Hedging interest rate risk by optimization in Banach spaces
The objective of this paper is to study a hedging problem that involves the term structure of interest rates (TSIR). The problem is to hedge a portfolio of multiple liabilities. The hedging instruments are coupon bonds. The authors draw on the classical one-period no-arbitrage approach of financial economics and analyze the time interval between the current date and the horizon planning period \(m\). The set of states of nature is a set of real functions on some time interval \([0,T]\) with \(T>m\) and corresponds to the feasible shocks on the TSIR. The market consists of \(n\) bonds and it is supposed that there exist functionals which provide a relationship between any shift on the TSIR and the value at \(m\) of the corresponding asset. In this framework the maximum strategies are introduced that play the role of hedging portfolios. They are introduced by means of semi-infinite mathematical programming problems. The convexity of the functionals is not necessarily required and the tax effects may be incorporated. The level of generality forces to consider a complex mathematical framework including the spaces of probability measures and other Banach spaces.
scientific article; zbMATH DE number 5189458