Formulating a Maximum-Stress-Loss Problem as a Linear Program

Summary

The document frames a portfolio stress test for zero-coupon bonds using key-rate DV01 exposures. Each maturity bucket has minimum and maximum allowed DV01 bounds, and the sum of the bucket exposures is subject to an overall limit. Given a stress vector across maturities, the proposed objective is to find the portfolio exposure combination that produces the largest loss under that scenario. This is naturally expressed as a linear optimization problem when the stress impact is linear in DV01.

The question highlights a modeling concern: how to include the aggregate DV01 restriction alongside per-maturity bounds. The document does not include an answer or a completed solution, so it supplies no worked optimization, numerical result, or evidence about a particular portfolio. The formulation is useful as a starting point, but implementation requires consistent sign conventions for DV01 and stress moves, plus precise definitions of the aggregate constraint and loss objective. The resulting maximum is conditional on the specified bounds and stress scenario.

Key ideas

• Represent each maturity bucket's bond risk with its DV01 exposure.
• Use the stress vector to define a linear loss objective over key maturities.
• Constrain each DV01 by its permitted minimum and maximum.
• Include the total DV01 restriction as an additional linear constraint.
• The maximum loss depends on the specified bounds, stress vector, and consistent sign conventions.

Tags

# LP for max stress test


# LP for max stress test












I'm trying to find a solution to the following problem:

> Assume a portfolio of $n$ zero coupon bonds mapped in risk by their respective DV01. Assume that the ZC portfolio created cannot exceed max and min set DV01 bounds on key maturities (1Y, 2Y, etc.). Also the total DV01 (sum of key maturities DV01) cannot exceed a given level (positive or negative). Assume we apply a stress vector on each key maturities. Find, for this given stress scenario, the maximum loss the portfolio could suffer from.

This seems like a classic LP problem where the objective function to minimize is the product of the actual DV01s and the stress vector, with constraints being max/min limits on individual DV01 and sum. I am getting the bounds constraints ok but having some difficulty to solve the entire problem with the additional constraint on the sum of DV01s.

Any idea how to solve this?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.