development
Gaussian Approximation
The expectation value M of the price is hence
M(T) ≈ p(x0(T), T) +
1
2
ij
γij (T)Ωij (T)
M(T) ≡ E[p(x(T), T)]
γij (T) ≡
∂2p(x0(T), T)
∂xi ∂xj
Ωij (T) ≡ E[∆xi (T)∆xj (T)]
For the variance V we obtain up to second order in ∆x:
V (T) ≈
ij
δi (T)δj (T)Ωij (T)
V (T) ≡ E[(p(x(T), T) − E[p(x(T), T)])2
]
δi (T) ≡
∂p(x0(T), T)
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Analysis
Models
Software Development
Gaussian Approximation
What can we learn?
Risk factor contributions
Matrix elements Ψij = δi (T)δj (T)Ωij (T) indicate contribution of
risk factors ij to total variance.
EE, PE
Knowning mean and variance of the Gaussian distribution, any
statistical quantity may be evalued.
Caveat
Depending on specifics of portfolio this approximation may be
more or less accurate: that is why we use Monte Carlo simulations
after all.
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68. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Practical Implementation
For t = 0: δ and γ from Market risk system. But: need
netting set level aggregation → deal level granularity
For t > 0 estimate future δ, γ by bumping
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69. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Trade Models
Requirements
Represent trades/products
Standardize for interoperability
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70. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Trade Models
Trade Parameters
Product represented by parameters
FpML
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71. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Trade Models
Trade Parameters
Pro/Con
⊕ standardized
logic in client
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72. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Trade Models
Cashflows
Product represented by casflows
Payoff macros
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73. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Trade Models
Cashflows
Pro/Con
⊕ simple
not expressive enough (just cash is exchanged)
single product (no interations)
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74. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Trade Models
Transaction Model
Approach
Multi agent simulation:
Time Map wall clock to simulation time
Market Events simulation time to events
Transactions events to transactions (e.g. cashflows)
Execution execute events
Pro/Con
⊕ general
⊕ all business logic in model → easy tooling
expensive
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75. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Pricing & Risk Models
Criteria for Model Choice
Categories
Independent of product Relate to Mathemathics or Physics
Dependent of product Specific to product type
Dependent of portfolio and market Context
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Credit Risk Mitigation
Model Implementation
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Regulatory Requirements and Basel III
Analysis
Models
Software Development
Pricing & Risk Models
Independent of Product
Coordinate Sytems
From Physics we know: dynamics must not depend on choice of
coordinates → dimension analysis.
Interpolation
How to interpolate r, σ. Interpolate dimension-less quantities: rt
and σ2t.
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77. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
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Regulatory Requirements and Basel III
Analysis
Models
Software Development
Pricing & Risk Models
Product Dependent
State Variables vs. Parameters
Liquidity Hedge frequency, transaction costs, close-out period
Completeness Unhedgeable risk, uniqueness of price
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78. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Pricing & Risk Models
State Variables and Parameters
Indicators of Model Quality
Parameter Dimensionality Avoid overparamerization
Stability of Parameters Frequent recalibration: indicator of poor
model performance
GBM w termstructure vs Garch
TS GBM Garch
dimension ∞ 3
recalibration frequently for short end less frequent
time-homogeneous N Y
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79. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
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Regulatory Requirements and Basel III
Analysis
Models
Software Development
Pricing & Risk Models
Arbitrage
Risk Model for Volatility surface
Directly modelling surface w/o arbitrage not trivial. Alternatively
model option prices with HJM-like framework.
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80. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Pricing & Risk Models
Market
Liquidity & Completeness
Liquidity Hedge frequency, transaction costs, close-out period
Completeness Unhedgeable risk, uniqueness of price
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81. Credit Risk Measures
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Model Implementation
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Analysis
Models
Software Development
Comparing Models
Assume state of the world evolves randomly:
Model as Process: Stochastic Differential Equation (Langevin
Equation)
dx
dt
= f (x) + g(x)ξ(t) Physics Notation
dx = f (x)dt + g(x)dW (t) Finance Notation
Wiener Process (SDE)
dx = dW (t)
W : Wiener Process
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Analysis
Models
Software Development
Comparing Models
Model as Measure P
P : Γ → µ(Γ) probability
Γ : t → x(t) some path
Wiener Process (SDE)
Γ ≡ {x1, . . . xN}
µ(Γ) ∼
i
G(xi , xi+1)
G : Gaussian
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Model Implementation
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Regulatory Requirements and Basel III
Analysis
Models
Software Development
Pricing & Risk Models
Parametric Models
Error Analysis
Infer from parameter uncertainty price/risk uncertainty.
