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Sequential decompositions at their limit

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  • Gero Junike
  • Hauke Stier
  • Marcus C. Christiansen

Abstract

Sequential updating (SU) decompositions are a well-known technique for creating profit and loss (P&L) attributions, e.g., for a bond portfolio, by dividing the time horizon into subintervals and sequentially editing each risk factor in each subinterval, e.g., FX, IR or CS. We show that SU decompositions converge for increasing number of subintervals if the P&L attribution can be expressed by a smooth function of the risk factors. We further consider average SU decompositions, which are invariant with respect to the order or labeling of the risk factors. The averaging is numerically expensive, and we discuss several ways in which the computational complexity of average SU decompositions can be significantly reduced.

Suggested Citation

  • Gero Junike & Hauke Stier & Marcus C. Christiansen, 2022. "Sequential decompositions at their limit," Papers 2212.06733, arXiv.org, revised Apr 2023.
    • Handle: RePEc:arx:papers:2212.06733
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    References listed on IDEAS

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    7. Solveig Flaig & Gero Junike, 2021. "Scenario generation for market risk models using generative neural networks," Papers 2109.10072, arXiv.org, revised Aug 2023.
    8. Anthony Shorrocks, 2013. "Decomposition procedures for distributional analysis: a unified framework based on the Shapley value," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(1), pages 99-126, March.
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    Cited by:

    1. Marcus C Christiansen, 2023. "Axiomatic characterization of pointwise Shapley decompositions," Papers 2303.07773, arXiv.org.

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