Super-Heston rough volatility, Zumbach effect and the Guyon’s conjecture

Mathieu Rosenbaum will present “Super-Heston rough volatility, Zumbach effect and the Guyon’s conjecture” on Apr 23: https://ethz.zoom.us/meeting/register/tJ0kfu6trD0oGtHBTVyMkSJDp-XRy1tblo3d?fbclid=IwAR1NIBwk2Q4j481dI7FJGnyV9Ekw61sTWi6LbCcRzTampfTAVdwDIkLqbYs

Reference paper: From quadratic Hawkes processes to super-Heston rough volatility models with Zumbach effect

Work with Paul Jusselin, Aditi Dandapani and Jim Gatheral

How to build a cross-impact model from first principles: Theoretical requirements and empirical results

Published on SSRN:

How to build a cross-impact model from first principles: Theoretical requirements and empirical results

Abstract: Cross-impact, namely the fact that on average buy (sell) trades on a financial instrument induce positive (negative) price changes in other correlated assets, can be measured from abundant, although noisy, market data. In this paper we propose a principled approach that allows to perform model selection for cross-impact models, showing that symmetries and consistency requirements are particularly effective in reducing the universe of possible models to a much smaller set of viable candidates, thus mitigating the effect of noise on the properties of the inferred model. We review the empirical performance of a large number of cross-impact models, comparing their strengths and weaknesses on a number of asset classes (futures, stocks, calendar spreads). Besides showing which models perform better, we argue that in presence of comparable statistical performance, which is often the case in a noisy world, it is relevant to favor models that provide ex-ante theoretical guarantees on their behavior in limit cases. From this perspective, we advocate that the empirical validation of universal properties (symmetries, invariances) should be regarded as holding a much deeper epistemological value than any measure of statistical performance on specific model instances.

From microscopic price dynamics to multidimensional rough volatility models

Published on arxiv:

From microscopic price dynamics to multidimensional rough volatility models

Abstract: Rough volatility is a well-established statistical stylised fact of financial assets. This property has lead to the design and analysis of various new rough stochastic volatility models. However, most of these developments have been carried out in the mono-asset case. In this work, we show that some specific multivariate rough volatility models arise naturally from microstructural properties of the joint dynamics of asset prices. To do so, we use Hawkes processes to build microscopic models that reproduce accurately high frequency cross-asset interactions and investigate their long term scaling limits. We emphasize the relevance of our approach by providing insights on the role of microscopic features such as momentum and mean-reversion on the multidimensional price formation process. We in particular recover classical properties of high-dimensional stock correlation matrices.

Optimal market making with persistent order flow

Published on arxiv:

Optimal market making with persistent order flow

Abstract: We address the issue of market making on electronic markets when taking into account the self exciting property of market order flow. We consider a market with order flows driven by Hawkes processes where one market maker operates, aiming at optimizing its profit. We characterize an optimal control solving this problem by proving existence and uniqueness of a viscosity solution to the associated Hamilton Jacobi Bellman equation. Finally we propose a methodology to approximate the optimal strategy.

Improving reinforcement learning algorithms: towards optimal learning rate policies

Published on arxiv:

Improving reinforcement learning algorithms: towards optimal learning rate policies

Abstract: This paper investigates to what extent we can improve reinforcement learning algorithms. Our study is split in three parts. First, our analysis shows that the classical asymptotic convergence rate O(1/\sqrt{N}) is pessimistic and can be replaced by O((log(N)/N)^{\beta}) with 1/2β1 and N the number of iterations. Second, we propose a dynamic optimal policy for the choice of the learning rate (\gamma_{k})_{k\text{\ensuremath{\ge}}0} used in stochastic algorithms. We decompose our policy into two interacting levels: the inner and the outer level. In the inner level, we present the PASS algorithm (for “PAst Sign Search”) which, based on a predefined sequence (\gamma_{k}^{o})_{k\text{\ensuremath{\ge}}0}, constructs a new sequence (\gamma_{k}^{i})_{k\text{\ensuremath{\ge}}0} whose error decreases faster. In the outer level, we propose an optimal methodology for the selection of the predefined sequence (\gamma_{k}^{o})_{k\text{\ensuremath{\ge}}0}. Third, we show empirically that our selection methodology of the learning rate outperforms significantly standard algorithms used in reinforcement learning (RL) in the three following applications: the estimation of a drift, the optimal placement of limit orders and the optimal execution of large number of shares.

From quadratic Hawkes processes to super-Heston rough volatility models with Zumbach effect

Published on arxiv:

From quadratic Hawkes processes to super-Heston rough volatility models with Zumbach effect

Abstract: Using microscopic price models based on Hawkes processes, it has been shown that under some no-arbitrage condition, the high degree of endogeneity of markets together with the phenomenon of metaorders splitting generate rough Heston-type volatility at the macroscopic scale. One additional important feature of financial dynamics, at the heart of several influential works in econophysics, is the so-called feedback or Zumbach effect. This essentially means that past trends in returns convey significant information on future volatility. A natural way to reproduce this property in microstructure modeling is to use quadratic versions of Hawkes processes. We show that after suitable rescaling, the long term limits of these processes are refined versions of rough Heston models where the volatility coefficient is enhanced compared to the square root characterizing Heston-type dynamics. Furthermore the Zumbach effect remains explicit in these limiting rough volatility models.

The Regulation and Operation of Modern Financial Markets – September 5th and 6th, 2019 – Iceland

Organisers: Mathieu Rosenbaum (École Polytechnique), Jean-Pierre Zigrand (London School of Economics), Ásgeir Jónsson (University of Iceland, Central Bank of Iceland), and Jon Þór Sturluson (The Financial Supervisory Authority, Iceland)

The conference studies the operations and workings of modern financial markets and their interactions with, and needs for, financial regulations.
Topics include the market microstructure (including algorithmic and high-frequency trading in fast markets), the effects of this microstructure on liquidity, efficiency and stability and the real-world effects and implementations of financial regulations, including regtech. We aim to achieve this by bringing together practitioners, regulators and academic researchers and create a fertile environment for discussion.

The conference is supported by the Financial Supervisory Authority (FME), Economic and Social Research Council (ESRC) [grant number ES/R009724/1], European Research Council (ERC) [679836 STAQAMOF] and by the project “Digging into High-Frequency Data: Present and Future Risks and Opportunities (Atlantis)” in the framework of the Trans-Atlantic Platform.

Link to the conference’s website

Optimal make take fees in a multi market maker environment

Just published on arxiv:

Optimal make take fees in a multi market maker environment

Abstract: Following the recent literature on make take fees policies, we consider an exchange wishing to set a suitable contract with several market makers in order to improve trading quality on its platform. To do so, we use a principal-agent approach, where the agents (the market makers) optimise their quotes in a Nash equilibrium fashion, providing best response to the contract proposed by the principal (the exchange). This contract aims at attracting liquidity on the platform. This is because the wealth of the exchange depends on the arrival of market orders, which is driven by the spread of market makers. We compute the optimal contract in quasi explicit form and also derive the optimal spread policies for the market makers. Several new phenomena appears in this multi market maker setting. In particular we show that it is not necessarily optimal to have a large number of market makers in the presence of a contracting scheme.