Semi-Parametric Pricing and Hedging of Barrier-Style Claims on Price and Volatility

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.

Introduction
SemiParametric Pricing
NonParametric Pricing
SemiParametric Approach
Assumptions
Model Assumptions
BarrierStyle Claims
Exponential Claims
Conditioning on the Path of Sigma
Replication Strategy
Pricing and Replication Strategy
Knockin Style Claims
Exponential Knockout Style Claims
Knockout Style Claim
European Style Claim
Example
Takeaway
Rebate Style Claims
How would you price and replicate
The payoff
The European claim
The main shortcoming
Time change exponential models
Variance swap
Shift operator
Proof
Discussion