Determination of continuous shifts in the term structure of interest rates against which a bond portfolio is immunized

In this paper we identify those shifts (continuous functions) of the term structure of interest rates, against which a given bond portfolio (BP) is immunized. The set of such shifts (IMMU) happens to be an (m − 1)-dimensional linear subspace in an m-dimensional linear space of all admissible shifts. In the proof we use triangular (Lagrange) functions, by means of which we build a base for IMMU. How this IMMU space varies in response to changes in the cash flow generated by bond portfolio, BP, is also discussed in the last section of the paper.