Construction of a k-immunization strategy with the highest convexity

• Autorzy: Zaremba L.
• Języki publikacji: EN

Abstrakty

EN

Assuming that interest rate shocks are proportional to their values plus one, we prove in Theorem 1 the existence of and construct a portfolio Z[sup *] with the highest convexity in the class of portfolios that solve the immunization problem to meet the liability to pay C dollars K years from now. Z[sup *] appears to be a barbell strategy with two zero-coupon bonds with the shorest and the longest maturities. This intuitively clear result has been obtained here in a rigorous way by means of the K-T conditions. In addition, we show that our result is stricly related to the problem of maximization of the unanticipated rate of return on a portfolio solving the above immunization problem (Theorem 2). Two more results concerning the unanticipated return after K years are provided with proofs. An example illustrating the role of convexity in maximization of the unanticipated return is included. Despite the fact that there exists a pretty vast literature on bond portfolio strategies, the present paper offers a new methodological approach to this area (see Ingersoll, Skelton, Weil, 1978).

Słowa kluczowe

EN

convexity; immunization; K-T conditions; unanticipated return

PL

immunizacja; wypukłość

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 1998
• Tom: Vol. 27, no 1
• Strony: 135--144
• Opis fizyczny: Bibliogr. 8 poz.,

Twórcy

autor

Zaremba L.

• Systems Research Institute, Polish Academy Sciences, Warszawa, Poland,