On the Impact of Stochastic Volatility, Interest Rates and Mortality on the Hedge Efficiency of GLWB Guarantees

Abstract

Variable annuity guarantees, and particularly guaranteed lifetime withdrawal benefit (GLWB) guarantees, have become very important in the wealth management industry. These guarantees, which provide to clients revenue protection while allowing them to retain equity market participation, exhibit significant systematic risks from the issuer's standpoint. Risk management of GLWB guarantees thus is a main concern for insurance companies. This paper assesses the impact of the guarantee liability modeling on the hedge efficiency of GLWB guarantees with respect to three significant systematic risks for these guarantees, that is to say, the stock market, interest rate and longevity risks. The present work thus aims to extend the hedge efficiency analysis performed in Kling et al (2011), which focuses on the stock market risk. In this paper, stochastic interest rates are shown to have primary importance in the guarantee liability modeling of GLWB guarantees. This paper also analyzes the impact of the outer loop modeling of mortality on the hedge efficiency of GLWB guarantees. A risk allocation between financial and longevity risks is used to show that longevity holds a significant share of the total risk of a hedged GLWB guarantee.