Parameter Uncertainty E.g. such that hedging instrument prices
still in bid-ask
Parameter Error Uncertainty of price/risk due to error in
parameters
GBM with vol uncertainty
(∆p)2 = ∂p
∂σ ∆σ
2
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Analysis
Models
Software Development
Benchmarking
Pricing/risk factor models Q, Q , empirical measure P
Comparing
Pricing Models Q vs Q
Risk Models P vs Q
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Analysis
Models
Software Development
Benchmarking
Distances
How far apart two models?
Need to define metric:
Expectation values E.g. differences of prices and EEs under
different measures
Distributions E.g. Kullback-Leibler entropy dP
P log dP
P dP.
Independent of quantity to average.
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Model Implementation
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Analysis
Models
Software Development
Model Uncertainty
Benchmarking giving limited answer:
Calibration-Consistent Measures
Define metric d to quantify goodness of calibration:
pP
i : model price calibration instrument i
pi : market price calibration instrument i
dP
=
i
(pP
i − pi )2
C = {P|dP
≤ }
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87. Credit Risk Measures
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Analysis
Models
Software Development
Model Uncertainty
Non-uniqueness
For d = 0:
Multiple measures
For single parametric measure, multiple solutions for
calibration → ill behaved
Incomplete market
For d > 0:
For single parametric measure: parameter risk
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88. Credit Risk Measures
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Model Implementation
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Analysis
Models
Software Development
Beyond Benchmarking
Pricing model descriptive:
Replicates prices of hedging instruments
Determines no-arbitrage price of illiquit product
How to asses quality of model?
There are implied predictions:
State variables vs parameters Prediction: parameters are constant
Martingale Total price of deal and self-financing hedges should
be 0 at any point in time
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89. Credit Risk Measures
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Analysis
Models
Software Development
State variables and parameters
State variables Temporal evolution or measure
Parameters Family of evolutions/measures
Analysis
Choice of state variables: qualitative assessment
Robustness of parameters: predicted are no changes
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Models
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Hedge Performance
If perfectly hedged: pathwise replication → P&L distribution
Unbiased
Sharply peaked (Dirac)
Hedge Simulations
Self Consistency Use state variables simulated with pricing model
Performance Historical state variables
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Analysis
Models
Software Development
Exposure
Goal
Estimate Credit Risk measures → need to estimate exposure/price
distributions in future.
The exposure e(t) at time t of a netting set is given by
e(t) = max 0,
i
pi (x, t) − C(t) (2)
where
pi price of trade i
x risk factors
C(t) price of collateral
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92. Credit Risk Measures
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Model Implementation
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Analysis
Models
Software Development
Calculating Exposure, CVA/DVA and Losses
Risk Factors&Counterparty Default Times
t
x
t
x
RT1 RT2
Risk Factors
Trades
t
x
t
x
R1 R2
Collaterals
Portfolio Prices
t
p
t
p
P1 P2
Collateral Prices
t
c
t
c
C1 C2
PDF of
Exposures
Default Times of
Counterparties
PDF of
Exposures
at Default
Expected
Exposure
Potential
Future
Exposure
Bootom-up
CVA/DVA
Top-down
CVA/DVA
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93. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
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Regulatory Requirements and Basel III
Analysis
Models
Software Development
Building Blocks
Components
Required for estimating risk measures for single and portfolios of
netting sets:
Pricing
Risk-factor
Collateral
Netting
Dependency
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94. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Pricing Models
Requirements
Need to be fast!
Ideally same as front office
Perform well under stressed state variables
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Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Pricing Models
Acceleration Techniques
Dumb lookup
Approximate price as function of few variables
define variables (e.g stock price)
define grid
recaluclate for each gridpoint price
interpolate
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96. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Pricing Models
Acceleration Techniques
Smart lookup
Approximate price as function of few variables
define variables (e.g stock price)
prices on grid are side effect of pricing at spot; e.g. pricing on
tree or AMC
interpolate
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Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Risk Factor Models
Pricing vs Risk Models
Purpose
Pricing Model Fit liquid market instruments; arbitrage-free
Risk Model Predict
Challenges for Risk Model
Dependency Simultaneously simulate all asset classes
Calibrationl Global calibration
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Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Risk Factor Models
Short vs Long term prediction
Long term prediction a challenge:
Reducing dimensionality
Economic macro factors
Co-integration
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99. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Risk Factor Models
Pricing model Dynamics
Arbitrage-free models used with risk calibration
GBM
HJM type of models
⊕ Well understood, tractable
Not intended for risk
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Analysis
Models
Software Development
Gaussian Dependency Modelling
Goal
Express random vector ξ with correlated ξi as
linear combination of
uncorrelated
random factors ηi :
ξ = Mη
E[ξi ξj ] − E[ξi ]E[ξj ] ≡ Ωij
E[ηi ηj ] − E[ηi ]E[ηj ] = λ2
i δij diagonal, pos. sem. def.
