A general moment formula
统一并推广了Lee矩公式、对数矩公式和修正的Piterbarg猜想，通过研究归一化波动率变换的渐近行为而非隐含波动率本身，推导过程初等且不依赖正则变化理论。
Abstract In this work, we provide a generalisation and unification of several moment formulæ: the Lee moment formula in Lee (Math. Finance 14:469–480, 2004), the log-moment formula in Raval and Jacquier (Math. Finance 33:1146–1165, 2023) and the modified Piterbarg conjecture in Gulisashvili (Int. J. Theor. Appl. Finance 15:1250020, 2012). We approach the problem via investigating the asymptotic behaviour of the normalising volatility transforms introduced in Fukasawa (Math. Finance 22:753–762, 2012), rather than the implied volatility itself. Our derivations are elementary and do not rely on regular variation theory.