In this paper, we measure the risk multipliers of health insurance of the four largest casualty insurance companies using their payment data from FY 2006 to FY 2010. To this end, we apply the collective risk model, and estimate the uncertainty of the parameters required for this model using the method proposed by the International Actuarial Association(IAA), along with the conventional method. The conventional method estimates uncertainty parameters with the annual variations of payment data whereas the IAA method adopts loss ratios and inflation rates.
As a consequence, we find that the risk multipliers calculated by the conventional method with real value data are larger than those of the IAA method. This is because the trends in the and of health insurance overstate the uncertainty parameters, implying that the trends, if any,might lead the conventional method to encounter model error risk.
In the IAA method, on the other hand, the uncertainty parameters are not directly affected by the trends in payment data. Nonetheless, a shortcoming of the IAA method is to assume that the uncertainty parameters in severity depend only on the variation in inflation. As such, this method does not reflect changes in public health insurance policy, and thus might be more appropriate in the absence of such significant changes.