Benchmark Pricing of Motor Insurance Liabilities : A Hybrid Financial–Insurance Market Approach Using Insurance-Linked Securities

Sammanfattning

This thesis develops a framework for valuing motor insurance liabilities in a hybrid financial–insurance market using the benchmark approach of Platen and Heath (2006).The analysis is grounded in empirical motor insurance claims data from Söderberg & Partners, which are used to calibrate a continuous-time stochastic model for cumulative losses driven by a Cox-–Ingersoll—Ross (CIR) claim intensity process. A stylized insurance-linked security (ILS) tranche written on cumulative losses is introduced as the single risky asset, and the growth optimal portfolio (GOP) is constructed numerically via the Kelly criterion using a precomputed pricing grid and trilinear interpolation.The benchmark approach is applied to price the insurer’s stop-loss liability, representing the tail of cumulative losses exceeding a retention threshold. Because the GOP holds the ILS tranche, it is exposed to the same loss drivers as the stop-loss claim, generating a risk-adjusted discount relative to the actuarial price. The benchmark price is found to be consistently lower than the actuarial price for all economically relevant retention levels, with a relative reduction ranging from 22% to over 40% depending on the retention threshold. This reduction reflects the economic value of partial hedging of insurance tail risk through capital market instruments. From a regulatory perspective, the result provides a market-consistent interpretation of the Solvency II cost-of-capital risk margin as arising from incomplete hedgeability of insurance liabilities. Overall, the thesis contributes by combining a data-calibrated stochastic loss model with a tractable hybrid financial–insurance market, and by quantifying how insurance-linked securities reduce the effective cost of non-diversifiable risk under the benchmark approach.