Actuarially Fair Premia for Deductible Insurance Policies

Abstract

We show how to construct uniform pricing frameworks for various insurance products that have pre-specified deductibles. It is shown that the deductible insurance policies' indemnity payoff functions resemble those of distinctive derivative securities; therefore, the actuarially fair premia can be obtained using option-pricing techniques. We analytically and numerically derive the actuarially fair insurance premium for each of the five most common deductible insurance policies, namely, a proportional deductible insurance policy, a franchise deductible insurance policy, a fixed deductible insurance policy, a disappearing deductible insurance policy, and a deductible insurance policy with an upper limit on coverage. These actuarially fair premia are also depicted graphically, and it is shown that an increase in the insured asset's volatility will increase the premia, ceteris paribus.