CIA 2004 Seminar for the Appointed Actuary PD-7 Reinsurance – Catastrophe Modeling

1. CIA 2004Seminar for the Appointed ActuaryPD-7 Reinsurance – Catastrophe Modeling Tim Tetlow, FIA, SVP Global Reinsurance Axis Specialty tim.tetlow@axis.bm

2. Various threats, each having associated frequency-severity relationship: EQ Terrorism - Conventional, NBCR Airplane crash Industrial Accident or Fire Tornado Natural biological epidemic - Flu War Asteroid Tsunami Heat wave Exposure: Life Number of lives in a given area Value of lives in the given area Property By Location TIV Policy terms Building construction characteristics etc Defining catastrophic risk in a WC/Life/Property Insurance portfolio

3. Tracking aggregations of Risk Data quality: • Property • Geo-coded location • Policy specific terms • Building construction details • WC • payroll/number of employees bystreet address • Life/PA • Volumes and number of certificates by state/province Coverage differences • EQ • Wind • Fire following • Terrorism

4. Tracking aggregations of Risk Considerations pertinent to pricing and risk accumulation that life exposures present: • Individual cf. group – what does volume by province really mean as people move? • Individual policies commute from into cities in daytime • How to include accumulations from one contract into the portfolio accumulation given data resolution issues? • Move exposure at a low resolution toward maximum accumulation at high resolution • Macro scale of data cf. micro scale of terror acts • Non-homogeneous distribution of face values • Toronto face values in one portfolio 3 x nationwide average

5. Tracking aggregations of Risk Portfolio needs to be accumulated across: • Insurance and reinsurance company subsidiaries consistently to calculate group-wide accumulations. • All product types consistently considering coverage differences • Property • WC • PA • Life • Intelligently handle data resolution issues. • Accumulate daily by profit center. • Revisit allocations of contribution to accumulation for profit centers on a quarterly basis for administration simplicity.

6. Tracking aggregations of Risk - EQ Need to look at loss potential at various return periods for portfolio: • 1 in 50 year loss potential • 1 in 100 year loss potential • 1 in 250 year loss potential ….. • 1 in 10,000 year loss potential

7. Tracking aggregations of Risk - Terrorism - US WC Industry study • E(LA|>100yr RP)/ E(LB|>100yr RP) ~ 450%

8. Tracking aggregations of Risk - Terrorism What is the Probable Maximum Loss? • Given lack of certainty in frequency of terrorism events concept needs revision. Accumulate using: • 400m/1,600m radius loss potential (2T truck bomb) • 550m/1,900m radius loss potential (10T truck bomb) • 5,500m/27,300m radius loss potential (5 kT nuclear bomb) • …. • Total province and contiguous province limits (Nuclear - Total Maximum Loss potential?) NB** Measurements are the threshold distance of 10% damage to buildings and total footprint

9. Modeling Risks • People are in buildings, additional sources of uncertainty over that for modeling property risks: • People move • Data deficiencies • Geographical resolution available of face value of policies • Volume collapse • construction behavior • Injury distribution uncertainty • Cost uncertainty • LTD under nuclear? • Time of day • WC only daytime exposure

10. Modeling Terrorism • Severity estimation methods for given type of attack reasonable • Frequency estimation a complete guess • A benchmark frequency pick provides a relative pricing tool • Data resolution vs event resolution • Due to difference in size of loss curve model needs to look explicitly at loss potential for each type of attack mode: • Nuclear (500,000 - 5kT nuclear bomb) • Biological (173,000 – 75kg anthrax attack) • Conventional (12,500 – 10T bomb) • Chemical (6,800 – 1,000kg Sarin attack) • Radiological (4 – 150kCu 60Co) • EQ (20,000)

11. Modeling Natural Perils The construction of a life and PA cat model from a WC cat model • Why build a Life/PA cat model? • There are currently no licensable life/PA cat models available, only WC cat models (and only for the US). • Consistent pricing independent of “type” of aggregate. • Property vs. WC vs. Life/PA • Consistent and complete: • Accumulation reporting across all products. • Incremental pricing.

12. How is the model constructed? • The “seeds” are: • the number of WC deaths. • the working population. • the life population. • the life benefit structure.

