Journal of Risk

Balance-sheet interest rate risk: a weighted Lp approach

Leslaw Gajek and Elzbieta Krajewska

  • A new interest rate risk measure is given in the Lp-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.

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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