Colloque / Séminaire

Insurance liabilities are in most cases (only) partially replicable by traded assets. This may be due to the fact that the payoffs of the underlying insurance contracts are defined in terms of a combination of hedgeable and unhedgeable claims (e.g. unit-linked insurance) or due to the existence of traded insurance-linked securities of which the payoff is correlated with the payoff of the insurance liability (e.g. CAT bonds). Since not all insurance claims can be perfectly replicated by traded assets, we face the problem of valuating claims in incomplete markets (i.e. markets in which some claims are not perfectly hedgeable).

The main goal of this presentation is to introduce different valuation frameworks for the determination of a fair valuation for insurance liabilities. The objective of this valuation is to merge the traditional actuarial valuation based on pooling and diversification with a market-consistent approach based on hedging and replication. In particular, we define a fair valuation as a valuation which is market-consistent (marked-to-market for hedgeable claims) and actuarial (marked-to-model for claims independent of financial market evolutions).

Among the different fair valuation frameworks, we introduce and investigate the class of `hedge-based valuations'. Under this approach, one unbundles the unhedgeable insurance claim in a hedgeable part and a remaining part. The fair value of the claim is then set equal to the sum of the respective values of the hedgeable and the unhedgeable parts, where the hedgeable part is valuated by the financial price of its underlying hedge, while the value of the remaining part is determined via an actuarial approach.