The Risk Management of Minimum Return Guarantees

Abstract. We analyse contracts which pay out a guaranteed minimum rate of return and a fraction of a positive excess rate, which is specied on the basis of a benchmark portfolio. These contracts are closely related to unit{linked life{insurance/savings plan products and can be considered as alternatives to a direct investment in the underlying benchmark portfolio. The option embedded into the savings plan is in fact a power op-tion, and thus the specication of the \fair " contract parameters is closely related to well known features of these nancial derivatives. The key issue, both in order to rigorously justify valuation by arbitrage arguments and to prevent the guarantees from becoming uncontrollable liabilities to the issuer, is the risk management of the embedded options by a tractable and realistic hedging strategy. The long maturity of life{insurance prod-ucts makes it necessary to lift the Black/Scholes assumptions and consider an uncertain volatility scenario, thus explicitly taking into account \model risk". In this context, we show how to determine the contract parameters conservatively and implement robust risk management strategies. This highlights the necessity of a careful choice of guarantees which are granted to the insurance customer and suggests a new role for a type of \bonus account " customary in many life{insurance contracts