Related papers: Second order approximations for limit order books
Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar…
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…
Motivated by the desire to bridge the gap between the microscopic description of price formation (agent-based modeling) and the stochastic differential equations approach used classically to describe price evolution at macroscopic time…
We introduce a Cox-type model for relative intensities of orders flows in a limit order book. The model assumes that all intensities share a common baseline intensity, which may for example represent the global market activity. Parameters…
Fluctuations from a hydrodynamic limit of a one-dimensional asymmetric system come at two levels. On the central limit scale n^{1/2} one sees initial fluctuations transported along characteristics and no dynamical noise. The second order of…
In this article, we delve into the applications and extensions of the queue-reactive model for the simulation of limit order books. Our approach emphasizes the importance of order sizes, in conjunction with their type and arrival rate, by…
Modeling the impact of the order flow on asset prices is of primary importance to understand the behavior of financial markets. Part I of this paper reported the remarkable improvements in the description of the price dynamics which can be…
We show that multivariate Hawkes processes coupled with the nonparametric estimation procedure first proposed in Bacry and Muzy (2015) can be successfully used to study complex interactions between the time of arrival of orders and their…
Conventional models of matching markets assume that monetary transfers can clear markets by compensating for utility differentials. However, empirical patterns show that such transfers often fail to close structural preference gaps. This…
We prove optimal convergence rates for the discretization of a general second-order linear elliptic PDE with an adaptive vertex-centered finite volume scheme. While our prior work Erath and Praetorius [SIAM J. Numer. Anal., 54 (2016), pp.…
In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…
Second-order optimization methods exhibit fast convergence to critical points, however, in nonconvex optimization, these methods often require restrictive step-sizes to ensure a monotonically decreasing objective function. In the presence…
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in…
We analyze a tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand. We establish the existence of a limiting distribution for the highest bid, and for…
We introduce a second-order stochastic model to explore the variability in growth of biological shapes with applications to medical imaging. Our model is a perturbation with a random force of the Hamiltonian formulation of the geodesics.…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
We consider a nonlinear differential equation under the combined influence of small state-dependent Brownian perturbations of size $\varepsilon$, and fast periodic sampling with period $\delta$; $0<\varepsilon, \delta \ll 1$. Thus, state…
With the proliferation of algorithmic high-frequency trading in financial markets, the Limit Order Book has generated increased research interest. Research is still at an early stage and there is much we do not understand about the dynamics…
We propose a unified mean-field framework that bridges the dynamics of informal financial markets and formal markets governed by Limit Order Books (LOBs). Both settings are modeled as interacting particle systems on a 1D price lattice, with…
In this paper, both semidiscrete and completely discrete finite volume element methods (FVEMs) are analyzed for approximating solutions of a class of linear hyperbolic integro- differential equations in a two-dimensional convex polygonal…