What to consider?
Ω?
correlation matrix?
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Analysis
Models
Software Development
Principal Component Analysis
Dimensional Analysis
Risk factors ξi not dimension-less!
interest rate :[T−1]
stock price :[Cash]
volatility: [T−1
2 ]
→ Ωij may have different dimensions,i.e. Ω in general not a
physically meaningful quantity!
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Analysis
Models
Software Development
Principal Component Analysis
Solution
Consider instead of Ω following matrix Φ:
Φij ≡
∂f (ξ)
∂ξi
∂f (ξ)
∂ξj
Ωij
f : some function
For dimensionality [Φ]:
[Φij ] =
[f ]
[ξi ]
[f ]
[ξj ]
[ξi ][ξj ] = [f 2
] ∀i, j (3)
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Analysis
Models
Software Development
GBM Risk Factor Model
Multivariate GBM
Xi (t + ∆t) = Xi e(µi −1
2
σi )∆t+σi
√
∆tξi (t)
µ : drift
σ volatility
ξi : Normal random
Cov(ln Xi (t + ∆t), ln Xj (t + ∆t)) = Ωij
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Models
Software Development
Dependent Gaussian Random Variables
Given uncorrelated Gaussian random number vector ζ. Need
build η:
Cov(ηi , ηj ) = Ωij
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Models
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Calibration
Definition
Calibration is the process to determine model parameters.
Approaches
Statistical Using historical data
Implied Market implied parameters
Economic Macro economical relation between rates, infaltion
Asumptions
Statistical Past is good predictor for future
Implied Information in spot market predicts future
Economic Some fundamental economic laws rule future
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Models
Software Development
Statistical Calibration
For simple models: ad hoc parameter estimation
averaging
fitting
Example
SimpleEstimation.xls
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Analysis
Models
Software Development
Maximum Likelihood Estimation
Systematic way to calibrate
Approach
Parametric model with parameters α ↔ parametric measure µα:
µα(Γ) = e−Sα(Γ)
D[Γ]
Assume: historical path ΓH is the most likely one. Find α∗ such
that:
µα∗ (ΓH) = max
α
µα(ΓH)
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Maximum Likelihood Estimation
Implementation
Assuming iid:
µα(Γ) = m(xi )
m(x) = e−s(x)
Γ = {x1, . . . , xn}
Maximizing m ↔ minimizing
i
s(xi ) : log-likelihood
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Models
Software Development
Maximum Likelihood Estimation
Example
MLE.xls
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Models
Software Development
Implied Parameters
Apply parameters used for pricing:
Drift and Volatility
Drift µ from T forward price (Covered Parity)
Volatility σ T years ATM implied volatility
Assumption
Risk neutral measure yield good predictor for real-world measure
Caveat
Carry trades
Supply/demand, risk premium
Perform analysis before using implied parameters!
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Models
Software Development
Economic Calibration
Parities connect for instance
FX rates
Inflation rates
Real interest rates
Nominal interest rates
Purchansing power
Example
Parities.xlsx
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Parities
Example (Relative Purchasing Power Parity)
pf (t1)(1 + if )X(t2) = pd (t2)(1 + id )
pd/f : domestic/foreign price
id/f : domestic/foreign 1 yr inflation rate
X : Exchange rate
Yields after averaging
E[X(t2)]
X(t1)
=
1 + Id
1 + If
where I is the expected inflation rate.
