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Robust One-Period Option Hedging

Department of Finance, Maastricht University, Tongerseweg 53, 6200 MD, Maastricht, The Netherlands
Department of Econometrics, Tilburg University, Tilburg, The Netherlands
Department of Quantitative Economics, Maastricht University, Maastricht, The Netherlands
f.lutgens{at}finance.unimaas.nl

We consider robust optimization to cope with uncertainty about the stock return process in one-period option hedging problems. The robust approach relates portfolio choice to uncertainty, making more cautious hedges when uncertainty is high. We represent uncertainty by a set of plausible expected returns of the underlying stocks and show that for this set the robust problem is a second-order cone program that can be solved efficiently. We apply the approach to find an optimal portfolio to hedge an index option.

Subject classifications: robust optimization; portfolio optimization; nonnegative cones; hedging.
History: Received December 2002; revision received October 2005; accepted October 2005.