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

Research output: Contribution to journalArticleScientificpeer-review

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.
Original languageEnglish
JournalASTIN Bulletin
DOIs
Publication statusE-pub ahead of print - 31 Oct 2019

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Variable annuities
Interest rates
Smoothing
Black-Scholes
Deviation
Payment
Investors
Wealth
Financial markets
Trade-offs
Constant relative risk aversion
Habit formation
Pensions
Optimal consumption

Keywords

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

Cite this

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title = "The effect of the assumed interest rate and smoothing in variable annuities",
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.",
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author = "Balter, {Anne G.} and Werker, {Bas J. M.}",
year = "2019",
month = "10",
day = "31",
doi = "10.1017/asb.2019.27",
language = "English",
journal = "ASTIN Bulletin",
issn = "0515-0361",
publisher = "Peeters Publishers",

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The effect of the assumed interest rate and smoothing in variable annuities. / Balter, Anne G.; Werker, Bas J. M.

In: ASTIN Bulletin, 31.10.2019.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - The effect of the assumed interest rate and smoothing in variable annuities

AU - Balter, Anne G.

AU - Werker, Bas J. M.

PY - 2019/10/31

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N2 - 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.

AB - 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.

KW - optimal consumption

KW - certainty equivalent loss

KW - variable annuities

KW - assumed interest rates

KW - conversion risk

KW - smoothing financial market shocks

U2 - 10.1017/asb.2019.27

DO - 10.1017/asb.2019.27

M3 - Article

JO - ASTIN Bulletin

JF - ASTIN Bulletin

SN - 0515-0361

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