After a brief introduction to the concepts and history of Risk Neutral derivative pricing in finance, and the basic practice of options trading, it will be shown how derivative problems can be connected to diffusion and quantum mechanics problems in physics, The concept of Path Integration will be developed from elementary considerations in the financial context by pricing an Average Rate Option, showing analogies to physics along the way Application to a real world Stochastic Volatility model will be presented Use of Path Integrals to improve Monte Carlo convergence, The Reflection Principle in Barrier Options, and Local Volatility as an Inverse Scattering problem may also be discussed if time permits.

John Ryan graduated from Lehigh in 1984 with a BS in Physics and later with a PhD from Brown University in 1989 For the past 30 years He has been working in mathematical finance including positions of head foreign exchange options modelling at both Morgan Stanly and Banco Santander.