I have a few technical queries around the article Risks of mis-estimating mortality by Stephen Richards (The Actuary, November).
I thought that the article was very well written and useful, particularly around Solvency II and risk pricing.
First, on the correlations between the two parameters:
Were these calculated from the data? If so, do you think some of the very small values (for example -1%) are spurious and should be modified to zero?
Richards: They were calculated from the log-likelihood, which itself was calibrated to the experience data. So, the data is involved, but indirectly, via its contribution to the log-likelihood.
The small values certainly support the assertion that some parameters are uncorrelated. Whether you set these to zero, or whether you use them unmodified, will make very little difference.
Do you believe that correlations between the parameters would vary by scheme? It seems more intuitive to me that these correlations should be a feature of mortality, and not vary by scheme, whereas the actual parameter values themselves should vary by scheme. If so, do you think these could be set using a much larger dataset?
Richards: Yes, because different portfolios exhibit different correlations (and often different risk factors).
Second, on the generation of parameter sets for each portfolio valuation:
Did you generate these assuming that the parameters formed a multi-variate normal distribution?
Richards: Yes. This assumption is well-grounded for joint maximum-likelihood estimators.
Do you think a copula-type approach, potentially allowing for tail dependence, could give different
results and do you think this could be more appropriate?
Richards: It would give different results, but I don't think it would be more appropriate. The multi-variate normal distribution assumption is a well-founded asymptotic feature of maximum-likelihood estimators.