Related papers: Second order approximations for limit order books

In this work, we present a continuous-time large-population game for modeling market microstructure betweentwo consecutive trades. The proposed modeling framework is inspired by our previous work [23]. In this framework, the Limit Order…

We discuss some aspects of the continuum limit of some lattice models, in particular the $2D$ $O(N)$ models. The continuum limit is taken either in an infinite volume or in a box whose size is a fixed fraction of the infinite volume…

Maglaras, Moallemi, and Zheng (2021) have introduced a flexible queueing model for fragmented limit-order markets, whose fluid limit remains remarkably tractable. In the present study we prove that, in the limit of small and frequent…

We propose an algorithm to numerically determined whether a second-order linear PDE problem satisfying a Garding inequality is well-posed. This algorithm further provides a lower bound to the inf-sup constant of the weak formulation, which…

In this paper we present a new method to compute the first-order approximation of the price of derivatives on futures in the context of multiscale stochastic volatility of Fouque \textit{et al.} (2011, CUP). It provides an alternative…

Using agent-based modelling, empirical evidence and physical ideas, such as the energy function and the fact that the phase space must have twice the dimension of the configuration space, we argue that the stochastic differential equations…

In this paper, we derive closed-form formulas of first-order approximation for down-and-out barrier and floating strike lookback put option prices under a stochastic volatility model, by using an asymptotic approach. To find the explicit…

We propose a modeling framework for the dynamics of a reduced form order book in event time and based on event sizes. Our framework for the order book is influenced by [9], but compared to [9] we allow the best bid ask spread to be larger…

We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density…

This paper proposes an alternative to the classical price-adjustment mechanism (called "t\^{a}tonnement" after Walras) that is second-order in time. The proposed mechanism, an analogue to the damped harmonic oscillator, provides a dynamic…

We develop a behavioral model for liquidity and volatility based on empirical regularities in trading order flow in the London Stock Exchange. This can be viewed as a very simple agent based model in which all components of the model are…

Using a regularization by putting the system in finite volume, we develop a novel approach to form factor perturbation theory for nonintegrable models described as perturbations of integrable ones. This permits to go beyond first order in…

This work's purpose is to understand the dynamics of limit order books in order-driven markets. We try to illustrate a dynamical trading mechanism attached to the microstructure of limit order markets. We capture the iterative nature of…

In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. Those spaces are constructed from local solutions of the partial differential equation…

We develop an empirical behavioural order-driven (EBOD) model, which consists of an order placement process and an order cancellation process. Price limit rules are introduced in the definition of relative price. The order placement process…

How condensed-matter simulations depend on the number of molecules being simulated ($N$) is sometimes itself a valuable piece of information. Liquid crystals provide a case in point. Light scattering and $2d$-IR experiments on…

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…

This work contains two single-letter upper bounds on the entropy rate of a discrete-valued stationary stochastic process, which only depend on second-order statistics, and are primarily suitable for models which consist of relatively large…

This paper concerns the numerical valuation of swing options with discrete action times under a linear two-factor mean-reverting model with jumps. The resulting sequence of two-dimensional partial integro-differential equations (PIDEs) are…

In dynamical system theory, the process of obtaining a reduced-order approximation of the high-order model is called model order reduction. The closeness of the reduced-order model to the original model is generally gauged by using system…