Duration measures for specific term structure estimations and applications to bond portfolio immunization

This paper explores duration measures which are induced by a polynomial approximation to the stochastic process that governs the term structure. The paper reaches two main conclusions: (1) Complete immunization is possible only by holding a zero coupon bond if the polynomial is of a degree which is not less than two. Hence, for such polynomials, measures of immunization risk should be used to construct portfolios so as to minimize these risks. (2) The paper derives risk measures based on the polynomial stochastic process. It explores their connection to the Fong– Vasicek risk measure. This measure is a particular case of the risk measures developed here and is shown not to measure risk effectively for some stochastic processes.