One-level limit order book models with memory and variable spread

Chávez-Casillas, Jonathan A.; Figueroa-López, José E.

doi:10.48550/arxiv.1407.5684

Cited by 1 publication

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“…A Brownian motion with drift is a reasonable approximation for intermediate intraday time horizons (such as a few minutes) as shown by some recent works (see, e.g., [5] and [4]). Also, we can see this model as the continuous-time counterpart of a correlated random walk (CRW).…”

Section: Toward the Optimal Placement Problem In Continuous Timementioning

confidence: 80%

“…In this paper, we discuss the optimal strategy when the price dynamics follow a diffusive model such as a Brownian motion (BM) or a Geometric Brownian motion (GBM). A BM model, often called the Bachelier model, can be seen as a reasonable approximation of asset price dynamics at intermediate intraday time horizons (see, e.g., [5] and [4]). Also, bridging with the work of [10], a BM with 0 drift (respectively, nonzero drift) appears as the limit of a symmetric (respectively, asymmetric) correlated random walk when the time step between price changes and the tick size goes to 0 in a certain way (cf.…”

Section: Introductionmentioning

confidence: 99%

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Optimal placement of a small order in a diffusive limit order book

2018

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We study the optimal placement problem of a stock trader who wishes to clear his/her inventory by a predetermined time horizon t, using a limit order or a market order. For a diffusive market, we characterize the optimal limit order placement policy and analyze its behavior under different market conditions. In particular, we show that, in the presence of a negative drift, there exists a critical time t0 > 0 such that, for any time horizon t > t0, there exists an optimal placement, which, contrary to earlier work, is different from one that is placed “infinitesimally” close to the best ask, such as the best bid and second best bid. We also propose a simple method to approximate the critical time t0 and the optimal order placement.

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Section: Toward the Optimal Placement Problem In Continuous Timementioning

confidence: 80%