SIMULTANEOUS TRADING IN ‘LIT’ AND DARK POOLS

M. Alessandra Crisafi () and Andrea Macrina
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M. Alessandra Crisafi: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
Andrea Macrina: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK2Department of Actuarial Science, University of Cape Town, Rondebosch 7701, South Africa

International Journal of Theoretical and Applied Finance (IJTAF), 2016, vol. 19, issue 08, 1-33

Abstract: We consider an optimal trading problem over a finite period of time during which an investor has access to both a standard exchange and a dark pool. We take the exchange to be an order-driven market and propose a continuous-time setup for the best bid price and the market spread, both modeled by Lévy processes. Effects on the best bid price arising from the arrival of limit buy orders at more favorable prices, the incoming market sell orders potentially walking the book, and deriving from the cancellations of limit sell orders at the best ask price are incorporated in the proposed price dynamics. A permanent impact that occurs when ‘lit’ pool trades cannot be avoided is built in, and an instantaneous impact that models the slippage, to which all lit exchange trades are subject, is also considered. We assume that the trading price in the dark pool is the mid-price and that no fees are due for posting orders. We allow for partial trade executions in the dark pool, and we find the optimal trading strategy in both venues. Since the mid-price is taken from the exchange, the dynamics of the limit order book also affects the optimal allocation of shares in the dark pool. We propose a general objective function and we show that, subject to suitable technical conditions, the value function can be characterized by the unique continuous viscosity solution to the associated partial integro-differential equation. We present two explicit examples of the price and the spread models, derive the associated optimal trading strategy numerically. We discuss the various degrees of the agent's risk aversion and further show that roundtrips are not necessarily beneficial.

Keywords: Stochastic control; optimal trading strategies; Hamilton–Jacobi–Bellman equation; viscosity solutions; limit order book; market impact; dark pools (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024916500552

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