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Title: Limit order books and liquidation problems
Author: Hewlett, Patrick
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2011
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This thesis concerns the mathematical modeling of limit order books. We study zero-intelligence ("ZI ") models of limit order books where order book events are governed by Poisson processes. Extending the mean-field approximations of [1] to the time-inhomogeneous case, we study the expected relaxation of the order book and mid price movement following an out-of equilibrium initial condition. The resulting equations are suggestive of how limit order book state might be used as a trading signal in liquidation algorithms or proprietary trading. The same mean-field techniques are used to study the mean response over time of the limit order book in different states to the submission of market orders of different sizes (loosely, the market impact function implied by ZI dynamics). We extend existing models of liquidation under risk aversion (e.g. [2]) to the case where the liquidating agent transacts using market orders against a limit order book with ZI dynamics. The resulting model has rich features, since expected price movement, volatility and temporary and permanent market impact all depend stochastically on the order book state. We propose methods for approximate solution of the resulting multiple optimal stopping problem and discuss extension to the case where our agent can transact using limit orders as well as market orders. We also discuss the extent to which stochastic market impact results in a model which is acceptable in terms being free of unrealistic arbitrage opportunities. In certain markets, the limit order book is only partially observable. Using HMM techniques, we consider inference ofthe distribution of order book state from observed book evolution and implications of partial observation for price prediction and liquidation algorithms. Finally, we step outside of the ZI paradigm to consider clustering of arrivals market orders. Following e.g. [3] we use Hawkes processes to model this clustering. Under the additional assumption of zero market maker profitability, we solve for the price impact function and optimal liquidation path of a large trader.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available