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On the skew-curvature power law relationship in a stochastic volatility model with infinite variation Lévy jumps

  • Òscar Burés
  • Josep Vives
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Abstract

The short-term blow up behaviour of the ATM-IV skew is commonly modelled by either a rough volatility process with small Hurst index or an infinite variation Lévy process in the log-price dynamics. In this paper, we examine which is the effect of mixed dynamics (i.e. rough volatility and infinite variation Lévy processes) on the ATM-IV skew and curvature. The results of the paper show that the analysis of the leading terms of the short-time expansion of both ATM-IV skew and curvature allow us to determine, from a mixed dynamics model, which mechanism originates the power-law behaviour on the skew and on the curvature. Apart from showing that the mixed model also originates a power law, it has also key implications in model design and calibration. Numerical evidences for the rough Heston model with CGMY Lévy jumps are provided.

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Cite

BibTeXRIS
BibTeX
@misc{bures2026skewcurvature,
  title = {{On the skew-curvature power law relationship in a stochastic volatility model with infinite variation Lévy jumps}},
  author = {Òscar Burés and Josep Vives},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23488},
  eprint = {2610.23488},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23488},
}
RIS
TY  - UNPB
TI  - On the skew-curvature power law relationship in a stochastic volatility model with infinite variation Lévy jumps
AU  - Òscar Burés
AU  - Josep Vives
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23488
UR  - https://arxiv.org/abs/2610.23488
AB  - The short-term blow up behaviour of the ATM-IV skew is commonly modelled by either a rough volatility process with small Hurst index or an infinite variation Lévy process in the log-price dynamics. In this paper, we examine which is the effect of mixed dynamics (i.e. rough volatility and infinite variation Lévy processes) on the ATM-IV skew and curvature. The results of the paper show that the analysis of the leading terms of the short-time expansion of both ATM-IV skew and curvature allow us to determine, from a mixed dynamics model, which mechanism originates the power-law behaviour on the skew and on the curvature. Apart from showing that the mixed model also originates a power law, it has also key implications in model design and calibration. Numerical evidences for the rough Heston model with CGMY Lévy jumps are provided.
ER  -