Portfolio Execution with a Dark Pool Under Stochastic Volatility and Liquidity

14 Pages Posted: 22 Oct 2014

Date Written: October 20, 2014

Abstract

In this paper we study a portfolio execution problem in a discrete-time model in which orders can be submitted to a standard exchange and a dark pool. We model volatilities and correlations as stochastic processes and assume that trading at the standard exchange causes price impact. Orders sent to the dark pool do not affect prices. But they are not always filled. An efficient execution strategy has to find the right balance between favorable transaction prices and immediacy. Our main result gives a closed form expression for strategies that minimize a weighted average of expected implementation costs and exposure to market risk. As an example we simulate the optimal acquisition of two correlated assets and compare it to a program which trades the assets separately without taking into account correlation or cross price impact.

Keywords: Portfolio execution, stochastic volatility, stochastic liquidity, dark pool, dynamic programming.

JEL Classification: C61, C63, D81

Suggested Citation

Cheridito, Patrick and Sepin, Tardu, Portfolio Execution with a Dark Pool Under Stochastic Volatility and Liquidity (October 20, 2014). Available at SSRN: https://ssrn.com/abstract=2512506 or http://dx.doi.org/10.2139/ssrn.2512506

Patrick Cheridito

ETH Zurich ( email )

Department of Mathematics
8092 Zurich
Switzerland

Tardu Sepin (Contact Author)

Bank of America Merrill Lynch ( email )

One Bryant Park
NY1-100-03-01
New York, NY 10036
United States

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