Case Reserve Adequacy Interpolation Model

 

Case Reserve Adequacy at valuation time t is a lognormal random variable with  µ = (meanlog at time t) and s = (sdlog at time t).  Here t is the fraction:

        t =  (valuation time minus report date) / (payment date minus report date)

          = ValuationLag / PaymentLag

 

The user enters the meanlog for times 0%, 40%, 70%, and 90% (the time 0 value is labeled “case reserve adequacy” in the model).  The meanlog for time 1.0 is set at 0.0.  For any other value of t, use linear interpolation to obtain its meanlog. The modeler would also input sdlog s for times 0%, 40%, 70%, and 90%. This would give us much more flexibility in controlling the variance of the reserve adequacy factor.

 

On the simulator screen, user achieves all the parameters by setting 4 lognormal distributions marked at 0%, 40%, 70%, and 90% times.

 

We have attached a spreadsheet with illustrations of how the parameters for the Reserve Adequacy factor vary between 0 and 1.  The purpose of the spreadsheet is to illustrate the behavior of the reserve adequacy factors over time under each method.  The negative case reserve adequacy meanlog at time 0 equals ln(0.90).

Notice how the reserve adequacy mean and standard deviations become quite large if the meanlogs are significantly larger than 0.