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<p>In this work, we provide a generalisation and unification of several moment formulæ: the Lee moment formula in Lee (Math. Finance 14:469–480, <CitationRef CitationID="CR15">2004</CitationRef>), the log-moment formula in Raval and Jacquier (Math. Finance 33:1146–1165, <CitationRef CitationID="CR22">2023</CitationRef>) and the modified Piterbarg conjecture in Gulisashvili (Int. J. Theor. Appl. Finance 15:1250020, <CitationRef CitationID="CR11">2012</CitationRef>). We approach the problem via investigating the asymptotic behaviour of the normalising volatility transforms introduced in Fukasawa (Math. Finance 22:753–762, <CitationRef CitationID="CR8">2012</CitationRef>), rather than the implied volatility itself. Our derivations are elementary and do not rely on regular variation theory.</p>

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A general moment formula

  • 期刊论文

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  • 发表日期：

    2025年8月12日

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  • Vladimir Lucic

摘要

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.