@article {Rz{\k a}dkowski28, author = {Grzegorz Rz{\k a}dkowski and Leszek S. Zaremba}, title = {New Formulas for Immunizing Durations}, volume = {8}, number = {2}, pages = {28--36}, year = {2000}, doi = {10.3905/jod.2000.319147}, publisher = {Institutional Investor Journals Umbrella}, abstract = {The concept of duration has long been established as a standard tool for measuring and managing the interest sensitivity of a fixed-income instrument or portfolio. One important use of duration is in setting up an immunization strategy, such that the risk attached to a given future cash flow is immunized against a shift in the term structure by an offsetting hedge position that has the same duration. Earlier models in the literature developed duration-based strategies for immunizing against specific types of yield curve shifts, for example, an additive shift of a fixed number of basis points at every maturity. This article offers several new duration formulas that greatly extend the range of allowable yield curve shifts. Three theorems develop duration-based immunization techniques that cover, in the most general case, a portfolio of instruments exposed to any sum of a finite number of piecewise continuous functions. The results of previous duration models are shown to be special cases of this general formulation.}, issn = {1074-1240}, URL = {https://jod.pm-research.com/content/8/2/28}, eprint = {https://jod.pm-research.com/content/8/2/28.full.pdf}, journal = {The Journal of Derivatives} }