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Correlation: Catastrophe Modeling’s Dirty Secret

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Presentation on 3G Correlation for catastrophe modeling by Bill Keogh, President of EQECAT, at the RAA Conference in Orlando, FL (Feb 2011).

Presentation on 3G Correlation for catastrophe modeling by Bill Keogh, President of EQECAT, at the RAA Conference in Orlando, FL (Feb 2011).

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  • This is intended to be the agenda slide. Hazard and vulnerability are discussed a lot, but not much on correlation. Very important and high impact on understanding tail risk. Northridge, steel construction, correlation matters.?
  • The big picture slide – who cares? The answers will be provided in future slides, but this slide gives the big picture answer: ILS covers extreme events, extreme events may be the result of the correlation between components, and ignoring correlation in cat modeling can have negative consequences.Can
  • This perhaps should be two slides. Idea is to provide a verbal / intuitive description of what we are talking aboutNOTE: one possibility would be to put the dictionary definition in grayed out background and have 2nd and 3rd points in foreground Tom’s thoughts:
  • "weather perils are clustered in heavy activity seasons due to persistent weather patterns that may last a season or more" Our models have clustering, and our usage of clustering is defendable with ample research and empirical data, non-poisonnian technique.
  • Need to check with Ken to make sure that we don’t say something unsupportable wrt EQ faultsDifference in clustering for weather than seismo events as weather clustering is likely on a yearly basis. Seismic clustering / time dependency… happens over much longer time frames.
  • Correlation does NOT impose identical behavior- but expresses the quantifiable likelihood of outcomes being similarPost-event observations of damage patterns identify pockets of damage that are explainable by common construction attributes (1971 San Fernando - extreme damage to House-over-Garage "Brady Bunch" split level houses, 1992 Hurricane Andrew destruction to new homes and apartments in Homestead, but much less damage in neighboring and windward Coral Gables, ...)Modeling of complex correlation matrix leads to 2G difficulty to be discussed laterCorrelation is quantifiable through analysis of claims dataNot all features result in correlated response (i.e. given all else being the same, like colored warehouses aren’t likely to have more highly correlated response to a hurricane than warehouses of different colors. But warehouses are more likely to respond in a more correlated fashion than a warehouse and a house)
  • On this slide or next, provide plot of distributions of the two pofs, AND tables with losses at varying probabilities.
  • The table with the penetration probabilities are numbers off the CDF for the two distributions (correlated, uncorrelated). I arbitrarily chose levels associated, with "working layer" (for my test, working layer attaches at about the mean), "cat" (mean + 50% or so is the attachment point), and "super cat" is a little more than double the mean. The point here is to reinforce the impact of this bias - for lower layers, the correlated group has a higher probability of very low losses (the outcome of low loss at site A & low loss at site B is higher if they are more likely to swing in tandem).Why is this an important point? Return back to the message of reducing "surprises". If a model has a consistent bias (always low, always high) it can be adjusted with scalars. If a model has an inconsistent bias, you don't know if your model result will be too high or too low until after the loss occurs (surprise!).
  • Consideration of correlation a modeling input just like vulnerability, hazard, etc. Yet this method may be overly simplistic compared to the other aspects of the model implementation

