Papers and presentations by members of the group:
This paper incorporates a Markovian signal in the optimal trading framework which was initially proposed by Gatheral, Schied, and Slynko and provides results on the existence and uniqueness of an optimal trading strategy. An explicit singular optimal strategy is derived for the special case of an Ornstein-Uhlenbeck signal and an exponentially decaying transient market impact. It is also shown that in the asymptotic limit where the transient market impact becomes instantaneous the optimal strategy becomes continuous. This result is compatible with the optimal trading framework proposed by Cartea and Jaimungal. Analysing nine months of tick by tick data on 13 European stocks from the NASDAQ OMX exchange it is shown that order book imbalance is a predictor of the future price move and it has some mean-reverting properties.
This paper shows that, under no-arbitrage, market impact can have only a power-law form and the macroscopic price is diffusive with rough volatility; there is a correspondence between the exponent of the power-law and the Hurst exponent of the rough volatility process. This takes into account recent results on hyper-rough stochastic Volterra equations.
The optimal setup for make-take fees considering an exchange and a market-maker is derived using a principal-agent approach as a function of the inventory trajectory for the market-maker and the assert’s volatility; the optimal quotes for the market-maker are derived as well, leading to a higher quality of liquidity and lower costs for investors.
This empirical study uses a unique data set provided by the French regulator Autorité des Marchés Financiers and at the change in the liquidity provision of high frequency traders under market stress.
With a simple microscopic model for the price of an asset based on Hawkes processes and some of the main features of market microstructure (high degree of endogeneity, no-arbitrage, buying/selling asymmetry and the presence of metaorders), we prove that when the first three of these stylized facts are considered within the framework of our microscopic model, it behaves in the long run as a Heston stochastic volatility model, where the leverage effect is generated. Adding the last property enables us to obtain a rough Heston model in the limit, exhibiting both leverage effect and rough volatility.
This paper demonstrates that the approach introduced in Dayri and Rosenbaum (Large tick assets: implicit spread and optimal tick size) allows for an ex ante assessment of the consequences of a tick value change on the microstructure of an asset. The pilot program on tick value modifications started in 2014 by the Tokyo Stock Exchange is analyzed with this methodology. We focus on forecasting the future cost of market and limit orders after a tick value change and show that our predictions are very accurate.
By showing that most of the microstructural properties of assets can be described by the (easily calculated parameter) η, including the effective spread (equal to η.α for large tick assets), the notion of optimal tick size can be defined. The behavior of relevant market quantities after a change in the tick value can then be forecasted.
During the time period where a reference price such as the mid price remains constant, the Limit Order Book is modelled as a Markov queuing system, with the intensities of the order flows only depend on the current state of the order book. A stochastic mechanism allows for switches from one period of constant reference price to another. The model reproduces accurately the behavior of market data, and it very useful as a market simulator.
For different classes of assets, log-volatility behaves as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale, and long memory in volatility might be an artifact from the application of classical statistical procedures to assets that follow the rough fractional stochastic volatility (RFSV) model. A seminal paper, it has defined a new area of research (Rough Volatility).
Summarizing the most recent developments in markets (fragmentation and the rise of high-frequency trading), this article examines how the price formation process has been reshaped by high frequency traders, with examples of their various strategies and their profitability. A final section discusses recent tools designed in order to assess and control the high frequency trading activity.
Very often, only nearly unstable Hawkes processes are able to fit high-frequency financial data properly. The authors show that after suitable rescaling, these processes asymptotically behave like integrated Cox-Ingersoll-Ross models. Extending this result to the Hawkes-based price model introduced by Bacry et al. under a similar criticality condition, this process converges to a Heston model. In both cases well-known stylized facts of prices, both at the microstructure level and at the macroscopic scale, are recovered.
In this work, the authors propose a notion of efficient price relevant at the ultra high frequency level, with a statistical methodology enabling to estimate this price form the order flow.
This paper provides a model with a continuous efficient price and the inherent properties of ultra high frequency transaction data (price discreteness, irregular temporal spacing, diurnal patterns…), with a stochastic mechanism for deriving
the transaction prices from the latent efficient price. If a transaction occurs at some value on the tick grid and leads to a price change, then the efficient price has been close enough to this value shortly before the transaction. Uncertainty zones are the bands around the mid-tick grid where the efficient price is too far from the tick grid to trigger a price change. In this setting, the width of these uncertainty zones quantifies the aversion to price changes of the market participants. Furthermore, from this model approximated values of the efficient price can be derived at some random times, which is particularly useful for building statistical procedures. Convincing results are obtained through a simulation study and the use of the model over ten representative stocks.
