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Portfolio wide Catastrophe Modelling
Practical Issues
Overview Applications of CAT models
– Pricing– Portfolio optimization– Input for DFA models
Difficulties with the above and possible solutions– Peril/country specific models compatibility issues– Personal lines versus commercial business– Effects of deductibles– Comparison with other lines of business
Pricing Expected loss cost
– Standard output
Expenses– Should know these
Loading– Capital charge – Volatility– Uncertainty
Treaty 1: – almost no effect on Portfolio wide 250 year loss
Treaty 1
EP
Loss
Relative Capital Charge
250 year event
Treaty 2: – Significant increase in 250 year loss
To achieve the same risk adjusted return treaty 2 will have to carry a much greater loading than treaty 1.
NB Though this example uses a VAR type measure, other means of splitting up the total allocated capital e.g. covariance could be used
EP
Loss
Relative Capital Charge
250 year event
Treaty 2
Volatility / Uncertainty This loading covers charges for
– Volatility of results
– Uncertainty in expected value Measured relative to expected loss cost both increase as you move up CAT XL programs
Loading for result volatility can be made using the Std deviation of the layer loss. This is a standard model output.
Model uncertainty (e.g. Parameter uncertainty) is not a standard model output.
Input for DFA
Hurricane
0.00
0.20
0.40
0.60
0.80
1.00
0 200 400 600 800 1,000
Return Period
Lo
ss
as
pro
po
rtio
n o
f L
imit
s
Vendor 1
PartnerRe Model
Vendor 2
Portfolio wide loss distributions are required for DFA CAT models can provide these distributions Output varies wildly within a region
Summary Points so far
Within one model– A metric can be chosen for optimization– A relative capital charge can be calculated based on this – Given a capital allocation to the peril and region an absolute capital charge can be calculated– Uncertainty can be estimated
Different models may produce different portfolio choices, because they produce significantly different portfolio loss distributions
Difficulties Peril/country specific models comparability issues
– How do you compare Turkish quake and US wind?
Example– A poorly constrained CAT model based on 20 years of data
indicates that all business in region A is very well priced and has a relatively low downside.
– A vastly superior model based on 200 years of data indicates that region B is profitable, but has a high downside.
– Based on raw model output region B will attract higher capital charges and some business may need to be turned away.
– Business in region A may well be grown as it looks like a good market.
CAT Model comparability Pricing Models are better in some countries than in others
WHY?
Hazard data quality Exposure data spatial resolution Exposure data details of insured risks
– Construction type– Insurance conditions
Previous loss information
CAT Model comparability
Which differences matter ?
Look at for effects that will be systematic over any given region
CAT Model comparability
Highly Correlated– Regional hazard model
Uncorrelated– Previous loss information
– Input data quality• resolution
• insurance conditions *
• Construction
*Highly correlated in some cases. e.g. systematically ignoring deductibles
Hawaii uncertainty study
Study of Hazard model uncertainty– A two parameter Weibull distribution was fitted to the relative
intensities from the 26 storms that passed within 250nm of Hawaii between 1949 and 1995.
– A Bayesian approach was followed. Assuming uniform priors the joint distribution of possible parameter values (posterior likelihood) must be proportional to the likelihood of observing the 26 historic relative intensities.
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1
1
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Hawaii uncertainty study
Study of Hazard model uncertainty (continued)– 1000 pairs of Weibull parameters were simulated using Monte
Carlo sampling of the Bayesian joint likelihood function.
– A Poisson distribution was used to model the frequency of storms within the study area. The parameters of this distribution were also simulated using a Bayesian approach.
– Overall 10,000 years of storm losses were simulated 1000 times
Return period of Iniki loss level as example of a tail loss – Chu and Wang 1998 estimate the Iniki intensity to have a 137 year return period within 250nm of Hawaii (Journal of Applied Meteorology)
This is an intermediate region, some areas have much better hazard information
Hawaii uncertainty study
Percentile
97.5
75
50
25
2.5
Return Period of loss
435
233
175
133
84
Comparing uncertain prices
•0
•0.045
•0 •2
95th %tiles
Well constrained case
Poorly constrained case
Commercial versus Personal lines
Personal lines CAT, portfolio losses lots of loss data
Commercial- less data, more assumptions
Modeling Deductibles Modeling of limits and deductibles is very dependent
on assumptions.– Particularly on the variance of the conditional loss distribution
for a given wind speed and building type.
0.0%0.5%1.0%1.5%2.0%2.5%3.0%3.5%4.0%4.5%
0 1 2 3
Coefficient of variation
MD
R
5% deductible: 150%
10% deductible: 600%
20% deductible: 1500%
Range
Calibrate with Loss Data
0.0%
0.1%
1.0%
10.0%
100.0%
0 50 100 150 200
Gust Wind Speed
Me
an
Da
ma
ge
Ra
tio
Illustrative Loss data
Data also gives us Coeff of Variation
0
1
2
3
4
5
6
7
8
0.0% 0.1% 1.0% 10.0% 100.0%
Mean Damage Ratio
Co
eff
Va
ria
tio
n (
sig
ma
/mu
)
The standard deviation of f(x) is a decreasing function of MDR
Modeling Deductibles Primary insurers with loss data have a significant data resource that they should leverage
Highly differentiated vulnerability classes – Reduce the variance within each class– May underestimate variance and overestimate deductible effects
Sharing the loss information with reinsurers – Reduces modeling uncertainties and reinsurance premiums. – The statement Vendor x’s model indicates that loss expectations are lower is less powerful than direct evidence.
Company wide DFA (liability models)
CAT is a major capital driver, but do ‘high quality’ CAT models overstate tail losses relative to loss models for other lines of business?
Why is this a problem?– Performance measurement, CAT business may be set unfairly
high return targets
Company wide DFA (Solutions)
Ensure that liabilty models are built systematically by business experts
BUT All models need to be vetted/adjusted by one central
Actuarial team
Encourage technical dialogue between business experts and modeling team
Avoid overstatement of model capabilities
Conclusions
CAT models are essential pricing and portfolio management tools
For worldwide applications there are problems of comparability between models
CAT models provide detailed quantification of the liabilities for some lines of business. Other lines don’t necessarily have such good liability models.
A combination of qualitative and quantitative measures can be used to resolve these issues
It is important not to delude oneself. Precision Truth