Modeling with scarce data: Credit and

Modeling with small data:
Credit and Operational Risk
13th congrès des actuaires, Peter Middelkamp, Small Data
Example 1: Operational Risk
13th congrès des actuaires | Peter Middelkamp | Small Data
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Operational Risk1 : (typically) Available Data
• Internal sources:
0.99
– Own loss history collected over
the past 5-10 years
0.98
0.97
– Expert judgement of loss
potentials
– Industry loss data from loss
data exchanges (eg: ORX)
– Public information
(eg: corporate filings, rating
agencies, news, Algo First)
0.96
F(x)
• External sources:
Empirical CDF
1
0.95
0.94
0.93
0.92
model
internal loss data
external data
0.91
0.9
0
500
1000
x
1500
2000
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severity distribution per scenario and legal entity
• truncated Pareto with one important input: A = Anticipated Loss Potential
for a given confidence level e.g. f = 99.5%.
13th congrès des actuaires | Peter Middelkamp | Small Data
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aggregation with dependence
• Dependence within operational risk:
– Dependence between legal entities
– Dependence between event categories
• External dependencies:
– Dependence to financial markets (more prevailing in banks)
– Dependence to pandemic events
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Conclusion Operational risk
• All parameters are mainly based on expert judgement that might be inspired
by historic events in the firm and that happened to peers.
• A simple dependence method is a must (e.g. mixture of full dependence,
independence)
• Number of parameters should be kept at a minimum to have a stable, easy
to understand "well behaved" model.
• Continue to collect data and use it as benchmark for the model.
• Model alternatives (rejected):
– LDA (not enough data)
– Standard Formula (based on industry averages)
– causal models with explicit control modelling (complicated, potentially unstable)
– combining loss data sources and expert judgement using Bayesian inference
(potentially unstable)
13th congrès des actuaires | Peter Middelkamp | Small Data
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Example 2: Credit Risk
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Compared to operational risk, there is plenty of data
AAA and BB history 1920-2013
• Default history
exposes large spikes.
10
8
BB
6
AAA
4
2
0
1920
1924
1928
1932
1936
1940
1944
1948
1952
1956
1960
1964
1968
1972
1976
1980
1984
1988
1992
1996
2000
2004
2008
2012
• Rating information
alone is not enough
to determine default
risk
12
Default rate [%]
• Some rating
categories never
experienced a
default within one
year
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13th congrès des actuaires | Peter Middelkamp | Small Data
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Multi year default probabilities can be used to estimate
one year default probabilities
Cumulative default probability
AAA rating
Fit
Data
10.000%
1.000%
0.100%
0.010%
0.001%
1
3
5
7
9 11 13 15 17 19
Years
• Note that a minimum default probability of 0.03% is applied to corporates,
0.01% to sovereigns.
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Modelled default probabilities should be able to reproduce
and go beyond historic realisations
• Credit portfolio risk
models capture historic
default history
(back-test)
DP
13th congrès des actuaires | Peter Middelkamp | Small Data
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Credit portfolio risk models should also capture historic
dependencies to financial markets (back-test)
• Default rates are higher
when equity markets
are down/ credit
spreads widen (not that
there is sometimes the
default rate lags behind
financial markets)
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