Mean Field Game (MFG) theory is used to analyze a stochastic order-driven market model with waiting costs and heterogenous traders, where offer and demand of liquidity drives price formation and traders anticipate future evolutions of the order book. Considering the coexistence of Institutional Investors and High Frequency Traders (HFT), with different order sizes, the paper shows that in markets with Institutional Investors only there are inefficient liquidity imbalances in equilibrium, with two symmetrical situations corresponding to what we call liquidity calls for liquidity. During these situations the transaction price significantly moves away from the fair price. However this macro phenomenon disappears in markets with both Institutional Investors and HFT, although a more precise study shows that the benefits of the new situation go to HFT only, leaving Institutional Investors with higher trading costs.
With a database of around 400,000 metaorders issued by investors and electronically traded on European markets in 2010, market impact is studied at different scales. Intraday, a square root temporary impact in the daily participation is confirmed, and a duration factor in 1/T at power gamma with gamma close to 0.25 reinforces the square root shape of impact. A power-law for the transient impact with an exponent between 0.5 (for long metaorders) and 0.8 (for shorter ones) is found, and no anticipation of the size of the meta-orders by the market is found. At the daily time scale, price moves after a metaorder can be split between realizations of expected returns that have triggered the investing decision and an idiosynchratic impact that slowly decays to zero. A class of toy models based on Hawkes processes (the Hawkes Impact Models, HIM) exhibits interesting features (transience and decay of impact), even with a simple formulation like the Impulsive-HIM model, despite its simplicity: a parameter C with the macroscopic interpretation of the ratio of contrarian reaction (i.e. impact decay) and of the “herding” reaction (i.e. impact amplification).
This paper is a review of the most relevant stylized facts of microstructure, such as the shape of the market impact of large metaorders, propagation models, signature plots and the Epps effect.
In this paper the trader trying to solve the optimal liquidation problem faces the uncertainty of price changes not only from “normal” uncertainty but those generated by other similar market participants. The formulation of this problem belongs to the class of “extended MFG” (MFG = Mean Field Games), and it is defined by the cost function of optimal trading. The authors provide a closed form formula of its solution, addressing the case of “heterogenous preferences” (when each participant has a different risk aversion), and give conditions under which participants do not need to instantaneously know the state of the whole system, but can “learn” it day after day, observing others’ behaviors.
The author shows how the methodology used for the Ibovespa index until 2013 generated significant rebalancing impacts from hedging of futures contracts at the relevant closing auctions and how local markets were distorted in 2013 due to the OGX debacle.
The author follows on Mathieu‘s Uncertainty Zones model and shows how exchanges can influence the quoting and trading characteristics of contracts with their choices of tick size and fee schedules and discusses the externalities of these choices.
The author shows how interest rate cycles within an inflation targeting framework lead to smoothness in the implied forwards of overnight-based interest rate curves.
The author shows how the methodology used for the Ibovespa index until 2013 generated significant rebalancing impacts from hedging of futures contracts exactly at the relevant closing auctions, and contrasts it against the usual results of the index effect.
The author implements Mathieu‘s Uncertainty Zones model, examining contracts with the same microstructure parameters but with different statistics, given the different profile of participants (HFT participation and liquidity consumers’ flow). A framework for simulating the behavior of the traded prices in this model given the microstructure parameters is discussed and implemented.
The authors investigate how a strict local martingale might arise from a true martingale as a result of an enlargement of the filtration, studying and implementing a particular type of enlargement for various SDEs and providing sufficient conditions in each of these cases such that the initial expansion can create a strict local martingale under an equivalent probability measure.
The authors define the Markovian and affine structure of the Volterra Heston model in terms of an infinite-dimensional adjusted forward process and specify its state space, showing that it satisfies a stochastic PDE and displays an exponentially-affine characteristic functional. Further deductions lead to another representation of the Volterra Heston model.
The authors design tractable multi-factor stochastic volatility models approximating rough volatility models with a Markovian structure, including the specific case of the rough Heston model. A numerical method for solving fractional Riccati equations appearing in the characteristic function of the log-price in this setting is derived.
A small-time Edgeworth expansion of the density of an asset price is given under a general stochastic volatility model, from which asymptotic expansions of put option prices and at-the-money implied volatilities follow. A limit theorem for at-the-money implied volatility skew and curvature is also given as a corollary. The rough Bergomi model is treated as an example.
The authors determine explicit hedging strategies for options in the rough Heston framework. The replicating portfolios contain the underlying asset and the forward variance curve, and lead to a theoretical perfect hedge.
