Tighter Bounds for Implied Volatility With the Dirac Delta Family Method
提出一种基于狄拉克δ族的算法，计算Black-Scholes隐含波动率的无模型边界，数值实验显示边界比现有文献更紧，结合Householder方法可适用于所有参数区间，并扩展到随机波动率模型下的敏感度和局部波动率计算。
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.