"Maximum duration of below par bonds: a closed-form furmula"

The nature of the relationship between bond’s duration and its term to maturity is somewhat complex and, contrary to what our intuition would suggest, there is not always a direct relationship between duration and maturity, in the sense that an increase in maturity does not necessarily entail an increase in duration. For bonds selling below par, an increase in maturity has the following effects: duration first increases, it reaches a maximum and then decreases. For this maximum we provide an explicit formula based on the LambertWfunction.