The effect of the assumed interest rate and smoothing in variable annuities

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2 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)131-154
Number of pages24
JournalASTIN Bulletin
Issue number1
Publication statusPublished - Jan 2020


  • optimal consumption
  • certainty equivalent loss
  • variable annuities
  • assumed interest rates
  • conversion risk
  • smoothing financial market shocks


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