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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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