A hybrid variable annuity contract embedded with living and death benefit riders

This paper examines a hybrid variable annuity (VA) contract combining guaranteed minimum accumulation benefit (GMAB) and guaranteed minimum death benefit (GMDB) riders, with policyholders retaining the option to surrender before maturity. The contract guarantees the return of premiums or a higher rolled-up value at maturity or upon death. A two-account structure is proposed: (i) an investment account linked to the underlying fund from which management fees are deducted, and (ii) a cash account from which GMAB and GMDB fees are deducted. This setup generalizes the traditional pricing model where all fees are continuously deducted from the investment account. The two-account framework reduces fees, discourages early surrender, and mitigates mortality risk mispricing. Additionally, bundling survival and death benefits yields higher prices, suggesting strong demand from both providers and policyholders. The model also considers taxation until a specified preservation age, aligning with practical design considerations.