Optimal Dynamic Longevity Hedge with Basis Risk
Tan, K.S., Weng, C., Zhang, J., 2021. Optimal Dynamic Longevity Hedge with Basis Risk. European Journal of Operational Research. In press.
30 Pages Posted: 22 Jul 2020 Last revised: 8 Jun 2021
Date Written: June 28, 2020
This paper proposes an optimal dynamic strategy for hedging longevity risk in a discrete-time setting. Our proposed hedging strategy relies on standardized mortality-linked securities and minimizes the variance of the hedging error as induced by the population basis risk. While the formulation of our proposed hedging strategy is quite general, we use a stylized pension plan, together with a specified ``yearly rolling” trading strategy involving q-forwards and a specified stochastic mortality model, to illustrate our proposed strategy. Under these specifications, we show that the resulting hedging problem can be formulated as a stochastic optimal control framework and that a semi-analytic solution can be derived through an extended Bellman equation. Extensive Monte Carlo studies are conducted to highlight the effectiveness of our proposed hedging strategy. We also consider a scheme to approximate the semi-analytic solution in order to reduce the computational time significantly while still retaining its hedge effectiveness. We benchmark our strategy against the ``delta" hedging strategy as well as its robustness to q-forwards’ maturity, reference age, interest rate, and stochastic mortality models. The proposed strategy has many appealing features, including its discrete-time setting which is consistent with market practice and hence conducive to practical implementation, and its generality in that the underlying hedging principle can be applied to other standardized mortality-linked securities and other stochastic models.
Keywords: Risk management, Pension liability management, Longevity risk, Dynamic programming, Mean-variance.
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