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Variable Annuities: Underlying Risks and Sensitivities

Author

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  • Imad Chahboun
  • Nathaniel Hoover

Abstract

This paper presents a quantitative model designed to understand the sensitivity of variable annuity (VA) contracts to market and actuarial assumptions and how these sensitivities make them a potentially important source of risk to insurance companies during times of stress. VA contracts often include long dated guarantees of market performance that expose the insurer to multiple nondiversifiable risks. Our modeling framework employs a Monte Carlo simulation of asset returns and policyholder behavior to derive fair prices for variable annuities in a risk neutral framework and to estimate sensitivities of reserve requirements under a real?world probability measure. Simulated economic scenarios are applied to four hypothetical insurance company VA portfolios to assess the sensitivity of portfolio pricing and reserve levels to portfolio characteristics, modelling choices, and underlying economic assumptions. Additionally, a deterministic stress scenario, modeled on Japan beginning in the mid?90s, is used to estimate the potential impact of a severe, but plausible, economic environment on the four hypothetical portfolios. The main findings of this exercise are: (1) interactions between market risk modeling assumptions and policyholder behavior modeling assumptions can significantly impact the estimated costs of providing guarantees, (2) estimated VA prices and reserve requirements are sensitive to market price discontinuities and multiple shocks to asset prices, (3) VA prices are very sensitive to assumptions related to interest rates, asset returns, and policyholder behavior, and (4) a drawn?out period of low interest rates and asset underperformance, even if not accompanied by dramatic equity losses, is likely to result in significant losses in VA portfolios.

Suggested Citation

  • Imad Chahboun & Nathaniel Hoover, 2019. "Variable Annuities: Underlying Risks and Sensitivities," Supervisory Research and Analysis Working Papers RPA 19-1, Federal Reserve Bank of Boston.
  • Handle: RePEc:fip:fedbqu:rpa19-1
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    References listed on IDEAS

    as
    1. Bacinello, Anna Rita & Millossovich, Pietro & Olivieri, Annamaria & Pitacco, Ermanno, 2011. "Variable annuities: A unifying valuation approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 285-297.
    2. Hua Chen & Samuel H. Cox, 2009. "Modeling Mortality With Jumps: Applications to Mortality Securitization," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 727-751, September.
    3. Bauer, Daniel & Kling, Alexander & Russ, Jochen, 2008. "A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities1," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 621-651, November.
    4. Milevsky, Moshe A. & Salisbury, Thomas S., 2006. "Financial valuation of guaranteed minimum withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 21-38, February.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    insurance risk; market risk; variable annuities; derivative pricing; policyholder behavior;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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