Abstract

This study examines valuation and optimal surrender strategies for variable annuities with guaranteed minimum benefits under a Lévy-driven equity market and Hull-White stochastic interest rates, explicitly incorporating their correlation as an essential market feature. We propose an enhanced two-dimensional Fourier cosine method that incorporates mortality and surrender effects into a recursive valuation framework, and we analytically derive the discounted joint characteristic function for the correlated Lévy-Hull-White dynamics. Numerical experiments confirm its fast convergence and stable performance across different Lévy specifications. The results show that while correlation minimally impacts non-surrenderable contract values, it significantly influences surrender premiums through complex interactions between interest rate levels and contractual features. The key findings indicate that the impact of correlation on surrender premiums differs across interest rate environments and that guarantee design features, such as floors and caps, shape how correlation affects surrender incentives. These results underscore the necessity of scenario-specific modeling when evaluating surrender options in hybrid equity-rate markets, particularly for contracts embedding path-dependent guarantees. Our methodology advances the numerical valuation of complex annuity products by integrating cross-market dependencies with policyholder behavior dynamics.