1. 1 Catastrophe Modeling & Analytics August 3, 2013 Bonnie Gill, FCAS, MAAA and Emily Stoll, FCAS, MAAA

2. 2 Catastrophe Modeling & Analytics Table of Contents Key Terms General Overview of Catastrophe Modeling Cat Modeling Input, Output, and Uses Why is Catastrophe Modeling Important? A Brief History of Catastrophe Modeling Model Validation, Uncertainty and Selection

3. 3 Key Terms - What is a Catastrophe? For Property &Casualty insurers, a catastrophe is generally defined as an infrequent event that causes severe loss to a large population of exposures. Specific definition of catastrophe differs by company and for the industry as a whole. Property Claim Service (PCS) declares catastrophes if direct insured losses to property is expected to exceed $25 million and the event affects a significant number of insureds and insurance companies. Insurance companies have their own definitions that may or may not line up with PCS declared events or other companies’ definitions. The definition itself is less important than having a concrete stance whereby companies consistently code losses and process data accordingly. American Academy of Actuaries. Insurance Industry Catastrophe Management Practices. Public Policy Monograph, June 2001.

4. 4 Key Terms - What is a Catastrophe Model? A catastrophe model is a computerized system that generates a robust set of simulated events for a particular peril and the estimated financial impact for each event Estimates the frequency, intensity and location Determines the amount of damage Calculates the insured loss

5. 5 General Overview - How do Catastrophe Models Work? An Example of Model Components: HAZARD MODULE Generate Events Local Intensity ENGINEERING MODULE Estimate Damage FINANCIAL MODULE Calculate Insured Loss Exposure Data Policy Information

6. 6 Catastrophe Modeling Process- Hurricane 1. Model Storm Path & Intensity Landfall probabilities Minimum central pressure Path properties (Storm Track) Windfield Land friction effects 2. Predict Damage Values of Covered Unit (building, contents, loss of use) Vulnerability functions 3.Model Insured Claims Limits relative to values Deductibles Reinsurance

7. 7 Historical event information is used… Event Generation - Frequency to create a robust set of events

8. 8 Event Generation - Severity Primary characteristics of hurricanes that may be used to simulate each storm and resulting wind speeds –Central pressure –Radius of maximum winds –Forward speed –Track angle at landfall –Storm track –Gradient wind reduction factor –Peak weighting factor http://coastal.er.usgs.gov/hurricanes/extreme-storms/images/hurricane-diagramLG.jpg Once key parameters have been generated, the meteorological relationships among them can be used to develop a complete time profile of wind speeds for each location such as –Gradient level wind speed –Adjustment to surface level –Storm asymmetry –Storm decay –Radial decay –Adjustment of wind speed for surface friction and averaging time

9. 9 Damage Estimation Once events are generated, damage is estimated based on event and property characteristics using damage functions Damage functions are built from engineering analyses and historical information http://www.dvice.com/archives/2010/03/architects_take.php Conceptual building designed to withstand earthquakes

10. 10 Types of Losses Output from the Model Direct Physical damage to buildings, outbuildings, and contents (coverages A, B, C) Work Comp; deaths, injuries Indirect Additional Living Expense Loss of rental income Business Interruption Loss Amplification / Demand Surge For large events, higher material and labor costs, and repair delays Repair delays drive higher indirect losses and potentially more property damage

11. 11 Insurance Module Once the property owner’s pure loss has been modeled, policy characteristics are applied to calculate insured loss –Limits –Deductibles Special deductible triggers Seasonal deductibles –Reinsurance coverage –Additional coverages purchased Guaranteed replacement cost Etc.

12. 12 High Quality Exposure Information Is Critical The model can be run without policy level detail or other location specific attributes, but the more detail the better. Cat Model Input Engineering Module: Occupancy Construction Height Age Roof characteristics Location Financial Module: Limits Deductibles Policy characteristics Reinsurance information

13. 13 Data provided at ZIP level, modelled at centroid Actual exposures were concentrated on barrier island Example: Policy level vs. ZIP aggregate Cat Model Input

14. 14 Uses of Catastrophe Modeling Enterprise risk management Setting capital and risk transfer needs Reinsurance/risk transfer analysis Allocation of cost of capital, cost of reinsurance Ratemaking (rate level and rating plans) Portfolio management & optimization Underwriting/Individual risk selection Loss mitigation strategies

