PERFORMANCE OF ROBUST HEDGES FOR DIGITAL DOUBLE BARRIER OPTIONS

Jan Obłój and Frédérik Ulmer
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Jan Obłój: Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford OX1 3LB, United Kingdom and Oxford-Man Institute of Quantitative Finance, Eagle House, Walton Well Road, Oxford OX2 6ED, United Kingdom
Frédérik Ulmer: Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford OX1 3LB, United Kingdom

Chapter 23 in Finance at Fields, 2012, pp 521-554 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractWe analyze the performance of robust hedging strategies of digital double barrier options of Cox and Obłój (2011) against that of traditional hedging methods such as delta and delta/vega hedging. Digital double barrier options are financial derivative contracts which pay out a fixed amount on the condition that the underlying asset remains within or breaks into a range defined by two distinct barrier levels. We perform the analysis in hypothetical forward markets driven by models with stochastic volatility and jumps, calibrated to the AUD/USD foreign exchange rate market. Our findings are strikingly unanimous and suggest that, in the presence of model uncertainty and/or transaction costs, robust hedging strategies typically outperform in a substantial way model-specific hedging methods.

Keywords: Mathematical Finance; Financial Mathematics; Risk Management; Asset Pricing; Computational Finance; Derivatives; Option Pricing; Portfolio Optimization (search for similar items in EconPapers)
Date: 2012
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