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A comparison principle between rough and non-rough Heston models—with applications to the volatility surface

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  • M. Keller-Ressel
  • A. Majid

Abstract

We present a number of related comparison results, which allow one to compare moment explosion times, moment generating functions and critical moments between rough and non-rough Heston models of stochastic volatility. All results are based on a comparison principle for certain non-linear Volterra integral equations. Our upper bound for the moment explosion time is different from the bound introduced by Gerhold, Gerstenecker and Pinter [Moment explosions in the rough Heston model. Decisions in Economics and Finance, 2019, 42, 575–608] and tighter for typical parameter values. The results can be directly transferred to a comparison principle for the asymptotic slope of implied variance between rough and non-rough Heston models. This principle shows that the ratio of implied variance slopes in the rough versus non-rough Heston model increases at least with power-law behavior for small maturities.

Suggested Citation

  • M. Keller-Ressel & A. Majid, 2020. "A comparison principle between rough and non-rough Heston models—with applications to the volatility surface," Quantitative Finance, Taylor & Francis Journals, vol. 20(6), pages 919-933, June.
    • Handle: RePEc:taf:quantf:v:20:y:2020:i:6:p:919-933
    DOI: 10.1080/14697688.2020.1714702
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