A diffusion approximation for limit order book models

Ulrich Horst and D\"orte Kreher

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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 $L^2_{loc}$-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.

Date: 2016-08, Revised 2017-08
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1608.01795

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