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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 measure adapted to our framework that allows us to obtain immunized portfolios by duration matching. A new concept of portfolio is introduced, the second best portfolio, that is the one that produces the minimum loss in the worst-case scenario. We obtain explicit expressions for this class of portfolios in the cases of short positions allowed and forbidden. It is also shown that, when immunization cannot be attained, the second best portfolio is the closest to the duration matching situation.