This document discusses trends in economic capital modeling from 2005 to the present. It outlines phases of development including initial analytics, workflow/governance improvements, and advanced reporting. Future areas of focus are described like faster calculations, improved credit risk modeling, and incorporating "trust metrics" into risk management dashboards. Methods like curve fitting and least squares Monte Carlo for proxying liabilities are also summarized. The benefits of using more scenarios are presented, along with addressing regulator feedback on credit risk modeling.

1. Curt Burmeister
IBM Risk Analytics
Insurance Risk North America
November 5th 2013
Trends in Economic Capital Modeling
© 2013 IBM Corporation

2. Economic Capital Modeling: 2005-present
Phase 1 - Analytics
(2005-2010)
 Complete capital numbers
at the Group and BU level
 Used simplified modeling
assumptions where
possible (e.g. curve fitting,
no roll-forward, simple
capital aggregation rules,
no ‘what-if’ runs/reports,
etc.)
Phase 2 –Workflow &
Governance
Typical Phase 2
(2009-2012)
 Use active data (i.e. run
model quarterly or other
frequency)
 Move to target operating
model (i.e. more
participation from BU
users)
 Auditability &
Transparency
Phase 3 – Reporting
(2010-2015)
 Regulatory Reporting
 Management Reporting
 ‘What-if’ and ad-hoc runs,
additional reporting
2
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3. Economic Capital Modeling: Looking ahead
Phase 4 - Analytics
 Curve Fitting & Least
Square Monte Carlo
 More scenarios
Phase 5 –Workflow &
Typical Phase 2
Governance
 Faster calculations
 Reduced IT costs
 Improved Credit Risk
Modeling
 Trusting the numbers
 Auditability, Transparency,
Traceability
 User annotations and
comments
3
Phase 6 – Reporting
 Incorporating “trust
metrics” into risk
management dashboards
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4. Why use 100,000 or more Real World Scenarios?
1. SCR/VaR/CTE convergence
2. Stability of capital attribution
3. Stability of SCR over time (Quarter to Quarter)
“To run just our with-profit model takes an hour, even if we squeeze every bit of efficiency out
of it. To run it 100,000 times would take 10 years”
– Large UK Insurer
… but everyone is looking for lower TCO
4
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5. Proxy the Liabilities
1. Replicating Portfolios
2. Sampling from Empirical & Analytical Distributions
3. Curve Fitting & Least Squares Monte Carlo
5
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6. Curve Fitting / Least Squares Monte Carlo
1
A collection of nested RW
and RN stress scenarios
on relevant risk factors
(MR + NMR).
1
Economic
Scenarios
2
3
A/L
Sample
2
The sample points
must be calculated
under each scenario
in the actuarial
valuation system.
8
3
Loss
Function
calibration
Choose a formula (e.g.
polynomial) and a fitting
method (e.g. linear
regression).
Perform the regression,
check goodness of fit
and fine tune.
.
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7. Curve Fitting
Example
Real World Scenarios = 20
Risk Neutral Scenarios per Real Work
Scenario = 1000
Total Scenarios = 20,000
Note - Real World scenarios are
typically instantaneous shocks
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8. Least Squares Monte Carlo
Example
Real World Scenarios = 2000
Risk Neutral Scenarios per Real
World Scenario = 1
Total Scenarios = 2,000
Note - Real World scenarios are
typically 1 year shocks
10
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9. Building the Equations
• Flexible User-Defined Formula: Cross Terms, Squares, Log, etc.
• Piecewise fitting allows to improve local precision.
• Fitting Choice of weights on observations.
• Linear Equations
• a + b * RF1 + c * RF2
• a + b * ln( RF1)
• a + b * Step Function(RF1)
• Non-Linear Equations
• a + RF1* Log(b)
• a * exp(b * RF1)
11
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10. Curve Fitting Example
 Liability
– German With Profits
 Risk Factors
– German Equity
– German Interest Rate
– Lapse
– Mortality
 Value of Liability under 30 Stress Tests
– Partitioned into two Samples of size 15
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11. Curve Fitting Equation
c+
Constant
a(EQ) + b(IR) + c(Lapse) + d(Mort) +
Function of risk factors
e(EQ2) + f(IR2) + g(Lapse2) + h(Mort2) +
Function of squared risk factors
i(Lapse*EQ) + j(Lapse*IR)
Cross Terms
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12. Curve Fitting Example – Summary Statistics
14
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13. Curve Fitting Example – Goodness of Fit
15
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14. Credit Risk
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15. Regulator Feedback
 The approach used in modeling credit risk seems overly simplistic, given the size and
complexity of the firm and the methodology appears to have been designed primarily to
deliver an overall group capital figure and does not appear to be capable of playing a key
role in an overall group-wide system for accepting, monitoring and controlling credit risk.
 It is unclear if the model is able to provide relevant and required information to stakeholders
within the firm. For example it does not breakdown the credit risk contribution due to spread
only, migration only and default only risks. The firm needs to show that the choice of model
and methodology reflects the risks which the firm believes that it is exposed to and that it
provides sufficiently granular information to ensure that it can play an important role in the
relevant management decisions, at both group and business unit level
 The firm should be able to explain links, if any, the firm believes exist between market
conditions and the changes in bond prices, driven by both spreads and migration and
defaults, over the next year.
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16. General Framework for Portfolio Credit Risk
1
Scenarios:
Market factors
2
Obligor
exposures
3
Systemic
risks &
conditional
credit states
4
Idiosyncratic
risk &
conditional
losses
Sampling
x
x
x xx x x
x
x
x
LLN
CLT
FFT
19
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17. Decompose Loses by Risk Type
Analyze risk contributions in expected
and unexpected loss percentiles
Simulate credit loss distributions
Joint default, migration and spread
Probability
Losses
Marginal contributions to loss percentiles
Spread only
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Default
Migration
Spread
99.5
99
99.5
99.9
Generate a credit loss distribution using Monte Carlo or Sobol Simulation
• Various loss distributions can be generated, such as one based only on spread volatility or
incorporating all spread, migration and default risks.
• Stand alone and Marginal contributions by risk type, scenario, issuer or asset type
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18. Enterprise Risk Governance
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19. Many Consume
Analytics
Production
Few Know
Methodology
Few Know
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20. Effectively, analytics are to most users a ‘black box’ that they
don’t understand.
The Black Square
Director: Hiroshi Okuhara
© 2013 IBM Corporation

21. TRUST
NETWORK
Quality Indicators
Social Viewpoints
Credibility Score
Point in Time Context
Many Consume
Instrumented Process
Backtest/Validation
Data Metrics
History
Audits
Control Sets
Few Know
Few Know
© 2013 IBM Corporation

22. © 2013 IBM Corporation

23. © 2013 IBM Corporation

24. RWA – June 2013 – Quality Analysis
300
250
200
150
100
50
0
Quality
100
RWA
No. of Calc
Errors
No. Dropped
Positions
50
User
Assessment
t-3
t-2
t-1
Timeliness of
Data
Today
Level
Trace Back System
1
Cognos
2
IRP fact table 16
2
IRP fact table 12
3-12
Data Stage Process Group 13
13
File #382, time stamp XYZ
14-32
Algo One, process 63 time stamp ABC
33
Trading System 1
33
Trading System 2
33
Bloomberg
More…
User 17 on XYZ said:
“The RWA values are unreliable this
month because of a failure in one of the
lending systems to properly convert
currencies. Revised, more accurate
values are expected before end of
August.”
Ref: Remedial Plan 74
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25. Comment
Agree
Disagree
Approve
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26. © 2013 IBM Corporation