The effect of the assumed interest rate and smoothing in variable annuities
Balter,Anne Werker,Bas J.M.
Balter,Anne
Werker,Bas J.M.
Abstract
In this paper, we consider the risk–return trade-off for variable annuities in a Black–Scholes setting. Our analysis is based on a novel explicit allocation of initial wealth over the payments at various horizons. We investigate the relationship between the optimal consumption problem and the design of variable annuities by deriving the optimal so-called assumed interest rate for an investor with constant relative risk aversion preferences. We investigate the utility loss due to deviations from this. Finally, we show analytically how habit-formation-type smoothing of financial market shocks over the remaining lifetime leads to smaller year-to-year volatility in pension payouts, but to increases in the longer-term volatility.
Description
Publisher Copyright: © 2019 Astin Bulletin.
Date
2020-01
Journal Title
Journal ISSN
Volume Title
Publisher
Research Projects
Organizational Units
Journal Issue
Keywords
optimal consumption, certainty equivalent loss, variable annuities, assumed interest rates, conversion risk, smoothing financial market shocks, G22 - Insurance ; Insurance Companies ; Actuarial Studies, G23 - Non-bank Financial Institutions ; Financial Instruments ; Institutional Investors, J26 - Retirement ; Retirement Policies, D81 - Criteria for Decision-Making under Risk and Uncertainty
Citation
Balter, A & Werker, B J M 2020, 'The effect of the assumed interest rate and smoothing in variable annuities', Astin Bulletin-The journal of the International Actuarial Association, vol. 50, no. 1, pp. 131-154. https://doi.org/10.1017/asb.2019.27