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Parities
Example (International Fisher Effect (Uncovered Parity))
(1 + rd/f ) = (1 + ρd/f )(1 + id/f )
rd/f : domestic/foreign nominal 1 yr interest rate
ρd/f : real rdomestic/foreign 1 yr interest rate
Assumingρd = ρf gives
E[X(t2)]
X(t1)
=
1 + rd
1 + rf
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Issues with standard GBM model
Issues
rigidity: calibration short vs long horizons → term structure of
parameters
dimensionality → factor models
underestimation of rare events and bursts (clustering) →
GARCH
not suitable where spread stationary process → cointegration
unable to capture some behabiour like regime-switches →
parametric models (Nelson-Siegel)
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GBM with Term Structure
Interpolation Principles
Interpolate dimension-less quantities
Forward Drift/Covariance
Dimensionality analysis → interpolate TΩ
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Factor Models
Issues with general covariance matrix
N risk factors →∝ N2 parameters
over-parametrization
for empirical parameters: problems with positive definiteness
Idea
Split return r of riskfactors into contributions from
Indices fn shared by multiple risk factors
Idiosycratic factors unique to each risk factor
r = α +
n
βnfn +
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Types of Factor Models
Classification
Macroeconomic Observables like changes in inflation, interest rate,
unemployment rate
Fundamental Portfolios associated to security attributes like
industry membership, book to market ratio, dividends
Statistical Factor analysis of covariance matrix
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Macroeconomic Factor Model
Fast/Slow
Slow variables Macro-economic state of the economy: inflation,
unemployment rate, GDP
Fast Asset prices
Pros and Cons
⊕ Designed to predict long-term evolution
⊕ Able to reflect systemic macro risks
Empirical evidence not convincing
Theories controversial
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Fundamental Factor Model
Sector/Region
1 Define for each sector/region pair an index
2 Associate stock to sector/region
3 Regress stock return vs index return → α, β
Example
FactorModel.xls
Pros and Cons
⊕ Designed to predict long-term evolution
⊕ Able to reflect systemic macro risks
Empirical evidence not convincing
Theories controversialc 2015 H¨aner Consulting CCR&CVA under Basel III 119 / 205
120. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Choice of Factors
How to know whether factors appropriate?
Analyze variance explained by factors
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121. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Volatility Clustering
: Spot : Log-returns
Figure: GBPUSD spot
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122. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Autocorrelation
: Autocorrelation: log-returns
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123. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Garch Model
Let Xn be the log-return of some foreign exchange rate f at
time tn:
Xn = ln
fn
fn−1
(4)
we may then express the foreign exchange rate fN at some future
sampling point time tN by the initial value f0 at t0 and a series of
returns:
fN = f0e
N
i=1 Xi
(5)
The observation points ti are typically defined in terms of number
of business days ∆T between them. For short time horizon
predictions we choose ∆T = 1 for larger horizon, we may choose a
less granular time grid.
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124. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Garch Model
The dynamics of the returns is then assumed to follow a
Garch(1,1) process
Xn = µ + n t ∼ iid(0, σ2
n) (6)
σ2
n+1 = α + βσ2
n + γ 2
n (7)
The asymptotic value σ2
∞ = limn→∞ E[σ2
n] is then obtained by
equation (7) noting, that E[ 2] = σ2 and E[σ2
n+1] → E[σ2
n]:
σ∞ =
α
1 − β − γ
(8)
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125. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Garch Model: Limit
Weak limit:
Stochastic variance
Mean reverting variance
dXt = µXtdt +
√
vtXtdWt
dvt = α(vt)dt + β(vt)dZt
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126. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Copula
Dependence under Stress
In stressed markets correlations increase between
downward price movements → systematic risk
implied default probabilities → contagion
Definition (Copula)
Separate
Marginal distributions from
Dependency
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127. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Cointegration
Long-run Relationship
Variables moving together:
Macro-economic Consumption-Income
Prices-Wages
Domestic prices - fpreign prices
Exogeneous For instance managed currencies
How to model processes. which stay close to each other?
GBM with ρij 1 not? No!
Need dynamic, where difference is stationary
Definition
Stochastic processes x, y are cointegrated:
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128. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Implementation
1 find parameters a, b by regression
2 show residuals are stationary (e.g. Dickey-Fuller Test)
Example
Cointegration.xlsx
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129. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Risk Factor Models
Empirical Models
Nelson-Siegel model
r(T) = r∞ + a(T)r0 + b(T)rm
r∞ : rate for long maturities
r0 : rate for short maturities
rm : rate for intermediate maturities
a, b : decay functions
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130. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Risk Factor Models
Empirical Models
Nelson-Siegel model
Normal/inverted curves
But not arbitrage-free
How to introduce dynamics? E.g. PCA of (r∞, r0, rm)
Example
NelsonSiegel.xlsm
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131. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Wrong Way Risk
Types
Specific Legal connection between underlying and
counterparty
General Dependence between prob. of default of counterparty
and exposure
SFT Transactions
Lend cash to counterparty A accepting their stock as collateral.
