Hedging Forward Positions: Basis Risk Versus Liquidity Costs

32 Pages Posted: 6 Jul 2012 Last revised: 19 Jun 2013

See all articles by Stefan Ankirchner

Stefan Ankirchner

University of Bonn

Peter Kratz

Humboldt University of Berlin

Thomas Kruse

University of Duisburg-Essen

Date Written: June 19, 2013

Abstract

Consider an agent with a forward position of an illiquid asset (e.g. a commodity) that has to be closed before delivery. Suppose that the liquidity of the asset increases as the delivery date approaches. Assume further that the agent has two possibilities for hedging the risk inherent in the forward position: first, he can enter customized forward contracts; second, he can acquire standardized and liquidly traded forward contracts. We assume that purchasing customized forwards perfectly eliminates the risk, but entails high liquidity costs charged by the counterparty. The standardized forwards can be acquired at considerably lower costs, but do not perfectly match the agent's risk and hence entail basis risk. By means of stochastic control we show how to obtain an optimal trade-off between liquidity costs and basis risk. To this end we reduce the hedging problem to a family of stopping problems. In two case studies we consider simple liquidity dynamics for which optimal hedging strategies can be calculated explicitly.

Keywords: illiquidity, basis risk, optimal liquidation, hedging, singular stochastic control, optimal stopping

Suggested Citation

Ankirchner, Stefan and Kratz, Peter and Kruse, Thomas, Hedging Forward Positions: Basis Risk Versus Liquidity Costs (June 19, 2013). Available at SSRN: https://ssrn.com/abstract=2100768 or http://dx.doi.org/10.2139/ssrn.2100768

Stefan Ankirchner

University of Bonn ( email )

Regina-Pacis-Weg 3
Postfach 2220
Bonn, D-53012
Germany

Peter Kratz

Humboldt University of Berlin ( email )

Unter den Linden 6
Berlin, Berlin 10099
Germany

Thomas Kruse (Contact Author)

University of Duisburg-Essen ( email )

Thea-Leymann-Stra├če 9
Essen, 45127
Germany

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