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

Loss

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prop

ortio

n of

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mits

Vendor 1PartnerRe ModelVendor 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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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

Percentile97.5

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

Mea

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amag

e R

atio

Illustrative Loss data

Data also gives us Coeff of Variation

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0.0% 0.1% 1.0% 10.0% 100.0%

Mean Damage Ratio

Coe

ff Va

riatio

n (s

igm

a/m

u)

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 expertsBUT 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