15. 15 Catastrophe models output loss distributions which can be used to calculate a variety of metrics including: Exceedance Probability (EP) Exceedance Probability (EP) Occurrence Occurrence Aggregate Aggregate Tail Value at Risk (TVAR) Tail Value at Risk (TVAR) Average Annual Loss (AAL) Average Annual Loss (AAL) EP TVAR AAL Cat Model Output

16. 16 Occurrence EP focuses on loss due to events Annual EP focuses on loss in a given year (accounts for multiple occurrences in a year) Curve shows the probability of exceeding various loss levels Used for portfolio management and reinsurance buying decisions Exceedance Probability: Probability that a certain loss threshold is exceeded. Exceedance Probability (EP)

17. 17 This company has a 0.4% chance of experiencing a loss of $204M or higher Occurrence EP

18. 18 “250-year return period EP loss is $204M”  Correct terminology “The $204M loss represents the 99.6 percentile of the loss distribution” “The probability of exceeding a loss of $204M from a single event is 0.4%”  Incorrect terminology It does not mean that there is a 100% probability of exceeding $204M over the next 250 events It does not mean that 1 event of the next 250 will have loss ≥ $204M “Hurricane Sandy was a 1 in 700 year event.” –Statements like these require contextual information to be fully understood. Exceedance Probability- Return Period Terminology

19. 19 A single return period loss does not differentiate risks with different tail distributions. Fails to capture the severity of less likely events. Variability in loss is not being recognized. A B C 1% RPL 1% = $50M Annual Probability of Exceedance Disadvantage of using EP as a Risk Metric

20. 20 Example:  250-year return period loss equals $204 million  TVAR is $352 million  Interpretation: "There is a 0.4% probability of a loss exceeding $204 million. Given that at least a $204M loss occurs, the average severity will be $352 million." TVAR measures not only the probability of exceeding a certain loss level, but also the average severity of losses in the tail of the distribution. Tail Value at Risk (TVAR): Average value of loss above a selected EP return period. Tail Value at Risk (TVaR) also known as Tail Conditional Expectation (TCE) Tail Value at Risk (TVAR)

21. 21 Tail Value at Risk (TVAR) TVAR is also known as Tail Conditional Expectation

22. 22 Can be calculated for the entire curve or a layer of loss AAL for layer of loss is a “window average loss” – can reflect a reinsurer’s share of loss Also called catastrophe load or technical premium Estimate of the amount of premium required to balance catastrophe risk over time. The amount of premium needed on average to cover losses from the modeled catastrophes, excluding profit, risk, non-cats, etc. Average Annual Loss: Expected value of the entire loss distribution “Area under the curve” Pure Premium Used for ratemaking Average Annual Loss (AAL)

23. 23 Why is Catastrophe Modeling Important? Limitations of Historical Hurricane Data: Hurricanes are relatively rare, potentially high severity events There are gaps in the historical record and also portions of the coast without historical events The frequency of hurricane activity has not been constant over time Therefore, the historical record does not reflect the full range of possible hurricane events

24. 24 Why is Catastrophe Modeling Important? Further Limitations of Historical Data: The ever-changing characteristics of the exposures further limits the value of historical data Property conditions have changed over the years in: –Geographic Concentration –Policy Conditions and Coverages, Deductibles –Building Materials & Building Designs –Company Marketing/Underwriting –Building Codes These limitations make the historical loss data unsuitable for directly estimating future losses

25. 25 Why is Catastrophe Modeling Important? Smith, Adam B. and Katz, Richard W. U.S. Billion-dollar Weather and Climate Disasters: Data Sources, Trends, Accuracy and Biases. http://www1.ncdc.noaa.gov/pub/data/papers/smith-and-katz-2013.pdf http://www1.ncdc.noaa.gov/pub/data/papers/smith-and-katz-2013.pdf

26. 26 Why is Catastrophe Modeling Important? An example of a change in geographic concentration –

27. 27 A Brief History of Catastrophe Modeling Before events such as Hurricane Andrew, catastrophe modeling was viewed as somewhat vague and unreliable, largely because catastrophe models produced estimates higher than events experienced to date –Example: AIR’s 1987 estimate of $20 - $30 billion hurricane loss vs. Industry experience < $1 billion

