Robust Pricing of Equity-Indexed Annuities under Uncertain Volatility and Stochastic Interest Rate

TL;DR

This paper introduces a new numerical method for pricing equity-indexed annuities with complex features under uncertain volatility and stochastic interest rates, incorporating early surrender risk analysis.

Contribution

It develops a tree-based numerical algorithm combining local volatility optimization for complex market models, and compares it with machine learning approaches.

Findings

The proposed algorithm is highly effective in numerical experiments.

It accurately captures the impact of uncertain volatility and stochastic interest rates.

The framework analyzes optimal surrender strategies under complex market dynamics.

Abstract

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. The proposed algorithm is compared with a machine learning-based algorithm. Extensive numerical experiments demonstrate its high effectiveness. 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.