A two-account pricing framework for hybrid variable annuity contract embedded with living and death benefit riders

This study investigates a hybrid variable annuity (VA) contract that combines guaranteed minimum accumulation benefit (GMAB) and guaranteed minimum death benefit (GMDB) riders, with the added flexibility for policyholders to surrender prior to maturity. The contract guarantees the return of premiums or a greater rolled-up value at either maturity or death. We propose a novel two-account structure: an investment account tied to the underlying fund, from which management fees are deducted, and a separate cash account for the deduction of insurance fees for funding the GMAB and GMDB riders. This design generalizes the conventional single-account model by decoupling fee sources. From the policyholder’s perspective, we derive actuarially fair insurance charges and show that the two-account framework delivers substantially lower guarantee fees compared to the classical design, improves contract characteristics by reducing the effective moneyness of embedded guarantees, thereby discouraging early surrenders and mitigating mortality risk mispricing. Furthermore, we show that bundling survival and death benefits results in higher fair fees than the sum of standalone riders, thereby enhancing the product’s appeal to insurers. The analysis also incorporates taxation considerations up to a predefined preservation age, reflecting regulatory and practical product design constraints.