Quantitative modeling of risk management strategies: Stochastic reserving and hedging of variable annuity guaranteed benefits

Abstract

Variable annuities are enhanced life insurance products that offer policyholders participation in equity investment with minimum return guarantees. There are two well-established risk management strategies in practice for variable annuity guaranteed benefits, namely, (1) stochastic reserving based on risk measures such as value-at-risk (VaR) and conditional-tail-expectation (CTE); (2) dynamic hedging using exchange-traded derivatives. The latter is increasingly more popular than the former, due to a common perception of its low cost. While both have been extensively used in the insurance industry, scarce academic literature has been written on the comparison of the two approaches. This paper presents a quantitative framework in which two risk management strategies are mathematically formulated and where the basis for decision making can be determined analytically. Besides, the paper proposes dynamic hedging of net liabilities as a more effective and cost-saving alternative to the common practice of dynamic hedging of gross liabilities. The finding of this paper does not support the general perception that dynamic hedging is always more affordable than stochastic reserving, although in many cases it is with the CTE risk measure.