Hedging and Valuation of Contingent Guarantees

We study the problem of hedging and pricing modern guarantee concepts in unit-linked life insurance policies, where the guaranteed amount grows contingent on the performance of the underlying investment fund. In contrast to standard hedging and valuation problems, the fund serves as both the underlying security and the replicating portfolio, rendering existing approaches from mathematical finance inadequate. Using the classical portfolio insurance framework, we transform the problem of hedging contingent guarantees into an equivalent fixed-point problem, whose solution leads to a set of derivatives super-replicating the guaranteed amount. Moreover, we establish sufficient conditions for the existence of such hedging derivatives and develop a fixed-point algorithm to construct them. The extended portfolio insurance framework can also be applied for the fair valuation and hedging of traditional participating life insurance policies which currently rely on approximation methods.     «

We study the problem of hedging and pricing modern guarantee concepts in unit-linked life insurance policies, where the guaranteed amount grows contingent on the performance of the underlying investment fund. In contrast to standard hedging and valuation problems, the fund serves as both the underlying security and the replicating portfolio, rendering existing approaches from mathematical finance inadequate. Using the classical portfolio insurance framework, we transform the problem of hedging c...     »