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Short-maturity skew stickiness ratio under local volatility

  • Masaaki Fukasawa
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Abstract

We prove that the skew stickiness ratio converges to two at short maturity under local volatility models. This appears to be the first rigorous proof of this limit for a general time-dependent local volatility function. As a by-product, we strengthen the one-half rule of the implied volatility skew by removing uniform ellipticity and global bounds on spatial derivatives of order at least two. The proof uses a first-order Watanabe expansion.

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Cite

BibTeXRIS
BibTeX
@misc{fukasawa2026shortmaturity,
  title = {{Short-maturity skew stickiness ratio under local volatility}},
  author = {Masaaki Fukasawa},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11586},
  eprint = {2609.11586},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11586},
}
RIS
TY  - UNPB
TI  - Short-maturity skew stickiness ratio under local volatility
AU  - Masaaki Fukasawa
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11586
UR  - https://arxiv.org/abs/2609.11586
AB  - We prove that the skew stickiness ratio converges to two at short maturity under local volatility models. This appears to be the first rigorous proof of this limit for a general time-dependent local volatility function. As a by-product, we strengthen the one-half rule of the implied volatility skew by removing uniform ellipticity and global bounds on spatial derivatives of order at least two. The proof uses a first-order Watanabe expansion.
ER  -