Immunization of bond portfolios: A new general framework

We present a new general setting for the classical immunization problem under which we recover and generalize many of the results in the literature related to immunization of bond portfolios. We also propose a new duration vector adapted to our framework that allows us to obtain immunized portfolios by duration matching. We introduce the concept of second-best portfolio that is the portfolio that produces the minimum loss in the worst-case scenario. We obtain explicit expressions for this class of portfolios when short positions are allowed or forbidden. We also show that, when immunization cannot be achieved, the second-best portfolio is the closest to the duration matching situation. Finally, we carry out a numerical illustration of our theoretical results, showing the effectiveness of the duration measures and the second-best portfolios.