Emerging Market CCY swap
We are long strong currency. Weakening of emerging market
currency, increased prob default → increase exposure
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132. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Modelling Wrong Way Risk
What is wrong with standard modelling?
p+ is not conditioned on default.
Need to add in price function default state χ of counterparty:
extending state of the world
Approaches
Given a model for default times either
Simulating counterparty’s default
Calculating price given default
Example
WrongWayRisk.xls
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133. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Collateral Modeling
Components
Margin Call Process Model margin calls with correct frequency
and close-out period
Collateral Price E.g. model bond price if collateral is bond
Simplification
Margin call process: just at spot → short-cut method
All collateral as cash → haircuts
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134. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Collateral Modeling
Short-Cut Method
Definition (Basel II Short-Cut Method)
EE and PE of collateralized trades given by EE and PE for
close-out period (5 days for SFT, 10d for OTC)
Benefits/Issues
⊕ Computationally cheap
⊕ No collateral exposure spikes at expity
Assumes exposures declining over time
Risk not accurately represented
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135. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Dependency Modelling
Among Risk Factors
Standard way to model dependence: Gaussian Copula.
Gaussian Copulas are Levy copulas. Replace Gaussian with other
Levy coupula and obtain Levy model.
Between Defaults
Simulate either
Default times τ E.g. by Marshall-Olkin Copulas
Default state at t:χτ≤t E.g. structural models
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136. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Dependency Modelling
Between a Default and Risk Factors
To caputure Wrong Way risk need to model dependence between
risk factor and default state
Example
WrongWayRisk.xls
Between a cross name Defaults and Risk Factors
Need modelling full state of the world (x(t), {χτ1≤t, . . . χτ1≤t}).
→ scenario consistency is system
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137. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Model Lifecycle
Organisation Execution
Problem
Definition
Analysis Implementation
Test
Deployment
MaintananceChanges
Figure: Model Development Lifcecyle
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138. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Specification
Approaches
Human readable Business and functional specs
Machine readable Specification ∼ test
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139. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Specification
Tools
ScalaTest Code
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140. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Specification
Tools
ScalaTest Output
Part of CI:
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141. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Implementation
Software
in-house
third-party
Require different validation strategies
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142. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Third Party
Strategies
Black-box, no code review
Reverse-engineering
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143. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Revision Control
Requirements
Audit Who changed what/when
Resurrect Roll-back to previous state
Collaborate Merge contributions from different authors
Approaches
Plain files Tag files/directories with version information
Local Local database contains version information (e.g
RCS)
Server Database on server (e.g. SVN)
Distributed Each developer has own databse with potentially
central db (e.g. Git)
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144. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Revison Control Tools
Approaches
MyDirectoryV1.0
MyDirectoryV1.1
MyDirectoryV1.2-bugfix1
: File based : Local VCS
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145. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Revison Control Tools
Approaches
: Centralized VCS : Distributed VCS
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146. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Revision Control Tools
Git
Figure: Git Gui (SourceTree)
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147. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Documentation
Requirement
Contain enough information to reverse-engineer.
Tools
Automated API doc (Doxygen, ScalaDoc, . . .)
Internal wiki (e.g. Confluence)
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148. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Testing
Test Types
Unit Library level
Integration System level
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149. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Testing
Unit Test
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150. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Release
Requirements
Regression
Impact analysis
Sign-off
Auditing
Lock-down
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151. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Maintance
Bugs/Enhanements
Tracking system
Failing test cases
Metrics: severity, resolution time
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152. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Analysis
Models
Software Development
Integrated Development Process
Robust system should have
Components
Revsion Control system
Build System
Bug tracking system
Wikin
Components integrated to workflow with high degree of
automation
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153. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
Overview
1 Credit Risk Measures
2 Credit Risk Mitigation
3 Model Implementation
4 Back Testing
5 Regulatory Requirements and Basel III
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154. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
Motivation
Impact of Credit risk model
Trading activity limits set by PE
Capital charges regularity capital dependent of EEPE
P&L EE enters CVA/DVA
Model Risk
Back-testing should quantify model risk affecting these quantities.
