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The nature of the dependence of the magnitude of rate moves on the rates levels: a universal relationship

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  • NICK DEGUILLAUME
  • RICCARDO REBONATO
  • ANDREY POGUDIN

Abstract

We look at the dependence of the magnitude of rate moves on the level of rates, and we find a universal relationship that holds across currencies and over a very extended period of time (almost 50 years). For the very low level of rates, we find a proportional behaviour; for rates of an intermediate level we find that the magnitude of moves becomes independent of the level. The linear dependence resumes, however, for very high rates. We find the results to be very robust across currencies, tenors and time periods. Even the data we have collected for the UK Consol yields going back to the XIX century conform closely to the same pattern. We discuss the importance of these findings for several theoretical and practical applications.

Suggested Citation

  • Nick Deguillaume & Riccardo Rebonato & Andrey Pogudin, 2013. "The nature of the dependence of the magnitude of rate moves on the rates levels: a universal relationship," Quantitative Finance, Taylor & Francis Journals, vol. 13(3), pages 351-367, February.
    • Handle: RePEc:taf:quantf:v:13:y:2013:i:3:p:351-367
    DOI: 10.1080/14697688.2012.740569
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    References listed on IDEAS

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    1. Rubinstein, Mark, 1983. "Displaced Diffusion Option Pricing," Journal of Finance, American Finance Association, vol. 38(1), pages 213-217, March.
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    Cited by:

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    2. Wujiang Lou, 2015. "Liability-side Pricing of Swaps and Coherent CVA and FVA by Regression/Simulation," Papers 1512.07340, arXiv.org.
    3. Alan L. Lewis & Dan Pirjol, 2021. "Proof of non-convergence of the short-maturity expansion for the SABR model," Papers 2107.12439, arXiv.org, revised Jul 2021.
    4. Chris Kenyon & Andrew Green, 2014. "VAR and ES/CVAR Dependence on data cleaning and Data Models: Analysis and Resolution," Papers 1405.7611, arXiv.org.
    5. Johan Hagenbjörk & Jörgen Blomvall, 2019. "Simulation and evaluation of the distribution of interest rate risk," Computational Management Science, Springer, vol. 16(1), pages 297-327, February.
    6. Arun Kumar Polala & Bernhard Hientzsch, 2024. "A case study on different one-factor Cheyette models for short maturity caplet calibration," Papers 2408.11257, arXiv.org.

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