Closed-Form Solutions of Higher Order Duration Measures

This paper derives formulas for higher order duration measures, including D(1) (i.e. Macaulay duration), D(2) (i.e., slope duration), D(3) (curvature duration), etc. We develop a general iterative method to obtain formulas for any higher order measure D(m), for an arbitrary positive integer value for m. The higher order duration measures can be used to hedge against virtually any type of interest rate shift. Our algorithm can be easily adapted for spreadsheet applications