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A general moment formula

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  • Vladimir Lucic

    (Imperial College London)

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.

Suggested Citation

  • Vladimir Lucic, 2025. "A general moment formula," Finance and Stochastics, Springer, vol. 29(4), pages 1233-1252, October.
    • Handle: RePEc:spr:finsto:v:29:y:2025:i:4:d:10.1007_s00780-025-00572-6
    DOI: 10.1007/s00780-025-00572-6
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    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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