Finance and Stochastics

, Volume 12, Issue 4, pp 441–468 | Cite as

Pricing by hedging and no-arbitrage beyond semimartingales

  • Christian Bender
  • Tommi Sottinen
  • Esko ValkeilaEmail author


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.


Arbitrage Pricing Quadratic variation Robust hedging 

JEL Classification

G10 G13 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Christian Bender
    • 1
  • Tommi Sottinen
    • 2
    • 3
  • Esko Valkeila
    • 4
    Email author
  1. 1.Institute for Mathematical StochasticsTU BraunschweigBraunschweigGermany
  2. 2.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  3. 3.School of Science and Engineering and School of BusinessReykjavík UniversityReykjavíkIceland
  4. 4.Department of Mathematics and Systems AnalysisHelsinki University of TechnologyHelsinkiFinland

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