Variable Annuities with High Water Mark Withdrawal Benefit
17 Pages Posted: 14 Dec 2016
Date Written: December 12, 2016
In this paper, we develop a continuous-time model for variable annuities allowing for periodic withdrawals proportional to the high water mark of the underlying account value as well as early surrender of the policy. We derive a HJB variational inequality characterizing the minimal superhedging price of such a contract and the worst-case policyholder behavior from an issuer's perspective. Based on these results, we construct a dynamic trading strategy which superreplicates the contract. In addition, we show how early surrender has to be penalized to disincentivize a worst-case policyholder from using this option. To treat the problem numerically, we develop a semi-Lagrangian scheme based on a discretization of the underlying noise process.
Keywords: variable annuities, early surrender, stochastic control, optimal stopping, Hamilton--Jacobi--Bellman variational inequality
JEL Classification: C61, C63, G22, J32
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