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Estimating the Cost of Commercial Airlines Catastrophes - A Stochastic Simulation Approach

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### Estimating the Cost of Commercial Airlines Catastrophes - A Stochastic Simulation Approach

Romel Salam, FCAS, MAAA

June 2003

Why a Stochastic Model?

- Airline risks are shared vertically by any number of primary players.
- This information is passed on to Reinsurers in the form of a questionnaire depicted in Exhibit 1.

Why a Stochastic Model?

- A primary company’s exposure can vary significantly from year to year as depicted in Exhibit 1.
- Averaging a primary company’s experience over several years likely amounts to adding apples and oranges.

Why a Stochastic Model?

- Why then not simply use an “as if” approach by applying historical ground-up airline losses to the primary company’s projected exposure?
- This would give a better picture of how the company would have performed given its current exposure level.
- However, this “as if” approach has many pitfalls as well.

Why a Stochastic Model?

- Historical Losses may not be representative of future losses as:
- Frequency of accidents (Accidents per departure unit) may have changed as a result of technological advances, better safety measures. Indications, in the US at least, are that frequency may be decreasing.
- Number of departures (or kilometers/miles flown) has been steadily increasing, doubling in the last twenty years.
- Airlines may have changed their fleet composition from say larger to smaller aircrafts or vice versa.

Why a Stochastic Model?

- Historical Losses may not be representative of future losses as:
- Passenger load factors (% of airline seating capacity that is filled) vary from year to year.
- Airlines\' passenger and destination profiles evolve.
- New aircraft models such as the Airbus 380, which could carry up to 840 passengers, are introduced in the future.
- Contracts and laws establishing the compensation of accident victims continue to evolve.
- Industry faces new risks of terrorism, war, and sabotage.

Why a Stochastic Model?

- Even 20 years of data may not be enough to produce statistically stable indications for layers exposed to rare events.
- Information on defunct airlines (say, Eastern, Pan Am) is lost.
- Indications based on an “as if” approach are likely understated even if losses are adjusted for inflation.

Why a Stochastic Model?

- A stochastic model will avoid most of the pitfalls of a traditional approach as it:
- Uses historical data to get accident rates.
- Projects trend in accident frequency.
- Applies projected frequency to current exposure units.
- Reflects current airline fleet, passenger load factors, passenger and destination profiles.
- Reflects impact of legal changes on liability costs.

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?Why a Stochastic Model?

- Only requires
- Reinsurance contract coverage information
- Cedant’s airline exposure
- Does not require
- Contract loss history
- Contract premium/rate history
- Loss triangulations

Projecting the Number of Airline Catastrophes

Choosing a frequency model

- Poisson
- Negative Binomial
- Non-parametric

Projecting the Number 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.

Projecting the Number 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.

Projecting the Number 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.

Projecting the Number 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.

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.

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.

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.

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.

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.

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.

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.

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.

A Reinsurance Example

- 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
- $1,000,000 per passenger fatality for US airlines
- $1,500,000 per injured passenger for US airlines
- $500,000 per passenger fatality for non-US Western airlines
- $750,000 per injured passenger for non-US Western airlines
- $50,000 per passenger fatality for all other airlines
- $75,000 per injured passenger for all other airlines
- Cover excludes acts of war and terrorism

A Reinsurance Example

- Layer: $4.5M XS $500K
- Covering losses occurring from Jan 1 through Dec 31, 20XX
- Reinstatements: One
- Airline exposure: from Exhibit 1

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.

Final Thoughts

- Some areas in need of more work:
- How to make realistic predictions for Third Party and Products Liability.
- Multi-aircraft collisions.
- Terrorism.

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