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European Finance Review 2003 7(1):75-102; doi:10.1023/A:1022506825795
© 2003 by European Finance Association
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Right arrow C61 - Optimization Techniques; Programming Models; Dynamic Analysis
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Local Expected Shortfall-Hedging in Discrete Time*

Marco Schulmerich1 and Siegfried Trautmann2

1 Barra International, Frankfurt, Germany E-mail: marco.schulmerich{at}barra.com
2 CoFaR Center of Finance and Risk Management, Johannes Gutenberg-Universität D-55099 Mainz, Germany E-mail: traut{at}finance.uni-mainz.de

This paper proposes a self-financing trading strategy that minimizes the expected shortfall locally when hedging a European contingent claim. A positive shortfall occurs if the hedger is not willing to follow a perfect hedging or a superhedging strategy. In contrast to the classical variance criterion, the expected shortfall criterion depends only on undesirable outcomes where the terminal value of the written option exceeds the terminal value of the hedge portfolio. Searching a strategy which minimizes the expected shortfall is equivalent to the iterative solution of linear programs whose number increases exponentially with respect to the number oftrading dates. Therefore, we partition this complex overall problem into several one-period problems and minimize the expected shortfall only locally, i.e., only over the next trading period. This approximation is quite accurate and the number of linear programs to be solved increases only linearly with respect to the number of trading dates. JEL Classifications: C61, G10, G12, G13, D81

Key Words: hedging • self-financing strategies • superhedging • myopic hedging strategies • expected shortfall • coherent risk measures


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