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PreprintarXiv licencearXiv

Yet another asymptotic formula for implied volatility

  • Masaaki Fukasawa
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Abstract

We derive a first-order representation of Black-Scholes implied variance in a continuous local martingale model. Total implied variance is the conditional expectation of the quadratic variation of the log price given its terminal value, up to a smaller-order term, for bounded standardized log-strikes. The framework incorporates small volatility-of-volatility, fast mean-reverting, and short-maturity asymptotics.

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Cite

BibTeXRIS
BibTeX
@misc{fukasawa2026another,
  title = {{Yet another asymptotic formula for implied volatility}},
  author = {Masaaki Fukasawa},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13961},
  eprint = {2609.13961},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13961},
}
RIS
TY  - UNPB
TI  - Yet another asymptotic formula for implied volatility
AU  - Masaaki Fukasawa
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.13961
UR  - https://arxiv.org/abs/2609.13961
AB  - We derive a first-order representation of Black-Scholes implied variance in a continuous local martingale model. Total implied variance is the conditional expectation of the quadratic variation of the log price given its terminal value, up to a smaller-order term, for bounded standardized log-strikes. The framework incorporates small volatility-of-volatility, fast mean-reverting, and short-maturity asymptotics.
ER  -