Estimating Insurance Premiums Using Exceedance Data and the Method of Moments
Estimating Insurance Premiums Using Exceedance Data and the Method of Moments
Some experts in finance theorize that the "fair" price for a layer of insurance is a linear combination of (1) the expected losses of that layer; and (2) the increment to the insurer's standard deviation of losses in its portfolio caused by assumption of that layer of insurance. This Demonstration explores the implications of this theory by letting you set the cumulative density function for some risk, the layer of losses that will be insured, and the linear combination of expected loss and standard deviation of loss that predict the premium.
You move locators to set the cumulative density function and use the setter bar at the top to determine the family of distributions for which parameters are to be estimated. The Demonstration responds by determining the parameters of that distribution whose first two moments match the observed values.
A second part of the Demonstration lets you use the computed probability distribution. You move the sliders to establish a layer (or "tranche", as it is often known) for which an insurer has responsibility. An insurer might, for example, have to pay the difference between the insured's loss and 0.6, with that value clipped between zero and 0.5. In the trade, this would be called a "0.5 XS 0.6 policy". The Demonstration uses the computed probability distribution to determine the expected value and standard deviation of the payments an insurer writing such a tranche would face. It then uses a conventional load coefficient and risk load coefficient that you set to determine the premium an insurer writing this layer would likely charge. The increment to the standard deviation of losses in the insurer's portfolio is approximated as a value proportional to the standard deviation of the losses of the specified layer of insurance.