A Nonparametric Approach to Bond Portfolio Immunization

Mathematics. 2019. Vol. 7. No. 11. P. 1121.

Lapshin V. A.

We consider the issue of short term immunization of a bond-like obligation with respect to changes in interest rates using a portfolio of bonds. In the case that the zero-coupon yield curve belongs to a fixed low-dimensional manifold, the problem is widely known as parametric immunization. Parametric immunization aims to make the price sensitivity of the hedged portfolio  for all parameters of the model zero. However, within a popular approach to estimating non-parametric (smoothing splines) structural terms, parametric hedging is not applied immediately. We present a non-parametric approach to hedging a bond-like obligation, allowing for a common form of assessment of the timing structure with possible smoothing. We show that our approach gives standard immunization on the basis of the maximum duration, when the degree of smoothing goes to infinity. We also reinstating the industry's best hedging approach, based on the length of the key rate, as another specific case. The hedging portfolio is easy to calculate using only the basic operations of linear algebra.

Keywords: immunization, term structure of interest rates, срочная структура процентных ставок, smoothing splines, сглаживающие сплайны, иммунизация, nonparametric hedging, непараметрическое хеджирование