Estimating the Cost of Commercial Airlines Catastrophes

1. Estimating the Cost of Commercial Airlines Catastrophes A Stochastic Simulation Approach by Romel Salam, FCAS, MAAA March 2003

2. Simulation Model Better reflects current environment in terms of exposures, frequency, fleet composition, liability and hull costs, passenger loads. Provides results that are statistically stable even for layers exposed to rare events. Allows one to better understand all the components in the loss process. More conducive to pricing covers with a lot of bells and whistles. Traditional Experience Rating May not reflect current environment Results not statistically stable, especially for layers exposed to rare events. No attempt to piece together loss components. Not very good for pricing covers with lots of contingent features. Why a stochastic Model?

4. Projecting the # of Airline Catastrophes Choosing a frequency model • Poisson • Negative Binomial • Non-parametric

5. Projecting the # of Airline Catastrophes Picking an exposure base: a) Departures b) Miles/Kilometers Flown C) Hours Flown • All three measures almost perfectly correlated. • If using different sources, make sure definitions are consistent. • Public Sources include: International Civil Aviation Organization (ICAO), International Air Transport Association (IATA), National Transportation Safety Board (NTSB). • Keep in mind these statistics were not produced with the actuary in mind.

6. Projecting the # of Airline Catastrophes Classification • May need to account for possible differences in expected frequency of catastrophic accidents amongst airlines. • US vs Rest of the World is a typical line of demarcation. Does it really make sense as far as frequency is concerned? • Rating variables could include: airline flag country, airline size, average age of fleet, fleet make up (i.e. western built vs. other). • A rating scheme is presented in Appendix A of this paper based on methodology introduced in prior writing.

7. Projecting the # of Airline Catastrophes Accounting for Trend in Frequency • Has the rate of accident changed over time? • How do we project accident rates 1, 2 or several years hence? • Use extrapolation carefully. • Choose trend curve carefully. A linear model may not be appropriate. • Simple linear regression may not be appropriate as some assumptions are violated (i.e. equal variance). • Be mindful of error of statistical estimates.

8. Accounting for Trend in Frequency

9. Projecting the # of Airline Catastrophes Modeling the number of aircrafts involved in an accident. • Need to account for the possibility of collision involving several aircrafts. • Cost of such accidents may be prohibitive. • Fortunately, these types of events are relatively rare. Hence, modeler needs to use judgment in establishing probabilities.

10. Projecting the Cost of Catastrophes Hull Cost • Need to know Airline fleet, utilization schedule and insured values as pre-agreed in contract. • If insured values are not known, find way to approximate these values. • Probability of any given aircraft involved in an accident may be based on its percentage utilization. • Others may use factors such as age and type of aircraft in figuring probability.

11. Projecting the Cost of Catastrophes Passenger Liability Cost • Need to know airline fleet, utilization schedule, approximate capacity of each aircraft, passenger load factors, survival ratios, destination profile. • Need to come up with average passenger award. • Award may vary by jurisdiction/country. • May focus on ratio of average passenger award to, say, income per capita. • May use a Classification scheme to group jurisdictions.

12. Projecting the Cost of Catastrophes Third Party Liability Cost • Highly volatile. • Not a lot of history. • One approach may be to lump Third Party Liability cost with Passenger Liability cost. • Build scenarios through judgment.

13. Projecting the Cost of Catastrophes Products Liability • Aircraft and parts manufacturers are often named in lawsuits resulting from airline accidents. • Need to allocate liability between operators and manufacturers. Specific allocation depends on determined cause of loss. • For given manufacturer, need to aggregate exposure over the universe of airline operators. • Much judgment may be needed.

14. Validation • Does the model work? Are the assumptions realistic? • Need to validate results. • Some results are easier to validate, i.e. # of accidents, # of passengers, # of fatalities. • Others are harder to validate, i.e. Passenger or Third Party Liability Costs. • One approach is to project latest ten years based on data available in all preceding years and compare with actual results.

15. Validation

17. Validation Our Hypothesis: The r’s are random draws from the F’s. Let the s’s = 1 when the r’s fall in the confidence interval, 0 otherwise. If our Hypothesis is true, then • The s’s are Bernoulli distributed w/ parameter p. • The sum of the s’s has a Binomial distribution with parameters (p,n) where n is the number of observations, 12 in this example. • Use our knowledge of the Binomial distribution to test our hypothesis. • Use same process for various values of p.

18. Terrorism • Actuary has to work with other experts to make proper assessment. Potential acts of terrorism include: • Hijackings. • Forced collision w/ other aircraft. • Surface to air missiles. • Sabotaging engine, electrical system, navigation system, or other vital equipment. • Tampering with food, water, or air. • Damaging garaged planes and equipment.

19. Terrorism • Unlike most pundits, actuary has to actually try to quantify the risk of terrorism. • Past history may not be a good guide. • Risk of terrorism is highly fluid. • Invariably, assessment will be very subjective.

20. A Simple Application • Cover for a hypothetical group of airlines for accidents occurring in the 2003 year that pays: • for the full insured value of a destroyed or damaged aircraft • $50,000 per passenger fatality • $100,000 per injured passenger • Cover excludes acts of war and terrorism

21. A Simple Application Information and Assumptions • Fleet, utilization profile, and seating capacity. • Projected departures for 2003. • Projected average passenger load. • Expected frequency of accidents per million departures. • Distribution of passenger survival ratios. • Conditional probability for the number of aircrafts involved in an accident.

22. A Simple ApplicationFleet, Utilization Profile, and Seating Capacity

24. Final Thoughts Similarly to the use of simulation in property catastrophe analysis, for commercial aviation, simulation may: • enhance the comprehensibility of prices. • reduce information risk. • promote stable pricing.

25. Final Thoughts Some areas in need of more work • How to make realistic projections for Third Party and Products Liability. • Multi-aircraft collisions • Terrorism.