Analytic Innovation and Derivation in Financial Engineering of Interest Rate Intensity Modelling and Computations

Abstract

The force of interest is a tool used to describe the instantaneous rate of growth or decline of life insurance asset over time. The core problem of this paper centers on how the instantaneous interest rate is modelled employing bivariate Taylor’s series expansion to reflect the influence of multiple interdependent factors and what implications does it have for the valuation of life insurance products. This paper explores the theoretical foundations, analytic behaviour, calibration methodology and the empirical performance of this novel model providing a more flexible and accurate approach to capturing the time-varying nature of interest rates. By extending the traditional one-dimensional Taylor series expansion, we derive a novel closed-form expression for the force of interest while incorporating the investment period horizon and allowing for the estimation of more complex, non-linear interest rate behaviors. This method analytically enables the modeling of interest rates that exhibits time-dependent changes. The two-dimensional expansion offers a powerful tool for computing the present value of future cash flows and assessing risk in financial portfolios which may be applicable in a variety of financial contexts such as bond pricing, loan amortization and pension fund valuation, highlighting its potential to enhance the robustness of traditional interest rate models