A Financial Engineering of Risk-Free Rate of Interest Determination: An Empirical Measurement and Implications for Life Insurance Valuation Under the Uniform Distribution of Death Assumption

To build confidence in the results of computational actuarial models, a key regulatory requirement is to establish a mathematically dependable process. The method employed for the estimation of interest intensities is analytically involving but only open to avid pricing actuaries. Understanding the investment process is essentially critical as actuaries seek alternative ways to develop new methodologies for the insurance industry. This paper deploys intuitive analytical and numerical representations to describe how interest rate intensities could be estimated for a broad range of configurations. The objective is carry-out an independent investigation in the analysis of nominal interest rate by constructing models for the continuous force of interest applicable in life insurance valuation. The main result consists of a generalisation of Bernoulli polynomial in modelling continuous interest rate intensity and the presentation of a series of analytically rigorous arguments. The central contribution includes the derivation of procedure for determining both lower and upper bound for the interest rate intensity. Given a tolerance limit of  ɛ = 0.04%, empirical evidence shows that the non-decreasing absolute difference of the estimated force of interest |δ_exaxct - δ_estimated| <0.4% exaxct estimated. This difference is an indication of fair performance of the model when computing the actuarial present value of expected claims and benefits.