Robust hedging of withdrawal guarantees

Withdrawal guarantees ensure the periodic deduction of a constant dollar amount from a fund for a fixed number of periods. If the fund is depleted before the last withdrawal, the guarantor has to finance the difference. Andreas Kunz derives a robust hedging strategy that leads to closed-form solutions for the guarantee value

In the life insurance industry, withdrawal guarantees have emerged in recent decades as a guarantee feature in variable annuity products. In typical guaranteed minimum withdrawal benefit (GMWB) policies, the initial annuitisation amount is invested into a fund from which fixed withdrawal payments are periodically deducted. These are guaranteed up to a specified maturity; if the fund is depleted beforehand, the guarantor has to finance the outstanding withdrawal payments (see, for example