Optimal VIX-linked structure for the target benefit pension plan

In this paper, we study the optimal VIX-linked target benefit (TB) pension design. By applying the dynamic programming approach, we show the optimal risk-sharing structure for the benefit payment exhibits a linear form that consists of three components: (1) a model-robust performance adjustment, (2) a counter-cyclical volatility adjustment that depends on the VIX index, and (3) a TB level that is partially indexed to the cost-of-living adjustment. Differences between our results and the previous literature are highlighted via both theoretical derivations and numerical illustrations.