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

Peter Carr, Roger Lee and Matthew Lorig

Applied Mathematical Finance, 2021, vol. 28, issue 6, 534-559

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.

Date: 2021
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DOI: 10.1080/1350486X.2022.2110130

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