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155. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
Requirements
Back-testing Process
Should provide
Definition of measure for model risk
Monitoring of metrics
Mitigating actions for model deficiencies
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156. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
BCBS Guidance
G1
G2
G3
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157. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
BCBS Guidance
G4
G5
G6
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158. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
BCBS Guidance
G7
G8
G9
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159. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
BCBS Guidance
G10
G11
G12
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160. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
BCBS Guidance
G13
G14
G15
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161. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
BCBS Guidance
G16
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162. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
What is the Question?
Types of Investigation
Hypothesis testing (Answer in percentage or yes/no)
Estimation of model uncertainty (Answer in cash terms)
Analysis at different levels: figure 9
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163. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
Domains
Economic Quantities
Regulatory
Capital
Limits CVA/DVA
Risk Measures
EEPE PE EE
Process Characterictics
Marginal
Distributions
Auto-Correlations N-Point Functions
Model-Dependent Quantities
Model Parameters Driver dynamic
Figure: Domainsc 2015 H¨aner Consulting CCR&CVA under Basel III 163 / 205
164. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
Definition
A model is represented by a measure Q.
May be generated by a stochastic process.
Quantifying Difference of Models
Comparing expectation values
Comparing probability distributions
Note: PDFs and CDFs may be expressed as expectation values
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165. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
Radon-Nikodym Derivative
Distance of model Q and end empirical measure P in terms of dP
dQ:
EP[f ] = EQ[
dP
dQ
f ] (9)
Compare P and Q
Direct dP
dQ ≈ id?
Expectation values Empirical expectation measures in terms of
model expectations
Relative Entropy Kullback-Leibler entropy → information
geometry (see [?])
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166. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
Radon-Nikodym Derivative
Let ξ be a scalar stochastic variable (e.g. portfolio price π(t))
Definition
P empirical, Q model CDF
Ψ : [0, 1] → [0, 1] (10)
Ψ(α) = P(Q−1
(α)) (11)
Radon-Nikodym derivative ψ
EP[f ] = EQ[ψ(α)f ] (12)
ψ(α) =
dΨ(α)
dα
(13)
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Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
Example
:
0.0 0.2 0.4 0.6 0.8 1.0
α
0.0
0.2
0.4
0.6
0.8
1.0
Ψ(α)
[x]=100.00;σ=0.40
[x]=110.00;σ=0.40
[x]=90.00;σ=0.40
[x]=100.00;σ=0.44
[x]=100.00;σ=0.36
0.8
1.0
1.2
1.4
1.6
1.8
ψ(α)
[x]=100.00;σ=0.40
[x]=110.00;σ=0.40
[x]=90.00;σ=0.40
[x]=100.00;σ=0.44
[x]=100.00;σ=0.36
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168. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
Cumulative Distribution Functions
Cumulative distribution function (CDF) for some state variable ξ
expressed as expectation:
Definition
P(ξ0) = EP[Θ(ξ − ξ0)] (14)
where Θ is the Heaviside function.
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169. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
Estimating
Ensemble averages E estimated well by time averages if
ergodic
stationary
CDF
P(ξ0) ≈
1
N
N
i=1
Θ(ξ(ti ) − ξ0) (15)
Ψ
Ψ(α) ≈
1
N
N
i=1
Θ(ξ(ti ) − Q−1
(α)) (16)
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170. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
Requirements for Estimation
Process neeeds to be
ergodic
stationary
iid price process
If empirical price process is iid, the ergodic.
iid process of underlying
Even if underlying process the price return process of the deal may
not be so, if deal not time homogeneus
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171. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
Distances
Point Distance
di = |Ψ(qi ) − qi | (17)
Curve Distance
(Weighted) quadratic distance d between functions q → Ψ(q)
and q → q:
d(q, Ψ(q)) =
i
wi (Ψ(qi ) − qi )2
(18)
qi e.g (0.01, 0.05, 0.3, 0.5, 0.7, 0.95, 0.99)
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Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
Hypothesis Testing
Null-Hypothesis
Null-Hypothesis, is that distances are 0.
