Capital asset pricing models with default risk : theory and applications in insurance
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The Capital Asset Pricing Model has been used frequently to derive a fair price of insurance. But the use of this model overestimates insurance premiums because it does not account for the insolvency risk of insurers. This paper examines how the insurance price should be fairly adjusted when insurers' default risk is considered. It develops a model which shows that fair insurance premiums are lower when insurance firms have a positive probability of being insolvent. Using data of property liability insurers during the period from 1943-99, the paper further estimates the effects of the insolvency risk on insurers' underwriting profit rate. It shows that the incorporation of the default risk of insurers in the model, by significantly reducing the required price for insurance, would lead to lower profit potentials. Some writers argue that including the insolvency risk when calculating insurance premiums is not so necessary because of the existence of states' guaranty insurance funds which protect consumers. However, as shown in the paper, these funds have provided inadequate protection to consumers. Therefore, because of the increase in the number of insolvencies in recent years, and because of the limited coverage provided by states' guaranty funds, it seems that considering the insolvency risk in insurance pricing has become very necessary.