Guaranteed Minimum Benefits and Variable Annuity Hedging
The income and death-benefit guarantees insurers bolt onto variable annuities, and why hedging them turns an insurance product into something that trades like a large, long-dated equity options book.
Prerequisites: Annuity Products: Immediate, Deferred and Variable
A variable annuity ties the buyer's account value to market performance, which is exactly what makes it attractive to sell alongside a guarantee — insurers found they could charge extra for a promise that softens the downside without capping the upside, and buyers loved it. These guaranteed minimum benefits (GMxBs) are the reason a life insurer's variable annuity book can end up looking, from a risk-management desk's point of view, much less like traditional insurance and much more like a giant book of long-dated equity derivatives.
The main guarantee types
A guaranteed minimum death benefit (GMDB) promises the beneficiary receives at least a specified amount (often the original investment) even if the account value has fallen due to poor market performance by the time the policyholder dies. A guaranteed minimum income benefit (GMIB) guarantees a minimum level of annuitized income later, regardless of how the underlying investments actually performed. A guaranteed minimum withdrawal benefit (GMWB) guarantees the policyholder can withdraw a set amount each year for life, even if the account value is drawn down to zero by markets and withdrawals combined. In every case, the insurer is effectively writing a long-dated put option on the underlying fund performance, embedded inside an insurance contract, but priced and sold as a retirement guarantee rather than a derivative.
That embedded option is exactly what has to be hedged: an insurer with a large GMxB book runs a dynamic hedging program, buying and selling equity index futures, options, and sometimes interest rate derivatives to offset the sensitivity of its guarantee liabilities to market moves — very similar in spirit to a bank's options desk managing delta and vega on a large book, except the "book" is spread across millions of individual policyholder contracts with lapse behavior (whether policyholders keep or surrender the contract) adding an extra, insurance-specific wrinkle that a normal derivatives desk doesn't have to model.
A concrete instance: during a sharp equity market decline, GMDB and GMWB guarantees written years earlier suddenly move deep into the money — the account values have fallen below the guaranteed floor — forcing the insurer's hedge book to absorb large, fast-moving losses on the hedges even as the guarantee liability itself grows, precisely the scenario the hedging program exists to manage.
What this means in practice
Insurers with large legacy GMxB books (many written in the low-rate, buoyant-market years before 2008) discovered that hedging an insurance guarantee is genuinely harder than hedging a plain option, because policyholder behavior — who surrenders, who keeps paying, who takes withdrawals — doesn't move in lockstep with the market the way a derivatives counterparty's behavior would.
GMxB guarantees on variable annuities are, economically, long-dated embedded options on fund performance, and insurers manage them with dynamic hedging programs that resemble a derivatives desk's book — complicated by policyholder behavior (lapse and withdrawal patterns) that a normal options book doesn't have to account for.
It's tempting to treat GMxB hedging as a straightforward options-hedging problem once you see the resemblance. The added twist — policyholder lapse rates change with market conditions in ways that are hard to model and can move against the insurer exactly when guarantees are deepest in the money — is what makes these books harder to hedge than their derivatives-desk resemblance suggests.
Further reading
- Society of Actuaries, Variable Annuity Guaranteed Living Benefits Survey