ALM through embedded interest rate floor in life annuity

Abstract

The Tax-Qualified Fixed-Rate Life Annuity could be considered as a bond with embedded interest rate options which expose insurers to interest rate risks. The embedded interest rate options that insurance companies sell are the surrender option which represents book value withdrawal rights to policyowners and the interest rate floor which represents the minimum interest rate provision. The test of the gross premium rate schedule and other policy elements of the life annuity is performed using the asset-share analysis with the assumption that the interest rate in year 2020 will be about 6%. Based on the asset-share calculation, simplified Value at Risk is calculated. In the case of the life annuity, not only disbursements but also premiums are dependent on interest rates. Using the effective duration concept, sensitivity of surplus to interest rates is calculated. Excessive Option-Adjusted Spread is calculated as another measure of interest rate risks of the life annuity. The disbursements of the asset-share simulation are used in calculating the principal amount of the interest rate floor. This calculation of the notional principal is crucial in evaluating the risk of the life annuity and similar to mortgage payments. Because of many assumptions in the asset-share analysis including forward interest rates, we use as simple a stochastic term structure model as possible. We use the simplified Black-Derman-Toy model with constant volatility of forward rates. These results are compared with those of Black``s model. Because of the surrender option and the embedded interest rate floor, insurers`` positions are similar to a short position in a straddle. The time value of the interest rate floor is an additional cost of the life annuity incurred by interest rate volatility. Because Korean financial markets have no interest rate derivatives as yet, this additional cost must be managed by surplus policies such as the expense management or changing the guaranteed cost...