Columbia & NYU Financial Engineering Colloquium: Jim Gatheral & Xin Zhang
RSVP
Jim Gatheral
Presidential Professor of Mathematics at Baruch College, CUNY
Title
Quadratic Rough Heston: SPX, VIX and the SSR
Abstract
We extend the hybrid scheme of Gatheral (2022) and apply the finite difference methodology of Bourgey et al. (2024) to compute the skew-stickiness ratio (SSR) under quadratic rough Heston. We find that the quadratic rough Heston model not only provides good joint fits to both SPX and VIX volatility smiles but also produces credible SSR values, whilst remaining extremely parsimonious. By examining the historical evolution of the quadratic rough Heston model, and relating it to well-known classical stochastic volatility models, we can begin to understand the underlying reasons for its seemingly unreasonable effectiveness.
This is joint work with Florian Bourgey.
Bio
Jim Gatheral is Presidential Professor of Mathematics at Baruch College, CUNY teaching in the Masters of Financial Engineering (MFE) program. Prior to joining the faculty of Baruch College, Jim was a Managing Director at Bank of America Merrill Lynch, and also an adjunct professor at the Courant Institute, NYU. His current research focus is on volatility modeling. Jim (along with Mathieu Rosenbaum) was awarded 2021 ‘Quant of the Year’ by RISK.net for his work on rough volatility modeling. His best-selling book, The Volatility Surface: A Practitioner’s Guide (Wiley 2006) is one of the standard references on the subject of volatility modeling.
Xin Zhang
Assistant Professor, Department of Finance and Risk Engineering, NYU Tandon
Title
Optimization of Win Martingales
Abstract
Prediction market is a market where people can trade based on outcomes of future events. It is widely used in sports games, elections, and pricing of digital options.
In math finance, prediction markets can be modeled by the so-called win martingales, which are continuous time martingales that end up with Bernoulli distributions. In this talk, choosing different divergences as objective functionals, we will solve a class of optimal win martingales. In some cases, we will get explicit formulas of optimizers, and make connections to Schrödinger, filtering problems, Wright-Fisher diffusion, and the problem of identifying most exciting games.
Bio
Xin Zhang is an Assistant Professor in the Financial and Risk Engineering (FRE) department at New York University. Before joining NYU, he was a University Assistant at the University of Vienna from 2021 to 2024. He earned his Ph.D. in Mathematics from the University of Michigan in 2021, after completing a B.S. in Mathematics at Fudan University in 2016. Xin Zhang’s research focuses on optimal transport, stochastic analysis and control, particularly their applications in Finance and Machine Learning. His specific interests include viscosity solutions of nonlinear partial differential equations and optimal transport in robust finance.
