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

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.

Automated summary

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.