Closed-form solutions for Guaranteed Minimum Accumulation and Death Benefits

Abstract

Guaranteed Minimum Accumulation Benefit (GMAB) is one of the variable annuity products, i.e. new type of insurance and retirement products offering participation at the financial markets and the guarantees at the same time. In particular, GMAB offers at maturity the maximum of account value and some guaranteed benefit. This paper considers four most popular options for this guaranteed amount: capital protection, minimum interest return, ratchet and the maximum of them. As these products are exposed to different risk factors, a multi-factor model is required. However, there is often a tradeoff between a realistic model and analytical tractability. Thus, some authors simplify the contract setup or/and the modeling framework to derive closed-form solutions, others use different numerical methods to price the guarantees. This work fills this gap by providing analytical formulas for GMAB with common riders in a hybrid model for actuarial and financial risks.