A Theory of Insurance Lapses
A Theory of Insurance Lapses
Having a good model of "lapse" is crucial to understanding insurance economics and insurance regulation. Here is why. Many life insurance policies, long-term care insurance policies, disability insurance policies, and other policies with a lengthy term generally excuse an insurer from any otherwise existing duty to pay benefits if the policy has "lapsed." Lapse means that the insured has failed to make periodic payments to the insurer required under the policy. A lapse can result in the insured "forfeiting" a large sum of money because for early years of the policy, these periodic premium payments significantly exceed expected indemnity payouts from the insurer. This excess is collected for a reason. If the policy does not lapse, during the later years of the policy when mortality or morbidity has increased significantly, but premiums have not increased commensurately, the insurer will then have earned enough profit on the policy to support the higher expected indemnity payments. Thus, the greater the likelihood of early lapse, the more an insurer tends to profit or, in a competitive market, to lower prices. "Non-forfeiture" payments the insurer is required by contract or regulation to make to the insured upon lapse thus have a tendency to reduce insurer profits or, in a competitive market, increase insurance prices. But these payments also reduce the "lapse risk" otherwise associated with purchase of an insurance policy.
This Demonstration sketches a mathematical model of lapse. The concept is that there is a distribution of insureds over vulnerability to lapse. In this Demonstration, that distribution is assumed to be beta-distributed over the interval . Some insureds who have limited ability to purchase insurance may be highly vulnerable to lapse; the smallest misfortune can cause them to divert resources to more immediate needs. Other insureds are less vulnerable; their financial situation or risk aversion induces them to keep paying even when misfortune hits. The probability of lapse during some period of time is then simply a multiple of vulnerability. As misfortunes randomly hit insureds, the most vulnerable tend to be selectively weeded out, leaving a more robust population in something resembling "the survival of the fittest". Thus, over time, lapse rates decline even if no individual changes their vulnerability.
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You model this process here by sculpting the distribution of vulnerability using two shape parameters and , which select a member from the family of beta distributions. You choose the lapse rate of the most vulnerable insured. You can see the resulting initial distribution of lapse probabilities in "initial lapse distribution" view. To see the evolution of the vulnerability distribution, choose "vulnerability distribution (3D)" for a three-dimensional view or "vulnerability distribution (Contours)" for a contour plot. To see the evolution of the number of insureds with unlapsed policies, choose "persistency over time" view. To see the evolution in the mean vulnerability of insureds, select "mean vulnerability over time" view. And to see the evolution of lapse rates, select "mean lapse over time" view. Various other controls described in the Details section let you customize the output for each of these views, including the ability to overlay some real world data collected by the United Kingdom's Financial Services Authority.
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