Semi-Parametric Replication of Barrier-Style Claims on Price and Volatility
We show how to price and replicate a variety of barrier-style claims written on the log price X and quadratic variation ⟨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 maybe 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. This is joint work with Peter Carr and Roger Lee.
Professor Lorig is an Associate Professor in the Department of Applied Mathematics at the University of Washington (UW). Prior to joining UW, he worked as a Postdoctoral Scholar and Lecturer in the Department of Operations Research and Financial Engineering at Princeton. He holds a Ph.D. in Physics from the University of California -- Santa Barbara. Professor Lorig has written papers on a variety of topics within financial mathematics, including implied volatility, optimal investment, robust replication of path-dependent claims, sports betting markets, technical analysis, and, most recently, cryptocurrencies and decentralized finance.