Robust pricing of equity-Indexed annuities under uncertain volatility and stochastic interest rate

In this paper, we propose a novel methodology for pricing equity-indexed annuities featuring cliquet-style payoff structures and early surrender risk, using advanced financial modeling techniques. Specifically, the market is modeled by an equity index that follows an uncertain volatility framework, while the dynamics of the interest rate are captured by the Hull-White model. Due to the inherent complexity of the market dynamics under consideration, we develop a numerical algorithm that employs a tree-based framework to discretize both the interest rate and the underlying equity index, enhanced with local volatility optimization. Extensive numerical experiments demonstrate the high effectiveness of the proposed algorithm, which has been tested against a machine learning-based approach and yields consistent results with substantially lower computational cost. Furthermore, the numerical framework is employed to analyze key features of the insurance contract, including the delineation of the optimal exercise region when early surrender risk is incorporated.