Closed-Form Solutions of Convexity and M-Square

7 Pages Posted: 23 May 2009

See all articles by Sanjay K. Nawalkha

Sanjay K. Nawalkha

University of Massachusetts Amherst - Isenberg School of Management

Nelson Lacey

University of Massachusetts at Amherst

Thomas Schneeweis

University of Massachusetts Amherst - Isenberg School of Management

Date Written: January 23, 1990

Abstract

Closed-form formulas for Macaulay duration, as given by Babcock and Chua, provide the user with a less cumbersome and more efficient procedure for calculating duration. Recent developments, however, have suggested alternative measures of bond portfolio immunization designed to overcome the severe restrictions that Macaulay duration places on permitted interest rate behavior. This note presents closed-form formulas for two such alternative measures - convexity and M-square and demonstrates how these measures can be used in an immunization strategy.

Keywords: bond convexity, M-square, interest rates, immunization, interest rate risk

JEL Classification: G10, G11, G12, G13, G21, G22, G23

Suggested Citation

Nawalkha, Sanjay K. and Lacey, Nelson J. and Schneeweis, Thomas, Closed-Form Solutions of Convexity and M-Square (January 23, 1990). Available at SSRN: https://ssrn.com/abstract=1408837 or http://dx.doi.org/10.2139/ssrn.1408837

Sanjay K. Nawalkha (Contact Author)

University of Massachusetts Amherst - Isenberg School of Management ( email )

Amherst, MA 01003-4910
United States
413-687-2561 (Phone)

Nelson J. Lacey

University of Massachusetts at Amherst ( email )

School of Management
Amherst, MA 01003
United States
413-545-5630 (Phone)
413-545-3858 (Fax)

Thomas Schneeweis

University of Massachusetts Amherst - Isenberg School of Management ( email )

Amherst, MA 01003-4910
United States
413-545-5641 (Phone)
413-545-3858 (Fax)

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