Balance-sheet interest rate risk: a weighted Lp approach

Leslaw Gajek; Elzbieta Krajewska

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A new interest rate risk measure is given in the L^p-space of financial instruments.
This measure is a product of two components: one is related to the specific risk of the portfolio and the other to the systematic risk of the market.
The measure bounds the expectation of the net present value of an insurer’s portfolio in a stochastic environment.
The bound is valid for the interest-sensitive cash flows.

Abstract

We introduce a new interest rate risk measure that is a product of two factors: one related to the distance between assets and liabilities in the Lp-space of financial instruments, and the other linked to the performance of the financial market. We prove a corresponding immunization inequality, showing that the expected deficit of assets, when compared with liabilities, is bounded from below by a linear function of this measure. We provide comparisons with other interest rate risk measures, such as duration gap and M² , and give examples of applications to some models of interest rates.

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