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. 

 

Key assumptions underlying this spreadsheet are 1) no correlation specified between lag and size of the loss, 2) all dates are at the same time in each month, so that all lags are whole months, and 3) the model is the single payment model.