Trading with Small Nonlinear Price Impact

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See all articles by Thomas Cayé

Thomas Cayé

Dublin City University - School of Mathematical Sciences

Martin Herdegen

University of Warwick - Department of Statistics

Johannes Muhle-Karbe

Imperial College London - Department of Mathematics

Date Written: July 9, 2018

Abstract

We study portfolio choice with small nonlinear price impact on general market dynamics. Using probabilistic techniques and convex duality, we show that the asymptotic optimum can be described explicitly up to the solution of a nonlinear ODE, which identifies the optimal trading speed and the performance loss due to the trading friction. Previous asymptotic results for proportional and quadratic trading costs are obtained as limiting cases. As an illustration, we discuss how nonlinear trading costs affect the pricing and hedging of derivative securities and active portfolio management.

Keywords: Nonlinear Price Impact, Portfolio Choice, Asymptotics

JEL Classification: G11, G12

Suggested Citation

Cayé, Thomas and Herdegen, Martin and Muhle-Karbe, Johannes, Trading with Small Nonlinear Price Impact (July 9, 2018). Available at SSRN: https://ssrn.com/abstract=

Thomas Cayé

Dublin City University - School of Mathematical Sciences ( email )

Dublin
Ireland

Martin Herdegen

University of Warwick - Department of Statistics ( email )

Coventry CV4 7AL
United Kingdom

Johannes Muhle-Karbe (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

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