6:00 PM Seminar Begins
7:30 PM Reception
Hybrid Event:
Fordham University
McNally Amphitheater
140 West 62nd Street
New York, NY 10023
Free Registration!
For Virtual Attendees: Please select Virtual instead of member type upon registration.
Abstract:
We introduce a unified framework for path dependence where past information is captured by the occupation flow. The latter records the "time" spent by the underlying path at arbitrary levels. We show the omnipresence of the occupation flow in finance, notably in the context of exotic options. Examples include corridor variance swaps, where the "time" corresponds to the cumulative variance of the asset, and Parisian, Asian, or lookback options using calendar time. The proposed framework leads to a tractable calculus striking a middle ground between the classical Ito calculus and the fully path-dependent setting introduced by Dupire. We discuss applications in financial modeling where the occupation flow dictates the asset price dynamics. The diffusion coefficient, termed occupied volatility, leads to a subclass of path-dependent volatility models that can be effectively simulated. We also show numerical advantages of the associated pricing partial differential equations (PDEs) in comparison with path-dependent PDEs.
Bio:
Valentin Tissot-Daguette is a quantitative researcher at Bloomberg. He recently obtained his PhD degree from the Operations Research and Financial Engineering department at Princeton University. Prior to his PhD, Valentin studied at EPFL and ETH Zurich in Switzerland where he completed a Bachelor's degree in Mathematics and a Master's degree in Financial Engineering. His research interests include exotic derivatives, free boundary problems for American options, and volatility modeling.
