The Pricing of Insurance-Linked Securities Under Interest Rate Uncertainty

Key structures for insurance risk transfer to capital markets are insurance-linked securities issued by industrial corporations and insurance-reinsurance companies. This paper develops an arbitrage approach to valuing these structured products for non-catastrophic events in a framework of stochastic interest rates. Stochastic interest rates can for instance be thought as obeying the Heath, Jarrow and Morton (1992) model, if one accepts Gaussian rates, or the Cox, Ingersoll and Ross (1985) model if not. We implement techniques of change of numeraire and time, and the valuation comes down to deriving first-passage time distributions of drifted Brownian motion. We provide closed-form solutions in some situations. We highlight that prices of these structured products are driven by an interest-rate factor in addition to a nature-risk factor, the impact of which must not be underestimated. In particular, the duration of insurance-linked securities is in most cases higher than the Macaulay duration of riskfree bonds, which implies that their alleged out-performance over the latter is illusory