Explore advanced quantitative finance concepts in this Fields Institute seminar presented by Dr. Matthew Lorig from the University of Washington. Delve into semi-parametric pricing and hedging techniques for barrier-style claims on price and volatility. Learn about model assumptions, replication strategies, and various claim types including knock-in, knockout, and rebate-style claims. Examine time-change exponential models, variance swaps, and shift operators. Gain insights into the shortcomings of current methods and discuss potential improvements in pricing and hedging complex financial instruments.