Impact of hedging on the cost of capital valuation for hybrid life insurance

In the Solvency II framework for insurance, the cost of capital rate is a critical metric that encapsulates the cost of holding capital to meet regulatory solvency requirements, while also reflecting the investor’s opportunity cost of capital allocation. It is therefore essential for insurers to rigorously justify the magnitude of this rate, particularly from the perspective of investors who perceive it as a required rate of return on capital. Albrecher et al. (2022) investigated the magnitude of this rate in the economic triangle of the policyholder, the shareholder, and the regulator. This paper seeks to extend that analysis by incorporating access to the financial market and focusing on hybrid life liabilities, which combine financial and mortality risks, thereby affording an asset-liability management perspective that insurers can employ to optimize business run-off. Furthermore, by incorporating partial hedging strategies, we show how hedging can affect both the numerator (i.e. the risk margin) and the denominator (i.e. the solvency capital requirement) of the cost of capital ratio. First, we assess whether the hedging operation has improved the insurer’s overall capital position. We then focus precisely on when the hedging operation is beneficial for both the policyholder and the shareholder, in the sense that it leads to a simultaneous reduction in their respective contributions.