Robust Replication of Barrier-Style Claims on Price and Volatility

36 Pages Posted: 6 Aug 2015

See all articles by Peter Carr

Peter Carr

New York University Finance and Risk Engineering

Matthew Lorig

University of Washington - Applied Mathematics

Date Written: August 3, 2015

Abstract

We show how to price and replicate a variety of barrier-style claims written on the log price X and quadratic variation 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, a zero-coupon bond, and European calls and puts with the same maturity as the barrier-style claim. We consider both single-barrier and double barrier claims in three varieties: knock-in, knock-out and rebate.

Keywords: robust pricing, robust hedging, knock-in, knock-out, rebate, barrier, quadratic variation

Suggested Citation

Carr, Peter P. and Lorig, Matthew, Robust Replication of Barrier-Style Claims on Price and Volatility (August 3, 2015). Available at SSRN: https://ssrn.com/abstract=2639454 or http://dx.doi.org/10.2139/ssrn.2639454

Peter P. Carr

New York University Finance and Risk Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States
9176217733 (Phone)

HOME PAGE: http://engineering.nyu.edu/people/peter-paul-carr

Matthew Lorig (Contact Author)

University of Washington - Applied Mathematics ( email )

Seattle, WA
United States

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