LOCAL RISK-MINIMIZATION WITH MULTIPLE ASSETS UNDER ILLIQUIDITY WITH APPLICATIONS IN ENERGY MARKETS

Panagiotis Christodoulou (), Nils Detering () and Thilo Meyer-Brandis ()
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Panagiotis Christodoulou: Department of Mathematics, University of Munich, Theresienstraße 39, 80333 Munich, Germany
Nils Detering: Department of Statistics & Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA
Thilo Meyer-Brandis: Department of Mathematics, University of Munich, Theresienstraße 39, 80333 Munich, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2018, vol. 21, issue 04, 1-44

Abstract: We propose a hedging approach for general contingent claims when liquidity is a concern and trading is subject to transaction cost. Multiple assets with different liquidity levels are available for hedging. Our risk criterion targets a tradeoff between minimizing the risk against fluctuations in the stock price and incurring low liquidity costs. We work in an arbitrage-free setting assuming a supply curve for each asset. In discrete time, we prove the existence of a locally risk-minimizing strategy under mild conditions on the price process. Under stochastic and time-dependent liquidity risk we give a closed-form solution for an optimal strategy in the case of a linear supply curve model. Finally we show how our hedging method can be applied in energy markets where futures with different maturities are available for trading. The futures closest to their delivery period are usually the most liquid but depending on the contingent claim not necessarily optimal in terms of hedging. In a simulation study, we investigate this tradeoff and compare the resulting hedge strategies with the classical ones.

Keywords: Local risk-minimization; quadratic hedging; liquidity cost; energy markets; multiple assets (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0219024918500280

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