Severity Trend and Alpha
Modeling

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The severity trend is input by month as annualized month-over-month values, to maintain consistency with the frequency trend. Thus a factor 1.12 for a particular month means that the effective monthly trend is 1.12^(1/12). From these inputs, we can calculate a cumulative trend factor for each month.

For guidance in how
severity trend works, Robert Bear's slide 16 from 2008’s CLRS presentation
reads:

“The user may specify monthly trend factors for severity. The ‘main’ trend is allowed to operate up to the accident date and a fraction of this trend, defined by Butsic’s ‘alpha’ parameter, is allowed to operate between accident and payment dates.”

The cumulative trend
amounts (“cum”) are calculated and then the trend multiplier is
calculated:

The spreadsheet shows this calculation
for four claim examples.