Project B02
Microstructural foundations of rough volatility models

Project description

This project focuses on microstructure models of financial markets, particularly rough volatility models. We aim to derive and analyze novel scaling limits for stochastic processes in market microstructure models, including convergence theorems for Hawkes processes, Donsker-type theorems for fractional Brownian motion, and a convergence theory for rough stochastic integrals and differential equations. The goal is to enhance our understanding of rough volatility models by incorporating more complex microscopic dynamics and improving the technical toolkit for analyzing their scaling limits. 

Principal Investigators

Christian Bayer (WIAS)

Ulrich Horst (HU Berlin)

Dörte Kreher (HU Berlin)

Project members

Sorelle Murielle Toukam Tchoumegne (WIAS)

Yang Yang (HU Berlin)

Publications

• Horst, U., Xu, W., 2025. Second-order regular variation and second-order approximation of Hawkes processes. Journal of Mathematical Analysis and Applications 550, 129546. https://doi.org/10.1016/j.jmaa.2025.129546

• Bank, P., Bayer, C., Friz, P.K., Pelizzari, L., 2025. Rough PDEs for Local Stochastic Volatility Models. Mathematical Finance mafi.12458. https://doi.org/10.1111/mafi.12458 (A07, B02, B03, B04)

• Horst, U., Xu, W., 2024. Functional limit theorems for Hawkes processes. Probab. Theory Relat. Fields. https://doi.org/10.1007/s00440-024-01348-3

Preprints

• Qiu, J., Ware, A., Yang, Y., 2025. Stochastic Path-Dependent Volatility Models for Price-Storage Dynamics in Natural Gas Markets and Discrete-Time Swing Option Pricing. http://doi.org/10.48550/arXiv.2406.16400 

• Jaber, E.A., Bayer, C., Breneis, S., 2024. State spaces of multifactor approximations of nonnegative Volterra processes. https://doi.org/10.48550/ARXIV.2412.17526

• Horst, U., Xu, W., Zhang, R., 2024. Path-dependent Fractional Volterra Equations and the Microstructure of Rough Volatility Models driven by Poisson Random Measures. https://doi.org/10.48550/arXiv.2412.16436

• Horst, U., Xu, W., Zhang, R., 2024. Convergence of Heavy-Tailed Hawkes Processes and the Microstructure of Rough Volatility. https://doi.org/10.48550/ARXIV.2312.08784