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Trends in Economic Capital Modeling
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© 2013 IBM Corporation
Trends in Economic Capital Modeling
Curt Burmeister
IBM Risk Analytics
Insurance Risk North America
November 5th 2013
© 2013 IBM Corporation
Economic Capital Modeling: 2005-present
Phase 1 - Analytics
(2005-2010)
Typical Phase 2
Phase 3 – Reporting
(2010-2015)
2
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
(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
‘What-if’ and ad-hoc runs,
additional reporting
Regulatory Reporting
Management Reporting
© 2013 IBM Corporation
Economic Capital Modeling: Looking ahead
Phase 4 - Analytics
Typical Phase 2
Phase 6 – Reporting
3
Curve Fitting & Least
Square Monte Carlo
More scenarios
Faster calculations
Reduced IT costs
Improved Credit Risk
Modeling
Phase 5 –Workflow &
Governance
Trusting the numbers
Auditability, Transparency,
Traceability
User annotations and
comments Incorporating “trust
metrics” into risk
management dashboards
© 2013 IBM Corporation
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
© 2013 IBM Corporation
Proxy the Liabilities
1. Replicating Portfolios
2. Sampling from Empirical & Analytical Distributions
3. Curve Fitting & Least Squares Monte Carlo
5
© 2013 IBM Corporation
Curve Fitting / Least Squares Monte Carlo
Loss Function
calibration
A/L Sample
Economic Scenarios
3 2
1
A collection of nested RW
and RN stress scenarios
on relevant risk factors
(MR + NMR).
1
The sample points
must be calculated
under each scenario
in the actuarial
valuation system.
2
Choose a formula (e.g.
polynomial) and a fitting
method (e.g. linear
regression).
Perform the regression,
check goodness of fit
and fine tune.
.
3
8
© 2013 IBM Corporation
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
9
© 2013 IBM Corporation
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
© 2013 IBM Corporation
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
© 2013 IBM Corporation
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
12
© 2013 IBM Corporation
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
13
© 2013 IBM Corporation
Curve Fitting Example – Summary Statistics
14
© 2013 IBM Corporation
Curve Fitting Example – Goodness of Fit
15
© 2013 IBM Corporation
Credit Risk
© 2013 IBM Corporation
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.
17
© 2013 IBM Corporation
General Framework for Portfolio Credit Risk
19
Scenarios: Market factors 1
x x x x x x x
x
x x
Sampling
LLN
CLT
Idiosyncratic risk & conditional losses
4
FFT
Systemic risks & conditional credit states
3 Obligor exposures 2
© 2013 IBM Corporation
Decompose Loses by Risk Type
21
Joint default, migration and spread Spread only
Losses
Probability
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
99.5 99 99.5 99.9
Marginal contributions to loss percentiles
Default
Migration
Spread
Simulate credit loss distributions Analyze risk contributions in expected
and unexpected loss percentiles
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
© 2013 IBM Corporation
Enterprise Risk Governance
© 2013 IBM Corporation
Analytics
Production Methodology
Few Know Few Know
Many Consume
© 2013 IBM Corporation
Effectively, analytics are to most users a ‘black box’ that they don’t understand.
The Black Square
Director: Hiroshi Okuhara
© 2013 IBM Corporation
Many Consume
Few Know Few Know
Instrumented Process
Backtest/Validation
Data Metrics
History
Audits
Control Sets
Quality Indicators
Social Viewpoints
Credibility Score
Point in Time Context
TRUST
NETWORK
© 2013 IBM Corporation
© 2013 IBM Corporation
© 2013 IBM Corporation
RWA – June 2013 – Quality Analysis
050
100150200250300
t-3 t-2 t-1 Today
No. of CalcErrors
No. DroppedPositions
UserAssessment
Timeliness ofData
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
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
More…
RWA Quality
100
50
© 2013 IBM Corporation
Comment
Agree Disagree Approve
© 2013 IBM Corporation