Robust replication of barrier-style claims on price and volatility

Peter Carr; Roger Lee; Matthew Lorig

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arXiv · 1508.00632

Robust replication of barrier-style claims on price and volatility

Peter Carr·Roger Lee·Matthew Lorig

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Abstract

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

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Peter Carr, Roger Lee, Matthew Lorig. 2015-08-04. Robust replication of barrier-style claims on price and volatility. https://arxiv.org/abs/1508.00632

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