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

Zaremba L. S., Rządkowski G.

Control and Cybernetics

2016

Vol. 45, no. 4

525--537

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.

On influenece of the Taylor series remainder on unanticipated rates of return on fixed income bond portfolios

Olbryś J.

Control and Cybernetics

1999

Vol. 28, no 4

789-797

Changes in spot rates, unknown aprriori to investors, induce unanticipated rates of return on all financial market instruments. In this paper we introduce and investigate a concept of the rest of a bond. The concept is related to the Taylor series remainder and gives a better approximation to an unanticipated rate of return of fixed income bonds and bond portfolios. It is shown that the rest of the portfolio composed of fixed income bounds is a convex combination of the rests of these bonds. A stronger version of the theorem on rates of return on fixed income bond portfolios is given.