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- Title
Pricing by hedging and no-arbitrage beyond semimartingales.
- Authors
Bender, Christian; Sottinen, Tommi; Valkeila, Esko
- 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.
- Subjects
ARBITRAGE; SECURITIES; STOCK exchanges; HEDGING (Finance); OPTIONS (Finance); PRICES of securities; STOCKS (Finance); STOCK funds; COMMODITY exchanges
- Publication
Finance & Stochastics, 2008, Vol 12, Issue 4, p441
- ISSN
0949-2984
- Publication type
Article
- DOI
10.1007/s00780-008-0074-8