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Article

A Nonparametric Approach to Bond Portfolio Immunization

National Research University Higher School of Economics, 101000 Moscow, Russia
Mathematics 2019, 7(11), 1121; https://doi.org/10.3390/math7111121
Received: 16 October 2019 / Revised: 8 November 2019 / Accepted: 14 November 2019 / Published: 16 November 2019
(This article belongs to the Special Issue Advanced Methods in Mathematical Finance)
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. View Full-Text
Keywords: bond portfolio immunization; nonparametric hedging; interest rate term structure; smoothing splines bond portfolio immunization; nonparametric hedging; interest rate term structure; smoothing splines
MDPI and ACS Style

Lapshin, V. A Nonparametric Approach to Bond Portfolio Immunization. Mathematics 2019, 7, 1121. https://doi.org/10.3390/math7111121

AMA Style

Lapshin V. A Nonparametric Approach to Bond Portfolio Immunization. Mathematics. 2019; 7(11):1121. https://doi.org/10.3390/math7111121

Chicago/Turabian Style

Lapshin, Victor. 2019. "A Nonparametric Approach to Bond Portfolio Immunization" Mathematics 7, no. 11: 1121. https://doi.org/10.3390/math7111121

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