Shifts of the term structure of interest rates against which a given portfolio is preimmunized

• Autorzy: Rzadkowski G. , Zaremba L. S.
• Języki publikacji: EN

Abstrakty

EN

In this paper we formulate an immunization problem, which is rarely stated. Instead of reconstructing an existing bond portfolio B with the aim of securing a desired amount of, say L dollars, q years from now, against uncertain future interest rates shifts (under various, sometimes strong assumptions), we identify the shifts of the current term structure of interest rates against which portfolio B is already preimmunized. We state this problem in two different mathematical settings, and solve it with the help of Proposition 2 from Barber (1999), or, equivalently, Theorem 1 from Rzadkowski and Zaremba (2000). In the first part of this paper shifts are supposed to be polynomials of degree less than a certain number n, while in the second part, where we employ a Hilbert space approach, the shifts are allowed to be continuous functions.

Słowa kluczowe

EN

immunization; term structure of interest rates; polynomial shifts; Hilbert space approach

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2010
• Tom: Vol. 39, no 3
• Strony: 857--865
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Rzadkowski G.

autor

Zaremba L. S.

• Institute of Information Systems, Polish Open University, ul. Domaniewska 37A, 02-672 Warszawa, Poland

Bibliografia

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• RZADKOWSKI, G. and ZAREMBA, L.S. (2000) New formulas for immunizing durations. J. of Derivatives 8, 28-36.
• ZAREMBA, L.S. (1998) Construction of a k-immunization strategy with the highest convexity. Control and Cybernetics 27, 135-144.