Effective Duration Analyses on the Policy Reserves of Life Insurance

Life insurers need to employ effective duration to measure the interest rate risk of policy reserves because the surrender rate depends on interest rates, which makes cash flows interest-rate-sensitive. This study uses a general surrender rate model and CIR interest rate model, besides assuming different interest rate sensitivities according to product characteristics. Products analyzed include term life insurance, endowment and pure endowment. We first calculate the effective durations of these products’ reserves by policy years. Then we calculate effective durations of reserves aggregated by products, and across products. Our results identify a new pattern of effective durations of policy reserves with time to maturity on three types of policies not reported by Tsai (2009). Furthermore, the gap between duration of using Treasury bonds to match policy reserves broadens as the interest rate falls.