In this project, we aim at solving important regulation issues on financial markets. Our approach in non-conventional in the sense that we use a financial engineering viewpoint: using tools from probability, statistics and stochastic control, we express important questions as...
In this project, we aim at solving important regulation issues on financial markets. Our approach in non-conventional in the sense that we use a financial engineering viewpoint: using tools from probability, statistics and stochastic control, we express important questions as clear and well-posed mathematical problems and try to provide solutions to them, paying of course attention to interpretation of our results.
We particularly focus on issues arising at the microstructure level: mitigating the effects of high frequency trading, optimal tick sizes, make-take fees systems, auctions, design of limit order books; and on the modelling and understanding of the volatility process
- Design of new, parsimonious models for the volatility process (called rough volatility models), together with associated pricing and hedging procedures. These models clearly outperform standard models in term of risk management.
- Understanding the rough nature of the volatility.
- Design of new and more efficient market design mechanisms at the microstructure level: optimal take sizes, make-take fees, auctions
- Building a framework enabling financial regulator to assess the impact of the various market participants on overall market quality.
- Design of an order book model leading to improved strategies in term of inventory risk.
We expect to continue rethinking financial regulation. The natural next step is probably to focus on derivatives products. We wish to find ways to design them optimally in order to guarantee market users the best possible tools for risk management. A principal/agent type approach should be quite suitable to solve these new issues.
We also wish to understand other features of the volatility process, such as the so-called Zumbach effect, and relate them to the behavior of financial agents at the microscopic level. Quadratic Hawkes processes could probably represent a relevant modelling tool here.
More info: https://quantreg.com/people/mathieurosenbaum/.