Portfolio wide Catastrophe Modelling

1. Portfolio wide Catastrophe Modelling Practical Issues

2. 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

3. Pricing • Expected loss cost • Standard output • Expenses • Should know these • Loading • Capital charge • Volatility • Uncertainty

4. Treaty 1: • almost no effect on Portfolio wide 250 year loss Treaty 1 Relative Capital Charge 250 year event EP Loss

5. Treaty 2 Relative Capital Charge 250 year event EP • 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 Loss

6. 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.

7. Input for DFA • Portfolio wide loss distributions are required for DFA • CAT models can provide these distributions • Output varies wildly within a region

8. 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

9. 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.

10. 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

11. CAT Model comparability • Which differences matter ? • Look at for effects that will be systematic over any given region

12. 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

13. 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.

14. 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

15. Percentile Return Period of loss 97.5 435 75 233 50 175 25 133 2.5 84 Hawaii uncertainty study • 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

16. Comparing uncertain prices Well constrained case 0.045 Poorly constrained case 0 0 2 95th %tiles

17. Commercial versus Personal lines • Personal lines CAT, portfolio losses lots of loss data • Commercial- less data, more assumptions

18. 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. Range 5% deductible: 150% 10% deductible: 600% 20% deductible: 1500%

19. Calibrate with Loss Data Illustrative Loss data

20. Data also gives us Coeff of Variation The standard deviation of f(x) is a decreasing function of MDR

21. 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.

22. 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

23. 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

24. 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