13. Simple example • Daytime, focus on 1 zip code, 1 earthquake scenario, 1 building occupancy class etc. • Industry working population of zip code = 10,000 • Industry deaths from EQ scenario = 100 • Mortality rate = 1% • Cedant has 2,000 people within the zip code • Cedants lives lost = Cedant population * Mortality rate • Cedants lives lost = (2,000 * 1%) = 20 • Average life policy face value = $100,000 • => $2M loss

14. What next? • An EQ scenario will affect: • More than 1 zip code • More than 1 building occupancy class • Sum up losses to cedant from each zip code-building occupancy class permutation for the EQ scenario • Look at many EQ scenarios

15. Treatment for nighttime and areas outside the US • WC mortality rate only really defined during the day within the models and territorially for the US only. • Need a proxy

16. Proxy selected • For all daytime events, calculate by magnitude by region a burn:

17. What does this look like?

18. Generation of the number of nighttime deaths • Assumption is that for a given night-time event the number of deaths for the industry =

19. Does this “life” model reproduce the WC model?

20. Rest of world? • Use the burn from the US model by day or night against: • Commercial property during the day. • Personal lines at night. • May loose resolution of occupancy class. • Possible “shift” in relationships: • (California EQ burn)Mag=x => (Japan burn)Mag=x • (US all other EQ burn)Mag=x => (Turkey burn)Mag=x-1

21. Ground up loss distributions

22. Excess loss distributions

23. Axis’s Dilemma: How do we combine our views of the various vendor models in a consistent manner for both contract pricing and portfolio accumulation?

24. Large license fees => use the vendor models Problems: • Some treaty types not easily modeled/incorporated: • Retro • Stop loss • Per risk • Contract types assumed to be losses occurring during, no consideration of risk-attaching treaties really allowed. • Contract periods generally assumed to be annual, how do we tackle partial year covers? • Prospective portfolio modeling is difficult, e.g. January 2005 in-force as at December 2004. • Portfolio optimization routines difficult to run within the models. • Difficult to test alternative frequency distributions for annual aggregate analysis, e.g. negative binomial for European Wind.

25. Why didn’t we use vendor model approach? • Problems illustrated above. • Implementation outside the vendor models would allow: • Different model selections for different peril/region combinations. • E.g. RMS for England, EQECat for Scotland, AIR for Wales. • Accumulation close to real time - we accumulate portfolio nightly based upon daily changes to contracts: • Loss pick changes • Status • Line size • Terms: premium, reinstatements etc. • Desire to incrementally price.

26. Some other reasons…. • Blank sheet of paper. • Intellectual challenge to do it “right”. • Consideration of who we wanted our peer group to be and what they do: • Banks • Top Bermudian reinsurers

27. Where are we trying to go? Essentially trying to make our loss picks by: • vendor model • region/peril • layer reproducible within one model through the use of modification factors by region/peril by layer.

28. Which models for which region/peril? • Impression of the modelers. • I’m not a meteorologist, seismologist, geophysicist, engineer…… • Spin • Market “suggested” model. • Questionnaire

29. Questionnaire • Historical events • Assessment of the return period for set of events • Loss estimates by LOB • Damage ratios at certain levels of exposure • Information on the source of claims data for the events • Industry exposure database (not available for all models/regions) • Source(s) of exposure database • Resolution • Extrapolation and methodology • Stochastic event module • Hazard • Exposure mapping • Vulnerability • Financial • Anything else?

30. Cost of Capital considerations – “Probabilistic” Perils • Different ROE methods utilized: • Incremental ROE • Incremental capital required to support the addition of a new contract to your portfolio – Expected Policyholder Deficit. • Considers extent to which a new contract diversifies or further stresses portfolio capital requirements. • Traditional ROE • Based on coefficient of variation as a measure of loss volatility as well as regional propensity for accumulation. • Provides a view of likely “market” price. • Impact on various return period metrics • Contribution to the 1 in 100 year, 1 in 250 year etc. events

31. Cost of Capital considerations – “Non-Probabilistic” Perils • ROE but what is E? • Traditional ROE • Based on coefficient of variation as a measure of loss volatility using our benchmark frequency terrorism model. • Again like our terrorism loss pick this metric ONLY provides a benchmark measure of profitability. • Roughly use same amount of capital per unit of loss to that required for natural catastrophes. • Supply demand metric for capital is complicated: • TRIA deductible increases will increase the capital threat to insurance companies • Axis as a group operates with both an insurance and reinsurance company • Monitor aggregations on a total limit basis by state to ensure able to meet commitments. • Particularly important for NBCR terrorism.

32. Evaluating functionality of Reinsurance • Functionality? • Price vs Value • Structure relative to clients needs • Can others pay in the case of a Nuclear event? What should you ask? • Accumulation methodology • PML vs Limits • Group-wide vs Individual entity • Considers correlations across all lines of business • Considers coverage differences • Considers terror “flavors” • Maximum loss possible • Capital

33. Evaluating functionality of Reinsurance • Proportional reinsurance limitations • Approximately 10% of volume of life companies is ceded proportionally to a small pool of reinsurers. • Earning per share versus profit center protection • Exposure versus Experience rating • 9/11 – clients show their WTC loss and are regional mid-America • Vita Capital – Swiss Re Capital Markets Adverse mortality cover • Appropriateness of Bootstrap Model over 93 years for this kind of cover? • Market share approach may be inappropriate • All losses in WTC tower 1 went to same group life insurer

34. Questions? tim.tetlow@axis.bm