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Pricing by hedging and no-arbitrage beyond semimartingales

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Abstract

We show that pricing a big class of relevant options by hedging and no-arbitrage can be extended beyond semimartingale models. To this end we construct a subclass of self-financing portfolios that contains hedges for these options, but does not contain arbitrage opportunities, even if the stock price process is a non-semimartingale of some special type. Moreover, we show that the option prices depend essentially only on a path property of the stock price process, viz. on the quadratic variation. We end the paper by giving no-arbitrage results even with stopping times for our model class.

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Authors and Affiliations

  1. Institute for Mathematical Stochastics, TU Braunschweig, Pockelsstr. 14, 38106, Braunschweig, Germany

    Christian Bender

  2. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland

    Tommi Sottinen

  3. School of Science and Engineering and School of Business, Reykjavík University, Kringlan 1, 103, Reykjavík, Iceland

    Tommi Sottinen

  4. Department of Mathematics and Systems Analysis, Helsinki University of Technology, P.O. Box 1100, 02015, Helsinki, Finland

    Esko Valkeila

Authors
  1. Christian Bender
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  2. Tommi Sottinen
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  3. Esko Valkeila
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Correspondence to Esko Valkeila.

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Bender, C., Sottinen, T. & Valkeila, E. Pricing by hedging and no-arbitrage beyond semimartingales. Finance Stoch 12, 441–468 (2008). https://doi.org/10.1007/s00780-008-0074-8

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  • DOI: https://doi.org/10.1007/s00780-008-0074-8

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