Expectation of local times and the Dupire formula

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In this paper, we give a sufficient condition under which the local martingale that appears in Itô’s formula is a true martingale. As a consequence, we obtain a rigorous proof of the Dupire formula on local volatility.

Original languageEnglish
Pages (from-to)1-6
Number of pages6
JournalStochastic Processes and their Applications
Publication statusAccepted/In press - 2019


  • Dupire formula
  • Itô–Tanaka formula
  • Martingales
  • Volatility

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