Journal
INSURANCE MATHEMATICS & ECONOMICS
Volume 114, Issue -, Pages 15-28Publisher
ELSEVIER
DOI: 10.1016/j.insmatheco.2023.10.003
Keywords
Equity-indexed annuities; Cliquet-style guarantees; Vasicek model; Stochastic interest rates
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The financial return of equity-indexed annuities depends on an underlying fund or investment portfolio complemented by an investment guarantee. This study introduces a novel scenario-matrix method for valuation and risk management, specifically for the cliquet-style or ratchet-type guarantee. Numerical tests show that this method outperforms existing approaches in terms of computation time and accuracy.
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.
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