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arXiv · 2609.13961

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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Masaaki Fukasawa. 2026-09-12. Yet another asymptotic formula for implied volatility. https://arxiv.org/abs/2609.13961

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