Microstructural Foundation of Rough Log-Normal Volatility Models
Abstract
We establish a microstructural foundation of the rough Bergomi model. Specifically, we consider a sequence of order driven financial market models where orders to buy or sell an asset arrive according to a Poisson process and have a long lasting impact on volatility. Using a recently established C-tightness result for càdlàg processes we establish the weak convergence of the price-volatility process to a log-normal rough volatility model. Our weak convergence result is accompanied by weak error rates that employ a recently established Clark-Ocone formula for Poisson processes and turn our microstructure model into a viable alternative to classical simulation schemes. The weak error rates strongly hinge on Poisson arrival dynamics and are novel to the rough microstructure literature. The talk is based on joint work with Paul Hager, Thomas Wagenhofer and Wei Xu.
About the speaker
Ulrich Horst is Professor of Applied Financial Mathematics in the Mathematics Department at Humboldt University Berlin. He is the co-spokesperson of the Collaborative Research Center “Rough Analysis, Stochastic Dynamics and Related Fields”, a Principal Investigator of the International Research Training Group “Stochastic Analysis in Interaction” and a member of the Berlin Mathematical School. He held visiting positions at Princeton University, the National University of Singapore, the Université Paris Dauphine and Bielefeld University. He is the Editor-in-Chief of Mathematics and Financial Economics and served on the board of many other journals including SIFIN and JEDC. His research focusses on stochastic control and game theory, microstructure foundations of financial price fluctuations and, more recently, applications of rough path theory to stochastic control and games.