Robust Replication of Barrier-Style Claims on Price and Volatility
Posted: 6 Aug 2015
Date Written: August 3, 2015
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