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

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  • Peter Carr
  • Roger Lee
  • Matthew Lorig

Abstract

We show how to price and replicate a variety of barrier-style claims written on the log price X and quadratic variation $ \langle X\rangle $ 〈X〉 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.

Suggested Citation

  • Peter Carr & Roger Lee & Matthew Lorig, 2021. "Semi-Robust Replication of Barrier-Style Claims on Price and Volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 28(6), pages 534-559, November.
  • Handle: RePEc:taf:apmtfi:v:28:y:2021:i:6:p:534-559
    DOI: 10.1080/1350486X.2022.2110130
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