Related papers: A Functional Limit Theorem for Limit Order Books w…
We use a recent, high-quality data set from Nasdaq to perform an empirical analysis of order flow in a limit order book (LOB) before and after the arrival of a market order. For each of the stocks that we study, we identify a sequence of…
We formulate a simplified model of a limit order book, in which the arrival process is independent of the current state. We prove a phase transition result: there exist prices $\kappa_b$ and $\kappa_a$ such that, for any $\epsilon > 0$,…
We use random walks to simulate the fluid limit of two coupled diffusive limit order books to model correlation emergence. The model implements the arrival, cancellation and diffusion of orders coupled by a pairs trader profiting from the…
We study the multi-level order-flow imbalance (MLOFI), which is a vector quantity that measures the net flow of buy and sell orders at different price levels in a limit order book (LOB). Using a recent, high-quality data set for 6 liquid…
We study an optimal execution strategy for purchasing a large block of shares over a fixed time horizon. The execution problem is subject to a general price impact that gradually dissipates due to market resilience. We allow for general…
We introduce the Estimated Dynamic Equilibrium Model (EDEM), an agent-based framework that treats supply and demand as a coupled stochastic process driven by heterogeneous, noisy agent valuations. The model's primary technical contribution…
We study functional limit theorems for linear type processes with short memory under the assumption that the innovations are dependent identically distributed random variables with infinite variance and in the domain of attraction of stable…
We consider the following Markovian dynamic on point processes: at constant rate and with equal probability, either the rightmost atom of the current configuration is removed, or a new atom is added at a random distance from the rightmost…
We study an ordinary differential equation (ODE) arising as the many-server heavy-traffic fluid limit of a sequence of overloaded Markovian queueing models with two customer classes and two service pools. The system, known as the X model in…
We consider an infinite system of coupled stochastic differential equations (SDE) describing dynamics of the following infinite particle system. Each partricle is characterised by its position $x\in \mathbb{R}^{d}$ and internal parameter…
I present an overview of some recent advancements on the empirical analysis and theoretical modeling of the process of price formation in financial markets as the result of the arrival of orders in a limit order book exchange. After…
Locational Marginal Price (LMP) is a dual variable associated with supply-demand matching and represents the cost of delivering power to a particular location if the load at that location increases. In recent times it become more volatile…
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 paper presents a novel model for simulating and analyzing sparse limit order books (LOBs), with a specific application to the European intraday electricity market. In illiquid markets, characterized by significant gaps between order…
While the market impact of aggressive orders has been extensively studied, the impact of passive orders, those executed through limit orders, remains less understood. The goal of this paper is to investigate passive market impact by…
This paper introduces a discrete limit order book model where new orders are placed with a fixed displacement from the mid-price. Further, the trade event occurs whenever the mid-price hits the price level on which there is some volume.…
Demand-side management provides a great potential for improving the efficiency and reliability of energy systems. This requires a mechanism to connect the market level and the demand side. The flexibility function is a novel approach that…
Market making (MM) is an important research topic in quantitative finance, the agent needs to continuously optimize ask and bid quotes to provide liquidity and make profits. The limit order book (LOB) contains information on all active…
We develop a theory of bid and ask price dynamics where the two prices form due to interaction of buy and sell orders. In this model the two prices are represented by eigenvalues of a 2x2 price operator corresponding to "bid" and "ask"…
We study the macroscopic behavior of a stochastic spin ensemble driven by a discrete Markov jump process motivated by the Metropolis-Hastings algorithm where the proposal is made with spatially correlated (colored) noise, and hence fails to…