A general moment formula

Vladimir Lucic ()
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Vladimir Lucic: Imperial College London

Finance and Stochastics, 2025, vol. 29, issue 4, No 8, 1233-1252

Abstract: 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.

Keywords: Implied volatility; Lee moment formula; Normalising volatility transforms; 91G60; 91G20; 60E10 (search for similar items in EconPapers)
JEL-codes: C58 G12 G13 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00780-025-00572-6

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