Asset Pricing of Insurance Loss Liabilities: Some Examples

I construct examples of valuing insurance loss liabilities with asset pricing models, comparing the Rubinstein2010Leland model with the better2010known CAPM. The two models give different values only if the loss payment is asymmetric and correlated with the market portfolio, conditions which can result from the nature of the underlying loss or from the impact of insolvency on the insurer's payment. In examples where insolvency is not possible and there is no liquidity cost of raising new equity on short notice, the value of a loss liability is equal to the value of the underlying loss, i.e., of the promised coverage, and depends neither on (1) the size of the loss pool; nor on (2) the unsystematic risk of the insurer's liabilities; nor on (3) the composition of an insurer's investment portfolio; nor on (4) the amount of insurer equity. These factors do affect the value of a loss liability in examples where insolvency and liquidity costs are considered. Other things equal, if a factor increases the likelihood of insolvency, the fair value of a loss liability is lower because the insured is partially self2010insuring; but the liquidity cost of maintaining solvency by raising new equity on short notice is higher, implying a higher fair value of the loss liability.