Generalization of the Annuity Factor

Abstract

The well-known Annuity Factor, restricted to constant payments only, can be generalized for time dependent payments. A Generalized Annuity Factor (GAF) broadens the application potential considerably as is shown exemplarily for the valuation of loans and pension obligations. For the first time for such linear and nonlinear payments over time, compressed closed-form formulae for important financial key numbers such as present value, duration, convexity or value at risk can be derived. Moreover, easy computation makes General Annuity Factors a useful valuation tool especially in the field of finance and accounting. As General Annuity Factors can be implemented as User Defined Functions in a spreadsheet program, calculations can also be done in smaller firms or public services. Because of its computational efficiency the new instrument is also suitable for far-sighted economical models such as Asset Liability Management models (ALM) or life-cycle valuation models concerning products or investments.