Abstract
We consider the problem 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 seeks to make the sensitivities of the hedged portfolio price with respect to all model parameters equal to zero. However, within a popular approach of nonparametric (smoothing spline) term structure estimation, parametric hedging is not applicable right away. We present a nonparametric approach to hedging a bond-like obligation allowing for a general form of the term structure estimator with possible smoothing. We show that our approach yields the standard duration based immunization in the limit when the amount of smoothing goes to infinity. We also recover the industry best practice approach of hedging based on key rate durations as another particular case. The hedging portfolio is straightforward to calculate using only basic linear algebra operations.
Highlights
Hedging a bond-like obligation with a bond portfolio is a classical topic in finance, first presented in [1]
The de facto industry standard of immunizing a bond-like obligation with a portfolio of bonds is based on key rate durations
It is nonparametric in its nature, but relies on having an exogenous reference term structure of interest rates determined via piecewise linear interpolation from a set of observed benchmark zero-coupon rates
Summary
Hedging a bond-like obligation with a bond portfolio is a classical topic in finance, first presented in [1]. Estimated the dominant term structure change patterns via principal component analysis for the purpose of bond portfolio immunization Another branch of research, which is non-parametric by nature, started with Fong and Vasicek [10]. When the obligation is itself bond-like, it makes sense to price it using the bond-implied term structure to avoid the necessity to estimate the basis between swap and bond zero-coupon rates. This makes the term structure endogenous and the problem of hedging an obligation with bonds different from what was studied in the literature.
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