Two models on limit order trading
- In this thesis we study two limit order trading models based on the one of Avellaneda and Stoikov (2008). For the first one, we study Avellaneda-Stoikov model under the condition when the underlying price is mean reverting. Our main result is that when time is far from the terminal, the optimal price for bid and ask limit orders is constant, which means that it does not track the underlying price. Numerical simulations confirm this behavior. When the underlying price is mean reverting, then for times sufficiently far from terminal, it is more advantageous to focus on the mean price and ignore fluctuations around it. Mean reversion suggests that limit orders will be executed with some regularity, and this is why they are optimal. We also explore intermediate time regimes where limit order prices are influenced by the inventory of outstanding orders. The duration of this intermediate regime depends on the liquidity of the market as measured by specific parameters in the model. The second model we study is a price impact model where the underlying price is affected by the mean field terms representing existing limit orders in the market. The main result on this model is that there are two different regimes for the representative trader in the solution of MFG: In the beginning, he trades aggressively which results in a large price impact; after a short period of time, he trades, by expectation, approximately symmetric about the underlying price. As a function of time, the price impact decays exponentially in the solution of MFG. Moreover the expectations of optimal prices for the representative trader are constants symmetric about a level close to the terminal value of expected underlying price.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Department of Mathematics.
|Statement of responsibility
|Submitted to the Department of Mathematics.
|Thesis (Ph.D.)--Stanford University, 2016.
- © 2016 by Weiluo Ren
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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