Variable annuities have grown tremendously in recent years, offering life insurers
significant growth opportunities. These equity and interest rate structured products offer a
broad range of guarantees to the policyholders, and insurers must manage their risks.
The insurer’s risk management program must consider modeling and implementation
challenges beyond that of the standard capital market approach. This paper proposes
solutions to six significant issues: (1) computational efficiency, (2) impact of equity
returns and interest rate correlations on the cost of guarantee, (3) uncertain surrendering
of policies and withdrawal of account value, (4) internal transfer of funds, (5) suboptimal
exercise of options, and (6) a cost/benefit analysis of a hedging program.
These solutions are extended from the traditional capital market approach. Specifically, in
this paper, I describe the fair valuation of the guarantees using a three factor model
incorporating interest rate and equity risks. Then I use the Linear Path Space
methodology to simulate and value the risks. Finally, I simulate the effectiveness of using
a combined static-dynamic hedging program in dealing with the practical considerations
mentioned above.
Keywords: variable annuities, static-dynamic hedging, key rate duration, linear path
space, insurer’s risk management, guaranteed minimum benefits
