The Risk Management of Minimum Return Guarantees

Abstract

Contracts 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.

Keywords: Minimum return guarantee, defined-contribution pension plans, life-insurance, uncertain volatility, conservative pricing, robust hedging, model misspecification, model risk

JEL Classification: G13, G22, G23