Valuing Lifetime Withdrawal Guarantees in RILAs

Abstract

In recent years, registered index-linked annuities (RILAs) have reinvigorated the equity-linked annuities market in the United States. Now insurers are beginning to add lifetime withdrawal guarantees (GLWBs) to these products. GLWBs have been well studied in the context of traditional variable annuities, where they are infamous for the risk exposure they create on insurers’ balance sheets. In this study, we present a simple pricing model for GLWBs embedded in RILA policies and offer an extensive numerical illustration that quantifies their pricing and risk exposure for various RILA contracts. We find that a GLWB rider—unlike for fixed index annuities—exposes RILA carriers to considerable long-term financial risks, comparable to a variable annuity account with a heavily reduced equity exposure (∼40%).

ACKNOWLEDGMENTS

We are grateful to the editor Michael Sherris as well as two anonymous reviewers and participants at the Virtual 24th International Congress on Insurance: Mathematics and Economics and at the 56th Actuarial Research Conference for their helpful comments.

Notes

1 Source: LIMRA Secure Retirement Institute.

2 The carriers are: Allianz, Athene, Brighthouse, CUNA, Equitable, Jackson, Lincoln, MassMutual/Great American, Nationwide, Protective, Prudential, RiverSource, and Symetra.

3 In addition, Hsieh et al. (2018) proposed embedding a GLWB rider in a long-term care annuity.

4 Which type and level of downside protection is preferable depends largely on the investor’s risk preferences (Moenig and Samuelson, 2022). Because RILA + GLWB contracts can theoretically be offered on either of these three mechanisms, we remain agnostic about this issue for the purpose of our study.

5 The investor can, of course, at any time terminate the policy and take the account value as a lump sum or convert it into a fixed annuity. However, this would mean that the investor has paid many years for a guarantee only to then not take advantage of it.

6 Note that withdrawals are initially taken from the investor’s RILA account and are only drawn from the insurer’s general account after the RILA account value has been reduced to 0.

7 Moenig (2022) further documented that insurers regularly adjust the cap rates in response to changing market conditions. That is, in the first contract year the investor may get a 12% cap rate but upon renewal of the contract for the second year the cap rate is reduced to 11% (or increased to 13%, depending on the new market prices of the underlying options).

8 For C = 0, the left-hand side of Equation (11)(11) $$A_t^{+}·\left(1-v_{t,\tau }\right)+A_t^{+}·{\phi }_R·\tau -H_t^D(C,P^u)=0,$$(11) is strictly positive. Moreover, the expression is monotonically and continuously decreasing in C (because a larger cap implies a lower surplus). Therefore, if there is no value $C\ge 0$ that satisfies Equation (11)(11) $$A_t^{+}·\left(1-v_{t,\tau }\right)+A_t^{+}·{\phi }_R·\tau -H_t^D(C,P^u)=0,$$(11) , the insurer must make a positive surplus even when the RILA contract offers unlimited upside potential.

9 Note that none of this is necessary in the absence of the GLWB rider, because the insurer can simply set the new cap rate each year based on observable option prices at the time. However, the GLWB fee rate ${\phi }_G$ must be set ahead of time and applies to the entire duration of the contract; hence the necessity for these long-term projections.

10 Systematic mortality risk can be incorporated via the survival probabilities ${}_t{p}_x.$

11 To keep the simulation finite, we set the maximum attainable age of the policyholder as 122 years.

12 Note that though an expected annual return of 8.25% may appear overly optimistic from the perspective of the year 2022, most of our analyses—with the exception of Table 4—are carried out under the risk-neutral probability measure and are thus not impacted by this expected return parameter choice.

13 Specifically, we simulate 1 million independent potential values of the insurer’s loss random variable L₀ based on a starting account value of 1000 and again based on a starting account value of 1001 (using the same simulated index returns). We then average these simulated values and apply the following formula to obtain the GLWB’s delta.

14 Interestingly, however, many RILA contracts tend to have a negative 95% “value at risk” for the insurer’s net loss from the GLWB rider. That is, under our baseline model specifications, less than 5% of simulated paths (under the real-world probability measure) result in the GLWB rider causing a net loss to the insurer for these contracts, because of projected GLWB payouts exceeding rider fees.

15 We implement Merton’s jump diffusion model (Merton 1976), calibrated to the same historical S&P index returns as the baseline specification. See the Appendix for details.