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Optimal Trading and Inventory Management in Electronic Markets

Crisafi, M; (2017) Optimal Trading and Inventory Management in Electronic Markets. Doctoral thesis , UCL (University College London). Green open access

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Abstract

In this thesis three distinct trading scenarios are considered and stochastic optimal control models are proposed to derive the optimal strategy the agent/firm should follow. First, we consider an agent who needs to liquidate a large amount of an asset and can trade in both a ‘lit’ exchange and a dark pool. We find the optimal selling schedule by solving numerically the resulting Hamilton-JacobiBellman (HJB) equation. Next, we consider a customised liquidity pool (CLP) that offers a market-making service, by showing bid and ask prices to its clients. The CLP earns the spread from each transaction and it is subject to an inventory risk deriving from potential unfavourable price movements. The CLP can hedge its position in the ‘lit’ pool by means of limit and/or market orders so to rebalance its position on the asset. Finally, we consider a firm that offers mixed principal-versus-agency trading to its clients, and which earns the spread from the principal portion and a fixed fee for the brokerage service. We find the optimal proportion of principal/agency liquidity that should be displayed to clients and the optimal hedging strategy. We make specific reference to the foreign exchange market and consider the cases of one currency pair and three currency pairs. We provide the pseudo-codes, which have been written for solving numerically the models presented in this thesis, as well as a concise review of the dynamic programming principle (DPP) and the viscosity solution theory, specifically applied to the models discussed herein.

Type: Thesis (Doctoral)
Title: Optimal Trading and Inventory Management in Electronic Markets
Open access status: An open access version is available from UCL Discovery
Language: English
UCL classification: UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI: http://discovery.ucl.ac.uk/id/eprint/1546249
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