Analyzing The Interest Rate Risk of Equity-Indexed Annuities Via Scenario Matrices

Equity-indexed annuities are popular insurance products whose performance depends on an underlying fund or investment portfolio that is complemented by an investment guarantee of an insurance provider. A technically complex version is a so-called cliquet-variant where a minimal annual return is granted. Its path-dependent payoff leads to some complexity in 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 Laplace transform 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 be converging quickly and outperforms the existing approaches in the literature in terms of computation time and accuracy