28. 28 A Brief History of Catastrophe Modeling Then… Hurricane Hugo (1989) - $6.6 billion industry insured losses The Loma Prieta Earthquake (1989) - $11.0 billion industry insured losses Hurricane Andrew (1992) - $21.6 billion industry insured losses The Northridge Earthquake (1994) - $17.0 billion industry insured losses The severity of these catastrophes demonstrated the limitations of relying exclusively on historical insurance data Due to the heightened interest in catastrophe modeling, there was an increase in the number of modeling companies, including: AIR Worldwide introduced a fully probabilistic catastrophe model in 1987 Risk Management Solutions (RMS) introduced its first earthquake model in 1988 and its first hurricane model in 1993

29. 29 A Brief History of Catastrophe Modeling Due to the size of the Northridge Earthquake and Hurricane Andrew, some insurance companies began limiting exposure in certain markets To help assure that insurance would be available for purchase, agencies were created such as –Florida Hurricane Catastrophe Fund (1993) –California Earthquake Authority (1996) Insurance and reinsurance companies increased their focus on the impact that large individual events or sequences of events could have on the insurers’ solvency, cash flow, and earnings There was a shift to using modeled data to estimate possible events with the earliest adopters being the property catastrophe reinsurance community Big push for more advanced modeling techniques

30. 30 Catastrophe Modeling Has Become the Standard Now… Catastrophe models have evolved into the industry standard –Rating Agencies (e.g. A.M. Best) now require the use of catastrophe models for determining property insurers’ ratings –Catastrophe modeling technology is used by primary insurers and reinsurance companies around the world In the US, adoption of catastrophe modeling has been primarily seen with hurricane and earthquake perils, but models for other perils are becoming more mainstream. Globally, catastrophe models are an industry standard for other perils, as well.

31. 31 Modeled Perils Natural Catastrophes –Tropical Cyclone (Hurricane/Typhoon) –Severe Thunderstorm (Tornado, Hail, Straight-line Winds) –Winter Storm (Wind, Freeze, Precipitation) –Flood –Earthquake (Shake and Fire Following) –Wildfire –Drought Man-made Catastrophes –Terrorism Other Catastrophes –EQ Workers’ Compensation –Pandemic

32. 32 Advantage of Catastrophe Models Catastrophe models provide comprehensive information on current and future loss potential. Modeled Data: Large number of simulated years creates a comprehensive distribution of potential events. Use of current exposures represents the latest population, building codes and replacement values. Historical Data: Historical experience is not complete or reflective of potential loss due to limited historical records, infrequent events, and potentially changing conditions. Historical data reflects population, building codes, and replacement values at time of historical loss. Coastal population concentrations and replacement costs have been rapidly increasing.

33. 33 Model Validation A model needs to be trusted in order to inform decisions. Actuarial Standard of Practice 38: Using a Model Outside the Actuary’s Area of Expertise The purpose of ASOP 38 is to address the actuary’s obligation to review the model When using a model outside of the actuary’s own area of expertise, the actuary should do the following: –Determine appropriate reliance on experts –Have a basic understanding of the model –Evaluate whether the model is appropriate for the intended application –Determine that appropriate validation has occurred –Determine the appropriate use of the model

34. 34 Model Uncertainty Process Risk – reflects expected variability in complex physical phenomena –law of large numbers can help to minimize Parameter Risk – additional uncertainty due to the inputs required by the model –Accurate detailed exposure data –Informed selection of assumptions Model Risk – the algorithms used may not mimic actual physical and financial processes at work in actual events –Continual update with latest science and engineering research –Augmentation to account for non-modeled sources of loss

35. 35 Model Selection It is important to consider several factors when considering which models to use (vendors/perils): –Market share / acceptance –Ease of use –Corporate cat management plans –Underwriting guidelines –Reinsurance buying history –Peril / geographic coverage –The “Best” fit for the given set of risks

36. 36 Summary Catastrophe models have become the industry standard for certain perils and may become even more prevalent in the future for additional perils Regardless of what peril is modeled, the basic structure of a catastrophe model is the same –Events are created –Damage is estimated due to those events –The resulting insured loss is calculated Quality exposure data is key to obtaining quality output There are many metrics than can be employed for many purposes Using catastrophe models can overcome many limitations inherent in using historical data to predict losses due to low frequency, high severity events As actuaries using catastrophe models, we need to be diligent in ensuring that the models are reasonable and being used for appropriate purposes

37. 37 Q & A Any Questions???