Reject Null-Hypothesis p-values smaller than some threshold
Challenges estimating p-values
Temporal dependence: overlap of time-windows
Ensemble dependence: returns of netting sets not independent
Good p values get bigger
Bad Estimation tricky
Need some simplifications, like effective sample sizes
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Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
Problems using metrics for Ψ
Issues using metrics for Ψ
Opaque no cash denominated measure
Economics Product Dependent with same distance different
moments drive deviations in EE (see figure (11))
Limited usefulness Passes test if not enough data available
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Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
Problems using metrics for Ψ
20 40 60 80 100 120 140 160
strike K
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
EE
EE
[x]=100.00;σ=0.40
[x]=110.00;σ=0.40
[x]=90.00;σ=0.40
[x]=100.00;σ=0.44
[x]=100.00;σ=0.36
Figure: Comparing EEs for a forward using log-normal distributions with
different parameters
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175. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulatory Requirements
Measuring Model Performance
Comparison using Cash denominated Quantities
Economically Relevant Model Dependent Quantities
Regulatory Capital depends on EE(t) (through EEPE)
Limits impacted by CDF
P&L impacted by EE(t)
Measure
These three quantities are functions of EQ.
Their value under empirical measure P estimated through
equation (12) → difference in cash terms
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176. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Overview
1 Credit Risk Measures
2 Credit Risk Mitigation
3 Model Implementation
4 Back Testing
5 Regulatory Requirements and Basel III
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Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Pillars of Basel II Framework
Minimum
Capital
Requirements
Pillar I
Credit Risk
Market Risk
Operational Risk
Supervisory
Review Process
Pillar II
Regulatory Framework
Supervisory Framework
Market
Discipline
Pillar III
Disclosure
Basel II Accord
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178. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Basel II
Capital Charges
Based on Expected Exposures (EE) of netting sets
Charge for default risk
No charge for credit spread risk
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179. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
New in Basel III
In 2008 crisis:
2
3 of losses not due to default but MtM changes due to credit
spread widening
Capture spread risk by VaR
Introduction of new capital charge linked to VaR: CVA charge
Capital Charges
Basel II Default charges
Basel III Default and CVA charges
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180. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
CVA charge
Advanced CVA Charge
VaR for credit spread for bond given by EE:
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181. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
CVA charge
Standardised CVA Charge
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182. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
CVA charge
Advanced vs Standardised
Advanced Standardized
Reflect Diversification ⊕
Accurate Credit Spreads ⊕
Regulatory Capital ⊕
Build/Approval Costs ⊕
Running Costs ⊕
Synergies with Market Risk ⊕
Integration with CVA desk ⊕
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183. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
IMM
Internal Model Method
Institutions who have IMM waiver may calculate their own
regulatory capital for
OTC transactions Swaps, exotic deals, . . .
SFT transactions Bond repos, stock borrow/lending, . . .
c 2015 H¨aner Consulting CCR&CVA under Basel III 183 / 205
184. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
IMM
Benefits
Reduced capital charges
More accurate risk measures
Consistent risk measures for
Regualtory capital
Limit monitoring
Improved
Processes
Quality of information
c 2015 H¨aner Consulting CCR&CVA under Basel III 184 / 205
185. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Wrong Way Risk
Specific Wrong Way Risk
c 2015 H¨aner Consulting CCR&CVA under Basel III 185 / 205
186. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Wrong Way Risk
Stressed Calibration
c 2015 H¨aner Consulting CCR&CVA under Basel III 186 / 205
187. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Stressed Calibration
Frquency of Comparison
c 2015 H¨aner Consulting CCR&CVA under Basel III 187 / 205
188. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Hedges
CVA Charges
c 2015 H¨aner Consulting CCR&CVA under Basel III 188 / 205
189. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Hedges
Default Charges
c 2015 H¨aner Consulting CCR&CVA under Basel III 189 / 205
190. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Collateral
Non Cash Collateral for OTC
c 2015 H¨aner Consulting CCR&CVA under Basel III 190 / 205
191. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Other
Proxy,Index Hedges
c 2015 H¨aner Consulting CCR&CVA under Basel III 191 / 205
192. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Elements of Application
A High-level overview and implementation plans
B Overview of your firm’s own self assessment against relevant
standards
C Summary of your firm’s approach in a number of key areas
D Details of the IMM models being used
E Sign-off
c 2015 H¨aner Consulting CCR&CVA under Basel III 192 / 205
193. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Overview/Implementation Plan
Impact Analysis
Scope
Rollout Plan
Orgchart
c 2015 H¨aner Consulting CCR&CVA under Basel III 193 / 205
194. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Self Assessment
Description of self sssessment process
Results: exceptions, remediation plan and status
c 2015 H¨aner Consulting CCR&CVA under Basel III 194 / 205
195. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Firm’s Approach
Governance of Counterparty Risk
Roles of senior management, risk functions, audit functions,
legal functions, collateral management functions, and the
functions of any committees
Governance of the model, covering the organisation charts
and reporting lines of the model owner, developers, and other
support functions; an overview of the management committee
structure which approved the model and; how external vendor
models, if any, are controlled;
ad-hoc and on going stress testing.
c 2015 H¨aner Consulting CCR&CVA under Basel III 195 / 205
196. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Firm’s Approach
Requirement for use of IMM
Show methodology used for the calculation of the IMM
exposure is closely integrated into its day-to-day risk
management processes.
