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Pricing by hedging and no-arbitrage beyond semimartingales. (English) Zbl 1199.91170
The authors construct a class of strategies for possibly non-semimartingale models that have the same quadratic variation as the Black-Scholes model or, more generally, as Brownian models with local volatility structures. It is shown that the aforementioned class of allowed strategies is free of arbitrage for a large class of non-semimartingale models, in particular, for the mixed fractional Brownian models. The non-arbitrage result demonstrates that some non-smooth functional behavior is required to construct arbitrage via distributional properties, which is not inherent in hedges of many interesting options. It is also shown that the no-arbitrage result still holds if a portfolio is changed abruptly at stopping times from a reasonably large class. It is emphasized that the option prices essentially depend only on the quadratic variation which can be viewed as a path property. Therefore option prices are robust with respect to probabilistic properties.

91G10 Portfolio theory
91G20 Derivative securities (option pricing, hedging, etc.)
60G15 Gaussian processes
60G48 Generalizations of martingales
Full Text: DOI
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