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The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a…

We propose a general framework to describe the impact of different events in the order book, that generalizes previous work on the impact of market orders. Two different modeling routes can be considered, which are equivalent when only…

In this paper, we use a database of around 400,000 metaorders issued by investors and electronically traded on European markets in 2010 in order to study market impact at different scales. At the intraday scale we confirm a square root…

Market impact is an important problem faced by large institutional investor and active market participant. In this paper, we rigorously investigate whether price trajectory data from the metaorder increases the efficiency of estimation,…

This work extends and complements our previous theoretical paper on the subtle interplay between impact, order flow and volatility. In the present paper, we generate synthetic market data following the specification of that paper and show…

We study the price impact of order book events - limit orders, market orders and cancelations - using the NYSE TAQ data for 50 U.S. stocks. We show that, over short time intervals, price changes are mainly driven by the order flow…

This paper introduces a novel algorithm for generating realistic metaorders from public trade data, addressing a longstanding challenge in price impact research that has traditionally relied on proprietary datasets. Our method effectively…

We introduce and study a simple model of a limit order-driven market. Traders in this model can either trade at the market price or place a limit order, i.e. an instruction to buy (sell) a certain amount of the stock if its price falls…

This note explores the consequences of nonlinear price impact functions on price dynamics within the chartist-fundamentalist framework. Price impact functions may be nonlinear with respect to trading volume. As indicated by recent empirical…

We study the market impact of a meta-order in the framework of the Minority Game. This amounts to studying the response of the market when introducing a trader who buys or sells a fixed amount h for a finite time T. This perturbation…

We model an informed agent with information about the future value of an asset trying to maximize profits when subjected to a transaction cost as well as a market maker tasked with setting fair transaction prices. In a single auction model,…

We study the problem of what causes prices to change. We define the mechanical impact of a trading order as the change in future prices in the absence of any future changes in decision making, and its it informational impact as the…

Statistical properties of an order book and the effect they have on price dynamics were studied using the high-frequency NASDAQ Level II data. It was observed that the size distribution of marketable orders (transaction sizes) has power law…

In this chapter we review some recent results on the dynamics of price formation in financial markets and its relations with the efficient market hypothesis. Specifically, we present the limit order book mechanism for markets and we…

This paper considers a Markovian model of a limit order book where time-dependent rates are allowed. With the objective of understanding the mechanisms through which a microscopic model of an orderbook can converge to more general diffusion…

We study the problem of the optimal execution of a large trade in the presence of nonlinear transient impact. We propose an approach based on homotopy analysis, whereby a well behaved initial strategy is continuously deformed to lower the…

In this research, we have empirically investigated the key drivers affecting liquidity in equity markets. We illustrated how theoretical models, such as Kyle's model, of agents' interplay in the financial markets, are aligned with the…

This paper proposes a novel model of financial prices where: (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically…

We propose a general non-linear order book model that is built from the individual behaviours of the agents. Our framework encompasses Markovian and Hawkes based models. Under mild assumptions, we prove original results on the ergodicity…

We briefly review data analysis of the Island order book, part of NASDAQ, which suggests a framework to which all limit order markets should comply. Using a simple exclusion particle model, we argue that short-time price over-diffusion in…