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Closed-Form Solutions of Higher Order Duration Measures
Sanjay Nawalkha University of Massachusetts at Amherst - Eugene M. Isenberg School of Management Nelson Lacey University of Massachusetts at Amherst January 10, 1988 Abstract: 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.
Keywords: Duration, interest rate hedging, immunization, term structure, bonds JEL Classifications: G10, G11, G12, G13, G21, G22, G23 Working Paper SeriesDate posted: May 14, 2009 ; Last revised: May 14, 2009Suggested CitationContact Information
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