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Hedging under arbitrage

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  • Johannes Ruf

Abstract

It is shown that delta hedging provides the optimal trading strategy in terms of minimal required initial capital to replicate a given terminal payoff in a continuous-time Markovian context. This holds true in market models where no equivalent local martingale measure exists but only a square-integrable market price of risk. A new probability measure is constructed, which takes the place of an equivalent local martingale measure. In order to ensure the existence of the delta hedge, sufficient conditions are derived for the necessary differentiability of expectations indexed over the initial market configuration. The recently often discussed phenomenon of "bubbles" is a special case of the setting in this paper. Several examples at the end illustrate the techniques described in this work.

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  • Johannes Ruf, 2010. "Hedging under arbitrage," Papers 1003.4797, arXiv.org, revised May 2011.
    • Handle: RePEc:arx:papers:1003.4797
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    References listed on IDEAS

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    Cited by:

    1. Constantinos Kardaras, 2012. "Valuation and parities for exchange options," Papers 1206.3220, arXiv.org, revised Nov 2014.
    2. Martin Larsson, 2013. "Non-Equivalent Beliefs and Subjective Equilibrium Bubbles," Papers 1306.5082, arXiv.org.
    3. Ke Du & Eckhard Platen, 2011. "Three-Benchmarked Risk Minimization for Jump Diffusion Markets," Research Paper Series 296, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Claudio Fontana & Wolfgang J. Runggaldier, 2012. "Diffusion-based models for financial markets without martingale measures," Papers 1209.4449, arXiv.org, revised Feb 2013.
    5. Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.

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