The authors show that the typical behavior of market participants at the high frequency scale generates the leverage effect and rough volatility, using Hawkes processes and these features of market microstructure: a high degree of endogeneity in the market, the no-arbitrage property, buying/selling asymmetry and the presence of metaorders. With the first three facts, the model behaves in the long run as a Heston SVM with the leverage effect. Adding metaorders enables us to obtain a rough Heston model in the limit.
Using an original link between nearly unstable Hawkes processes and fractional volatility models, the authors compute the characteristic function of the log-price in rough Heston models. It is shown that for rough Heston models the characteristic function is expressed in terms of the solution a fractional Riccati equation.
This paper extends the momentum risk premium model of Bruder and Gaussel (2011) to the multivariate case, finding the main properties from the literature and new theoretical findings; the payoff and the hedging properties of trend-following strategies are studied in detail.
To solve the agent’s control problem (executing a small amount over a short time interval using limit orders, market orders and cancellations), the authors build an order book model and optimize an expected utility function based on the price impact, deriving the equations satisfied by the optimal strategy and solving them numerically. This optimal tactic outperforms significantly naive execution strategies.
The paper models the behavior of three agent classes: market makers (MM), high-frequency trading (HFT) firms, and institutional brokers (IB), and their actions on the LOB, assuming the dynamics presented in Simulating and analyzing order book data: The queue-reactive model and different optimization schedules for each class of participant. The variational PDEs for the value functions of the MM and HFT are deduced with their almost optimal control and the resulting interactions.
Based on labelled trade data, the authors determine how market participants accept or not transactions via limit orders as a function of liquidity imbalance; then a theoretical stochastic control framework is developed to help translate knowledge on liquidity imbalance into control of limit orders, and the role (cost) of latency in this framework is measured.
Books by members of the group:
Market Microstructure in Practice
This book exposes and comments on the consequences of Reg NMS and MiFID on market microstructure. It covers changes in market design, electronic trading, and investor and trader behaviors. The emergence of high frequency trading and critical events like the”Flash Crash” of 2010 are also analyzed in depth. Using a quantitative viewpoint, this book explains how an attrition of liquidity and regulatory changes can impact the whole microstructure of financial markets. A mathematical Appendix details the quantitative tools and indicators used through the book, allowing the reader to go further independently.
The Brazilian financial markets operate in a very different way to G7 markets. Key differences include onshore and offshore markets, exponential rates, business days day-counts, and price formation from the futures markets (instead of the cash markets).
This book provides a quantitative, applied guide to the offshore and onshore Brazilian markets, with a focus on the financial instruments unique to the region. It offers a comprehensive introduction to the key financial ‘archaeology’ in the Brazil context, exploring interest rates, FX and inflation and key differences from G7 market finance. It explores the core industry investment banking business in detail, from FX to interest rates and cash and inflation. Finally it introduces the region’s unique financial instruments, as well as their pricing and risk management needs.
Covering both introductory and complex topics, this book provides existing practitioners in Brazil, as well as those interested in becoming involved in these markets, everything they need to understand the market dynamics, risks, pricing and calibration of curves for all products currently available.
6¦5 is the first book ever in French about high-frequency trading (HFT), released in 2013 and 2014 by Zones sensibles in two parts. 6, composed as a an easy-read data-thriller (the narrator being a – real – algorithm named Sniper (cf. Rust, Miller, Palmer, 1993), the first part is mainly about the rise of HFT around New York in the 1980-1990’s (Thomas Peterffy’s engines, Island, the Nasdaq scandal about spreads, etc.) as well as a precise and dense account of the way market microstructure changed due to the computerization of the exchanges, the new legal rules (Reg. NMS, decimalization), and the use of new kind of algorithms (and the scientific knowledge behind them), resulting in a new and highly technological ecosystem where speed is everywhere, at least for some participants: the new specialists (or market makers, connected to hundreds of data centers). The second part, 5, is a technological and ecologic history of the two main Chicago exchanges (CME and CBOT), from the first commodity markets within the pits, driven by hand signals (which was then the fastest way to trade) to the new Globex software who replaced human traders (some of the old pit traders were among those who built very powerful HFT firms at the end of the 1990’s). This research is driven by a precise analysis of the way the exchanges went from human face-to-face trading to non-human algorithmically-generated trades. The book, which met both commercial and critical success (due to be translated in Italian and German soon), will be released in French in paperback in October 2018 at the same time as its author will release a sequel, 4/3, mainly about market structure, telecommunication infrastructures, intellectual property, statistical arbitrage and religion.