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We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that…
Managing high-frequency data in a limit order book (LOB) is a complex task that often exceeds the capabilities of conventional time-series forecasting models. Accurately predicting the entire multi-level LOB, beyond just the mid-price, is…
This paper proposes a parametric approach for stochastic modeling of limit order markets. The models are obtained by augmenting classical perfectly liquid market models by few additional risk factors that describe liquidity properties of…
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…
We define a stochastic model of a two-sided limit order book in terms of its key quantities \textit{best bid [ask] price} and the \textit{standing buy [sell] volume density}. For a simple scaling of the discreteness parameters, that keeps…
Trading large volumes of a financial asset in order driven markets requires the use of algorithmic execution dividing the volume in many transactions in order to minimize costs due to market impact. A proper design of an optimal execution…
Market making is a fundamental trading problem in which an agent provides liquidity by continually offering to buy and sell a security. The problem is challenging due to inventory risk, the risk of accumulating an unfavourable position and…
Machine learning (especially reinforcement learning) methods for trading are increasingly reliant on simulation for agent training and testing. Furthermore, simulation is important for validation of hand-coded trading strategies and for…
We propose a parametric model for the simulation of limit order books. We assume that limit orders, market orders and cancellations are submitted according to point processes with state-dependent intensities. We propose new functional forms…
This paper investigates real-time detection of spoofing activity in limit order books, focusing on cryptocurrency centralized exchanges. We first introduce novel order flow variables based on multi-scale Hawkes processes that account both…
Automated matching engines execute millions of orders per session, yet systematic asymmetries in latency, order size, and market access compound into persistent execution disparities that erode participant trust. We formulate provably fair…
In this work, we investigate the market-making problem on a trading session in which a continuous phase on a limit order book is followed by a closing auction. Whereas standard optimal market-making models typically rely on terminal…
In this paper we complete and extend our previous work on stochastic control applied to high frequency market-making with inventory constraints and directional bets. Our new model admits several state variables (e.g. market spread,…
In a recent paper, Alfonsi, Fruth and Schied (AFS) propose a simple order book based model for the impact of large orders on stock prices. They use this model to derive optimal strategies for the execution of large orders. We apply these…
Although behavioral economics has demonstrated that there are many situations where rational choice is a poor empirical model, it has so far failed to provide quantitative models of economic problems such as price formation. We make a step…
In this paper, reinforcement learning is applied to the problem of optimizing market making. A multi-agent reinforcement learning framework is used to optimally place limit orders that lead to successful trades. The framework consists of…
We consider the problem of controlling a fully specified Markov decision process (MDP), also known as the planning problem, when the state space is very large and calculating the optimal policy is intractable. Instead, we pursue the more…
Volume imbalance in a limit order book is often considered as a reliable indicator for predicting future price moves. In this work, we seek to analyse the nuances of the relationship between prices and volume imbalance. To this end, we…
Optimal order execution is widely studied by industry practitioners and academic researchers because it determines the profitability of investment decisions and high-level trading strategies, particularly those involving large volumes of…
In this paper we develop a new form of agent-based model for limit order books based on heterogeneous trading agents, whose motivations are liquidity driven. These agents are abstractions of real market participants, expressed in a…