Hedging guarantees in variable annuities (under both market and interest rate risks)

Abstract

In order to prevent possibly very large losses, insurance companies have to devise risk management strategies for the guarantees provided by variable annuities. When hedging the options embedded in these guarantees, due to their long maturities and sensitivity to the underlying accounts tail distributions, it is important to use an appropriate model for the stochastic evolution of the account values as well as the stochastic interest rates. This paper illustrates the discrete hedging of lookback options embedded in guarantees with ratchet features, under jump risk and interest rate risk. Since discrete hedging and the model considered for the underlying price dynamics lead to an incomplete financial market, we compute hedging strategies using local risk minimization. Our numerical results show that computing the hedging strategies under a joint model for the real-world underlying price dynamics and the short interest rates, leads to effective risk reduction. We investigate the performance of hedging using underlying assets and hedging using liquid options. We illustrate that the additional effectiveness in risk reduction, achieved by hedging using options instead of the underlying, can be lost if the interest risk is not accurately modeled in the hedging computation. However, when both equity and interest rate risks are appropriately modeled, hedging with options is superior to hedging with the underlying assets. We also analyze the sensitivity of the hedging performance to the correlation between the underlying asset and the short interest rate.