In previous posts on multi-modeling, Claire Souch and I discussed the importance of validating models and the principles of model blending. Today we consider more practical issues: how do you blend, and how does it affect pricing, rollup, and loss investigation?
No approach to blending is superior. There are trade-offs between granularity of blending ratios allowed, ease of implementation, mathematical correctness, and downstream functionality. For this reason, several methods should be examined.
Hybrid Year Loss Table (YLT)
The years, events, and losses of a hybrid YLT are selected from source models in proportion to their assigned blending weights. For example, a 70/30 blend of two 10,000-year YLTs is composed of 7,000 years selected at random from Model A and 3,000 years selected at random from Model B.
Hybrid YLTs preserve whole years and events from their source models, and drilling down and rolling up still function. But the blending could have unexpected results, as users are working with YLTs instead of directly altering EP curves. Blending weights cannot vary by return period, which may be a requirement for some users.
Simple blending produces a weighted average EP curve across the common frequencies or severities of source EP curves. Users might take a weighted average of the loss at each return period (severity blending) or a weighted average of the frequency of loss thresholds (frequency blending). Aspen has produced an excellent comparison of the pros and cons of blending frequencies vs. severities.
Simple blending is appealing because it is easy to use and understand. Any model with an EP curve can be used—it need not be event-based—and weights can vary by return period or loss threshold. It is also more intuitive: instead of modifying YLTs to change the resulting EP curve in a potentially unexpected way, users operate on the same base curves. Underwriters may prefer it because they can explicitly factor in their own experience at lower return periods.
While this is useful for considering multiple views at an aggregate level, the result is a dead end. Users can’t investigate loss drivers because a blended EP curve cannot be drilled into, and there is no YLT to roll up.
Scaled Baseline: Transfer Function
Finally, blending with a transfer function adjusts the baseline model’s YLT with the resulting EP curve in mind. Event losses are scaled so that the resulting EP curve looks more like the second model’s curve, to a degree specified by the user.
Unlike the hybrid YLT and simple blending methods, the baseline event set is maintained, and the new YLT and EP curve can be used downstream for pricing and roll-up. Blending weights can also vary by return period.
However, because it alters event losses, some drill-downs become meaningless. For example, say Model A’s 250-year PML for US hurricane is mostly driven by Florida, while Model B’s is mostly driven by Texas. If we adjust the Model A event losses so that its EP curve is closer to Model B’s, state-level breakouts will not be what either model intended.
Given the downstream complexities of blending, it may be preferable to adjust the baseline model to look more like an alternate model, without explicitly blending them. This could be a simple scaling of the baseline event losses, so that the pure premium matches loss experience or another model. Or with more sophisticated software, users could modify the timeline of simulated events, hazard outputs, or vulnerability curves to match experience or mimic components of other models.
Where does that leave us?
Over the past month, we’ve explored why and how we can develop a multi-model view of risk. Claire pointed out that the foundation to a multi-model approach first requires validation of the individual models. Then I discussed the motivations for weighting one model over another. Finally, we turned to how we might blend models, and discovered its good, bad, and ugly implications.
Multi-modeling can come in many forms: blending results, adjusting baseline models, or simply keeping tabs on other opinions. Whatever form you choose, we’re committed to building a complete set of tools to help you understand, take ownership of, and implement your view of risk.