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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

Cite Score 2018: 0.85

SCImago Journal Rank (SJR) 2018: 0.354
Source Normalized Impact per Paper (SNIP) 2018: 0.604

Mathematical Citation Quotient (MCQ) 2018: 0.36

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On arbitrage and replication in the fractional Black–Scholes pricing model

Tommi Sottinen / Esko Valkeila
Published Online: 2009-09-25 | DOI: https://doi.org/10.1524/stnd.


It has been proposed that the arbitrage possibility in the fractional Black–Scholes model depends on the definition of the stochastic integral. More precisely, if one uses the Wick–Itô–Skorohod integral one obtains an arbitrage-free model. However, this integral does not allow economical interpretation. On the other hand it is easy to give arbitrage examples in continuous time trading with self-financing strategies, if one uses the Riemann-Stieltjes integral. In this note we discuss the connection between two different notions of self-financing portfolios in the fractional Black–Scholes model by applying the known connection between these two integrals. In particular, we give an economical interpretation of the proposed arbitrage-free model in terms of Riemann–Stieltjes integrals.

About the article

Published Online: 2009-09-25

Published in Print: 2003-02-01

Citation Information: Statistics & Decisions/International mathematical Journal for stochastic methods and models, Volume 21, Issue 2/2003, Pages 93–108, ISSN (Print) 0721-2631, DOI: https://doi.org/10.1524/stnd.

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