Semi-Robust Replication of Barrier-Style Claims on Price and Volatility

Peter Carr, Roger Lee, Matthew Lorig

Research output: Contribution to journalArticlepeer-review


We show how to price and replicate a variety of barrier-style claims written on the log price X and quadratic variation (Formula presented.) of a risky asset. Our framework assumes no arbitrage, frictionless markets and zero interest rates. We model the risky asset as a strictly positive continuous semimartingale with an independent volatility process. The volatility process may exhibit jumps and may be non-Markovian. As hedging instruments, we use only the underlying risky asset, zero-coupon bonds, and European calls and puts with the same maturity as the barrier-style claim. We consider knock-in, knock-out and rebate claims in single and double barrier varieties.

Original languageEnglish (US)
Pages (from-to)534-559
JournalApplied Mathematical Finance
Issue number6
StatePublished - 2021


  • barrier
  • knock-in
  • knock-out
  • quadratic variation
  • robust hedging
  • Robust pricing

ASJC Scopus subject areas

  • Finance
  • Applied Mathematics


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