Enhancement of the bond portfolio immunization under a parallel shift of the yield curve

Hedging under a parallel shift of the interest rate curve is well-known for a long date in finance literature. It is based on the use of a duration-convexity approximation essentially pioneered by Fisher-Weil [2]. However the situation is inaccurately formulated such that the obtained result is very questionable. Motivations and enhancement of such approximation have been performed in our recent working paper [5],"Enhancement of the Fisher-Weil bond technique immunization". So it is seen that the introduction of a term measuring the passage of time and high order sensitivities lead to very accurate approximation of the zero-coupon price change. As a result, the immunization of a portfolio made by coupon-bearing bonds may be reduced to a non-linear and integer minimization problem. In the present work, we show that actually a mixed-integer linear programming is needed to be considered. This last can be handled by making use of standard solvers as the CPLEX software. -- yield curve ; Bond portfolio ; immunization ; optimization ; linearization