CHAPTER 4
Managing Interest Rate
Risk under Non-Parallel
Changes: An Application
of a Two-Factor Model
Manuel Moreno
4.1 INTRODUCTION
Two decades ago, fixed-income markets experienced a great increase in the
volatility of assets dealt in those markets.^1 Because of this academics and
market participants developed and implemented tools and techniques to
manage the interest rate risk. In particular, we will consider default-free
securities and liquid markets. We will distinguish two types of risk: market
risk and the yield curve one, associated to parallel and non-parallel changes
in the yield curve, respectively.
The classic solution in managing market risk is to use duration to immu-
nize a certain bond portfolio. The main assumption of duration is that the
yields of different securities change in a parallel way. Hence, duration can
be an appropriate tool to manage market risk.
However, non-parallel movements^2 in the yield curve limit the use of
duration.^3 Several duration measures associated to non-parallel movements
in the yield curve have been proposed and tested in different papers, for
example in Bierwag, Kaufman and Toevs (1983), Elton, Gruber and Michaely
(1990), Klaffky, Ma and Nozari (1992), Ho (1992) and Reitano (1992, 1996).
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