Risk Margin Calculation for Lapse Risk in Guaranteed Minimum Accumulation Benefit of Variable Annuities-A Market-Consistent Approach

Abstract

In 2002, variable annuities were introduced in South Korea and have shown enormous success since then. They are life-insurance products with investment guarantees. Variable annuities allow policyholders to allocate premiums into a wide range of investment vehicles such as stocks, bonds, money market instruments, or some combinations of them. Due to the investment guarantee which is called guaranteed living benefits (GLBs), the benefit is always the greater of (1) the account value of the policyholder investment and (2) the guaranteed amount. Life insurance companies set aside reserves for the guarantees in the general account. Just as the account value depends on the performance of investments, VA lapses also rely on the performance of investments. For example, policyholders will not terminate the contracts when account value is way lower than the guaranteed amount. Considering that lapses determine the total benefit of VAs that a insurance company should pay, calculating risk margin for lapse is a key issue in the VA business. In this study, risk margin for VA lapses is estimated with Wang transform suggested by Wang (2000, 2002).