EQECAT's 3G Correlation™ with 3D Output
EQECAT's transparent, multi-faceted Third Generation (3G) Correlation with Three Dimensional (3D) Output leads to greater confidence in catastrophe model results, particularly losses from uncertain or unprecedented events. RQE™ and 3G enable insurers and reinsurers to retain uncertainty quantification and integrate correlation into risk allocation, underwriting, and portfolio management.
Benefits of 3G Correlation
3G Correlation helps the insurance and reinsurance industry avoid surprises that can arise from incomplete accounting for correlation. Incomplete modeling of correlation tends to underestimate extreme losses. In catastrophe risk models, correlation describes relationships among simulated events, losses, and their uncertainty. It is through correlation that a catastrophe model transforms statistical simulations into rational expectations for "real-life" losses.
Quantifying Uncertainty & Risk
Correlation is essential to quantifying uncertainty, particularly for the rarest losses, where the methodology for correlation and uncertainty matter most.
With 3G Correlation, insurers minimize the risk that a loss exceeds reinsurance cover, and re-insurers minimize underestimation of portfolio risk at the tail of the curve. Correlation affects decisions informed by low-probability, high-consequence losses:
- Risk of ruin
- Capital decisions
- Communicating risk to stake holders
- Reinsurance purchasing decisions
- Setting expectations about risk
Table 1: The highest and lowest curves depict perfect correlation (highest) and independent cases (lowest). EQECAT's exceedance curve is based on a complex correlation matrix developed from analyzing billions of dollars of claims data. The 20/80 labeling on the third curve is a common approximation used in catastrophe modeling. It combines perfect correlation and independent cases using assumed weights (in this plot 20% and 80%) in building the exceedance curve.
3G Correlation with 3D Output allows insurers and reinsurers to allocate risk and uncertainty across operational units with a statistically stable and coherent methodology, both forward and in reverse. Catastrophe losses can be incorporated directly into enterprise risk management:
- Without further simulation
- Using simple arithmetic
- Without assumptions on event loss distributions
Limitations of 1G/2G Correlation
RQE raises correlation modeling to the third generation by integrating robustness with ease of use.
First Generation - Simple and Fixed Rules
A first generation (1G) approach to correlation uses simple rules, for example, estimating a constant proportion of sites for which damage is statistically independent. The advantage of 1G is ease of use: fixed rules are straightforward and transparent to replicate when using event losses to aggregate and allocate portfolio risk.
With fixed rules for correlation, however, tail results are highly sensitive to the rule chosen. Models using 1G correlation suffer discrepancies between estimated results and observed event losses. 1G risk simulation effectively ignores tail risk because it does not allow users to carry the standard deviation into capital allocation modeling.
Second Generation - Sophisticated but Hidden
A second generation (2G) approach to correlation allows for different modeled correlation between different components of the loss distribution calculation: distance and exposure characteristics. Characterization of correlation is based on empirical analysis of loss data. The extent of correlation varies by peril and region. 2G applies different correlation relationships to each component of the loss calculation.
2G correlation models observed phenomena and robustly represents complex distributions. However, 2G results are not easy to use because the complexity and directionality of 2G calculations preclude aggregation/disaggregation of results outside of the model.
Correlation Modeling in RQE
RQE's 3G correlation modeling uses layers of multi-dimensional matrices to dynamically assess correlation with distance, time, and structure/occupancy type within a given event. Unique features of 3G include:
- Each region has a unique distance matrix with varying dimensions, as large as 30,000.
- Residing within each cell of the distance matrix is a 72x72 matrix of exposure characteristics.
- Unique correlation relationships for each pair of sites in the portfolio.
- Correlation varies with frequency and severity.
- RQE uses a high-resolution simulation with a 300,000-year horizon, the necessary level of refinement to capture extremely rare losses with confidence, yet lean enough to remain computationally efficient.
3D Output: RQE's Year Loss Table
RQE 3G Year Loss Table - Possible Event Outcomes
3G Correlation is expressed through RQE's Year Loss Table. This YLT is unique in reporting the third dimension of output: explicit representation of uncertainty as captured through multiple loss outcomes from each event. The remaining two dimensions are mean event losses and simulation year. Intra-event correlation is preserved through usage of ranked samples.
With 3G Correlation and 3D output, RQE achieves what has not yet been possible: integration of catastrophe risk model uncertainty into enterprise risk management. Risk aggregation or allocation across regions, perils, and business units retains robust representation of correlation and uncertainty with 3G and 3D.
RQE 3D Output
Conventional loss metrics can be derived from EQECAT's 3D YLT with queries or sums:
- Expected Annual Loss (EAL) = Mean sum of losses for all years
- Per Occurrence Exceedance (OEP) = Sort vector of max loss per year
- Annual Aggregate Exceedance (AEP) = Sort vector of sum of losses in each year
- Event Loss Table (ELT) = Mean & standard deviation of losses for each event
Request information about RQE catastrophe risk modeling software platform.