Hedging Non-Tradable Risks with Transaction Costs and Price Impact

27 Pages Posted: 27 Apr 2018 Last revised: 16 Jun 2018

See all articles by Álvaro Cartea

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Ryan Francis Donnelly

University of London - Faculty of Natural and Mathematical Sciences

Sebastian Jaimungal

University of Toronto - Department of Statistics

Date Written: June 7, 2018

Abstract

A risk-averse agent hedges her exposure to a non-tradable risk factor U using a correlated traded asset S and accounts for the impact of her trades on both factors. The effect of the agent's trades on U is referred to as cross-impact. By solving the agent's stochastic control problem, we obtain a closed-form expression for the optimal strategy when the agent holds a linear position in U. When the exposure to the non-tradable risk factor is non-linear, we provide an approximation to the optimal strategy in closed-form, and prove that the value function is correctly approximated by this strategy when cross-impact and risk-aversion are small. We further prove that when exposure to U is non-linear, the approximate optimal strategy can be written in terms of the optimal strategy for a linear exposure with the size of the position changing dynamically according to the exposure's "Delta" under a particular probability measure.

Keywords: algorithmic trading, hedging, price impact

JEL Classification: G10, G11, C41

Suggested Citation

Cartea, Álvaro and Donnelly, Ryan Francis and Jaimungal, Sebastian, Hedging Non-Tradable Risks with Transaction Costs and Price Impact (June 7, 2018). Available at SSRN: https://ssrn.com/abstract=3158727 or http://dx.doi.org/10.2139/ssrn.3158727

Álvaro Cartea

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Ryan Francis Donnelly (Contact Author)

University of London - Faculty of Natural and Mathematical Sciences ( email )

Strand
London, England WC2R 2LS
United Kingdom

Sebastian Jaimungal

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

HOME PAGE: http://www.utstat.utoronto.ca/sjaimung

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