Hedging guarantees in variable annuities under both equity and interest rate risks

Effective hedging strategies for variable annuities are crucial for insurance companies in preventing potentially large losses. We consider discrete hedging of options embedded in guarantees with ratchet features, under both equity (including jump) risk and interest rate risk. Since discrete hedging and the underlying model considered lead to an incomplete market, we compute hedging strategies using local risk minimization. Our results suggest that risk minimization hedging, under a joint model for the underlying and interest rate, leads to effective risk reduction. Moreover, hedging with standard options is superior to hedging with the underlying when both equity and interest rate risks are appropriately modeled.