A diffusion approximation for limit order book models

Ulrich Horst and Dörte Kreher

Stochastic Processes and their Applications, 2019, vol. 129, issue 11, 4431-4479

Abstract: This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an R+-valued best bid price process and an Lloc2-valued volume process. It is shown that under suitable assumptions the sequence of interpolated discrete time models is relatively compact in a localized sense and that any limit point satisfies a certain infinite dimensional SDE. Under additional assumptions on the dependence structure we construct two classes of models, which fit in the general framework, such that the limiting SDE admits a unique solution and thus the discrete dynamics converge to a diffusion limit in a localized sense.

Keywords: Functional limit theorem; Diffusion limit; Scaling limit; Convergence of stochastic differential equations; Limit order book (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:11:p:4431-4479

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DOI: 10.1016/j.spa.2018.11.023

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