Management information where the IMM generated exposure
and any other outputs from the methodology is presented
Management information used by senior management to
monitor and control counterparty and market risk including
the composition / profile of the portfolios, concentration risk,
wrong way risk and the results of stress testing
c 2015 H¨aner Consulting CCR&CVA under Basel III 196 / 205
197. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Firm’s Approach
Data Management and Integrity
Standards of data management; data architecture
Process to ensure the accuracy, completeness and
appropriateness
Timeliness and robustness of the production systems
Reconciliation finance and risk systems
Business continuity
c 2015 H¨aner Consulting CCR&CVA under Basel III 197 / 205
198. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Firm’s Approach
Validation
Accountability, independence, scope, documentation and
monitoring the effectiveness of the model on an ongoing basis
Explanation of how senior management obtain comfort that
the outputs from the IMM model are sufficiently robust for
the business
Summary of your approach to back testing, including the
methodology and assessment of the results
c 2015 H¨aner Consulting CCR&CVA under Basel III 198 / 205
199. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Firm’s Approach
Documentation
List of all the internal documents you hold that you consider
relevant to the application, including a brief description of
their contents. Relevant documentation would cover
documentation specific to the IMM as well as the controls
surrounding it
c 2015 H¨aner Consulting CCR&CVA under Basel III 199 / 205
200. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Details of the IMM models being used
A description of the model coverage, in terms of businesses
units, products and risk factors
Documents relevant to the IMM, with dates when last
updated. Including any pre-processing performed on
transaction level information, features of the model,
assumptions used, use of proxies, approximations, limitations
of the output, modelling of risk factors, modelling of collateral
and netting and, treatment of margins
Use of market data
Valuation analytics including assessment of how assumptions
and approximations impact accuracy of the models
c 2015 H¨aner Consulting CCR&CVA under Basel III 200 / 205
201. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Details of the IMM models being used
Assessment of the model’s fitness for purpose in the light of
the risks presented by the portfolio (e.g. correlation between
counterparties’ exposures, wrong way risk)
Analysis performed on an ad hoc or on going basis to monitor
model performance
Materiality, of any relevant risk factors not covered by the
IMM
Validation reports
Enhancement plans
c 2015 H¨aner Consulting CCR&CVA under Basel III 201 / 205
202. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
Beyond Basel III: FRTB
Fundametal Review of the Trading Book (FRTB)
BCBS proposals for next next generation Market Risk Framework
(”Basel IV”):
Fundamental review of the trading book: A revised Market
Risk Framework, BCBS October 2014
Consultative Document Review of the Credit Valuation
Adjustment Risk Framework, BCBS July 2015
c 2015 H¨aner Consulting CCR&CVA under Basel III 202 / 205
203. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
FRTB Proposals
Boundary between banking and trading book (→ capital
arbitrage)
Improved granularity of Standardized Risk Charge
Disclosure of Standardized Risk Charge
c 2015 H¨aner Consulting CCR&CVA under Basel III 203 / 205
204. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
FRTB Proposals: Internal Model Approach
Expected Shortfall (ES) replaces VaR; liquidity horizons )
Incremental Default Risk (IDR): jump to default of bond and
equity positions
Modellable/non-modellable risk factors
Capital add-on from stress-testing for non-modellable risk
factors
c 2015 H¨aner Consulting CCR&CVA under Basel III 204 / 205
205. Credit Risk Measures
Credit Risk Mitigation
Model Implementation
Back Testing
Regulatory Requirements and Basel III
Regulation
IMM Waiver Application
Beyond Basel III
FRTB Proposals: FRTB-CVA
Goal: make CVA charge consistent with FRTB Market Risk
Framework:
IMM-CVA → FRTB-CVA:
Expected Shorfall instead of VaR
Allow accounting CVA
Sensivity of CVA wrt all risk factors instead of just spread
CVA desk required
c 2015 H¨aner Consulting CCR&CVA under Basel III 205 / 205