Correlation: Catastrophe Modeling’s Dirty Secret Presentation Transcript

  • 1. Correlation: Catastrophe Modeling’s Dirty Secret
  • 2. Correlation: Catastrophe Modeling’s Dirty Secret
    Why is it important?
    The phenomena of correlation
    The evolution of modeling of the phenomena
    Setting rational expectations about risk
  • 3. Why Correlation is important
    Extreme events
    The “tail of the curve” is where correlation has a large impact
    correlation not accounted for can result in unpleasant surprises
    Like hazard and vulnerability, correlation modeling affects model performance
    Overestimation and underestimation both problematic
    Setting rational expectations about risk
  • 4. Why it matters
    The more leverage, the more it matters (i.e. further out on the tail)
    What decisions do we make out in the tail?
    Risk of ruin
    Pricing
    Capital decisions
    Communicating risk to stake holders
    Reinsurance purchasing decisions
    Setting expectations about risk
    Setting rational expectations about risk
  • 5. The Phenomena of Correlation
    Dictionary definition - Statistics . the degree to which two or more attributes or measurements on the same group of elements show a tendency to vary together.
    Correlation is the measure of how likely distributions of outcomes are to behave the same way, or not
    Cat modeling involves quantifying outcome distributions (uncertainty) – correlation describes the tendency or lack thereof of distributions to be in lockstep
    Setting rational expectations about risk
  • 6. High correlation
    Setting rational expectations about risk
  • 7. Low correlation
    Setting rational expectations about risk
  • 8. Dimensions of correlation
    Spatial
    Temporal
    Loss response
    Setting rational expectations about risk
  • 9. The Phenomena of Correlation: Spatial
    Correlated hazard / losses due to large footprint events
    Cyclones affecting multiple regions in a basin
    Earthquake rupture descriptions: cascading fault ruptures
    Windstorm footprints
    Correlation through event definition: Ike and inland losses
    Setting rational expectations about risk
  • 10. Spatial Correlation in Europe
    Windstorm Daria
    Setting rational expectations about risk
  • 11. The Phenomena of Correlation: Spatial
    Hazard characterization implies regional correlation (intended or not)
    Are adding Eurowind portfolios, for example France only portfolio to Germany only portfolio
    Diversifying (uncorrelated)
    Concentrating (correlated)
    Setting rational expectations about risk
  • 12. The Phenomena of Correlation: Temporal
    Clustering: weather perils are clustered due to atmospheric conditions
    Global temporal weather correlation does exist
    AMO for North Atlantic Hurricanes
    ENSO cycle
    Setting rational expectations about risk
  • 13. The Phenomena of Correlation: Temporal
    Earthquake events may have complex correlations to each other
    Events on same fault may be negatively correlated (time dependency)
    Stress release / transfer could provide mechanism for positive correlation
    Global correlation possible, but
    still under investigation
    Setting rational expectations about risk
  • 14. Loss Response
    Setting rational expectations about risk
  • 15. The Phenomena of Correlation: Loss Response
    In an event, damage response of structures IS correlated to varying degrees among different classes of exposure
    Level of correlation between exposure classes differ – > multi-dimensional correlation matrix
    Examples:
    Occupancy
    Distance
    Response characteristics (based on construction, building height, components)
    Setting rational expectations about risk
  • 16. Modeling of Correlation: example
    Correlated: Significant probability of high-severity additive outcome
    +
    =
    fy(y)
    fx(x)
    Uncorrelated: Additive sum clustered close to the mean
    fxy(x+y)
    Setting rational expectations about risk
  • 17. Modeling of Correlation: sensitivity and impact on layering (illustration)
    The impact upon conditional probabilities of penetration is an inconsistent (insidious) bias: sometimes high, sometimes, low.
    Not accounting for correlation will always under-estimate tail event probabilities
    Setting rational expectations about risk
  • 18. First Generation Correlation Modeling (1G)
    Assume a reasonable but simple rule for correlation (i.e. 80/20)
    But ignores wealth of empirical data we have on this problem
    Provides a transparent means for adding portfolios (aggregation of risks)
    Calculation methods straight-forward
    Tail results will be highly influenced by the rule chosen
    but not robust….
  • 19. Second Generation Correlation Modeling (2G)
    Allow for model differing correlations between different components of the loss distribution calculation:
    Occupancy
    Location
    Structural Characteristics
    Base characterization of correlation on study of loss data (empirical –varies by peril and region)
    Apply differing correlation relationships to different aspects of the loss calculation
    Setting rational expectations about risk
  • 20. Second Generation Correlation Modeling (2G)
    Provides more robust modeling of phenomena
    Represents complex distributions more precisely
    Complexity and directionality of calculations precludes aggregation / disaggregation outside of the model
    Setting rational expectations about risk
  • 21. Second Generation Correlation Modeling (2G)
    but not easy…
    Setting rational expectations about risk
  • 22. Third Generation Correlation Modeling (3G)
    Will employ the robustness of 2G approach
    And the ease of use of 1G approach
    Setting rational expectations about risk
  • 23. EQECAT WORLDCATenterprise Re-architecture
    Performance 
    Step change in speed
    Reliability 
    Reduce need for hot fixes
    Completeness
    Most robust data base schema
    Consistency
    Common building and occupancy classifications
    Transparency 
    Access to insight
    Setting rational expectations about risk
  • 24. Delivering 3G correlation
    June 2011 – Robust correlation and the ability to aggregate portfolios analytically and extract event output
    2012 – robust correlation and the ability to aggregate and disaggregate portfolios “on the fly” and outside of the model.
    Setting rational expectations about risk