Tighter Bounds for Implied Volatility With the Dirac Delta Family Method

Zhenyu Cui, Yanchu Liu and Yuhang Yao

Journal of Futures Markets, 2025, vol. 45, issue 11, 1970-1988

Abstract: Over decades, accurate computation of the Black–Scholes implied volatility (IV) is crucial yet still challenging for quantitative finance researchers and practitioners. In this paper, we propose a novel and robust algorithm to compute model‐free bounds of IV based on the Dirac delta family method. Numerical experiments demonstrate that these bounds are tighter than representative ones in the literature. Further combined with the Householder method, our bounds can be applied universally to all parameter regimes with higher accuracy than the alternative methods in the literature. Our method is also extended to accurately calculate IV sensitivities and the equivalent local volatility function when the underlying asset follows a stochastic volatility model.

Date: 2025
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https://doi.org/10.1002/fut.70024

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