Analytical pricing of variable annuities

Increasing life expectancy as well as decreasing levels of state retirement pensions in several countries have led to the rapid growth of variable annuities (VA), products allowing guaranteed payments and participation in the financial markets at the same time. These fund-linked annuity products are frequently combined with additional living and death benefits. Due to the complex structure of these so-called Guaranteed Minimum Benefits and their exposure to different risk factors, consistent pricing of variable annuities becomes a comprehensive task. As there is often a tradeoff between realistic modeling and analytical tractability, several studies in the academic literature were either focusing on closed-form solutions and thus simplifying modeling assumptions or proposing numerical routines for the multi-factor models. This work aims to bridge the gap between these two approaches and shows how explicit analytical expressions for prices of different VA products currently offered on the market can be derived in a hybrid model for financial, insurance, and behavioral risks.