Abstract
AbstractContracts paying a guaranteed minimum rate of return and a fraction of a positive excess rate, which is specified relative to a benchmark portfolio, are closely related to unit-linked life-insurance products and can be considered as alternatives to direct investment in the underlying benchmark. They contain an embedded power option, and the key issue is the tractable and realistic hedging of this option, in order to rigorously justify valuation by arbitrage arguments and prevent the guarantees from becoming uncontrollable liabilities to the issuer. We show how to determine the contract parameters conservatively and implement robust risk-management strategies.
Highlights
Many modern life-insurance policies specify minimum-rate-of-return guarantees on the capital accumulated during the life of the contract
The present paper has analysed a minimum-rateof-return guarantee combined with participation in the excess return of a given benchmark portfolio
The main focus, is on the derivation of meaningful and tractable pricing bounds on the basis of hedging strategies which are robust with respect to uncertain volatility, explicitly acknowledging the considerable model risk involved in pricing derivative financial instruments with very long maturities
Summary
Many modern life-insurance policies specify minimum-rate-of-return guarantees on the capital accumulated during the life of the contract. In this paper we seek tractable and realistic hedging strategies to justify meaningful prices for options embedded in insurance products.4 This is not an extension of existing valuation results: Given the very long maturities of the products under consideration, in order to be practically meaningful, prices and hedging strategies must take into account a high degree of uncertainty about the true dynamics of the underlying asset. The risk-management of minimum return guarantees embedded in life-insurance products appears a far more practicable application of superhedging using volatility bounds than it would be for pure financial derivatives For the latter, superhedges are typically considered too expensive to implement at a marketable price.
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