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Analyzing the interest rate risk of equity-indexed annuities via scenario matrices

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  • Günther, Sascha
  • Hieber, Peter

Abstract

The financial return of equity-indexed annuities depends on an underlying fund or investment portfolio complemented by an investment guarantee. We discuss a so-called cliquet-style or ratchet-type guarantee granting a minimum annual return. Its path-dependent payoff complicates valuation and risk management, especially if interest rates are modelled stochastically. We develop a novel scenario-matrix (SM) method. In the example of a Vasicek-Black-Scholes model, we derive closed-form expressions for the value and moment-generating function of the final payoff in terms of the scenario matrix. This allows efficient evaluation of values and various risk measures, avoiding Monte-Carlo simulation or numerical Fourier inversion. In numerical tests, this procedure proves to converge quickly and outperforms the existing approaches in the literature in terms of computation time and accuracy.

Suggested Citation

  • Günther, Sascha & Hieber, Peter, 2024. "Analyzing the interest rate risk of equity-indexed annuities via scenario matrices," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 15-28.
    • Handle: RePEc:eee:insuma:v:114:y:2024:i:c:p:15-28
    DOI: 10.1016/j.insmatheco.2023.10.003
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    More about this item

    Keywords

    Equity-indexed annuities; Cliquet-style guarantees; Vasicek model; Stochastic interest rates;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • 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
    • G52 - Financial Economics - - Household Finance - - - Insurance

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