Put-call symmetry: Extensions and applications

Peter Carr, Roger Lee

Research output: Contribution to journalArticlepeer-review


Classic put-call symmetry relates the prices of puts and calls at strikes on opposite sides of the forward price. We extend put-call symmetry in several directions. Relaxing the assumptions, we generalize to unified local/stochastic volatility models and time-changed Lévy processes, under a symmetry condition. Further relaxing the assumptions, we generalize to various asymmetric dynamics. Extending the conclusions, we take an arbitrarily given payoff of European style or single/double/sequential barrier style, and we construct a conjugate European-style claim of equal value, and thereby a semistatic hedge of the given payoff.

Original languageEnglish (US)
Pages (from-to)523-560
Number of pages38
JournalMathematical Finance
Issue number4
StatePublished - Oct 2009


  • Barrier option
  • Local volatility
  • Put-call symmetry
  • Semistatic hedging
  • Stochastic volatility
  • Time-changed Lévy process
  • Volatility smile

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics


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