On numerical stability of recursive present value computation method

TL;DR

This paper investigates the numerical stability of recursive present value calculations, revealing exponential error growth at positive discount rates and proposing a reversed calculation method for improved robustness.

Contribution

It introduces a reversed recursive approach that enhances numerical stability in present value computations compared to traditional methods.

Findings

Error grows exponentially with positive discount rates in standard recursion

Reversing the recursion direction improves numerical stability

Revised method reduces computational inaccuracies in PV calculations

Abstract

We analyze numerical stability of a recursive computation scheme of present value (PV) amd show that the absolute error increases exponentially for positive discount rates. We show that reversing the direction of calculations in the recurrence equation yields a robust PV computation routine.