A general moment formula
File(s)
Published version
Author(s)
Lucic, Vladimir
Type
Journal Article
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.
Date Issued
2025-10-01
Date Acceptance
2025-02-20
Citation
Finance and Stochastics, 2025, 29 (4), pp.1233-1252
ISSN
0949-2984
Publisher
Springer
Start Page
1233
End Page
1252
Journal / Book Title
Finance and Stochastics
Volume
29
Issue
4
Copyright Statement
© The Author(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4315582
Subjects
implied volatility
Lee moment formula
normalizing volatility transforms JEL Classification: C58 -G12 -G13 Mathematics Subject Classification: 91G60 -91G20 -60E10
Publication Status
Published
Date Publish Online
2025-08-12