Analyzing the interest rate risk of equity-indexed annuities via scenario matrices
针对股权指数年金中路径依赖的棘轮式保底收益，提出情景矩阵方法，在Vasicek-Black-Scholes模型下推导出终值及矩母函数的闭式解，避免蒙特卡洛模拟，快速准确计算价值和风险指标。
The financial return of equity-index 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.