On arbitrage and replication in the fractional Black–Scholes pricing model
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Tommi Sottinen
Summary
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.
© 2003 Oldenbourg Wissenschaftsverlag GmbH
Articles in the same Issue
- On arbitrage and replication in the fractional Black–Scholes pricing model
- On the construction of efficient estimators in semiparametric models
- The Bahadur risk in probability density estimation
- On preferences of general two-sided tests with applications to Kolmogorov–Smirnov-type tests
- Estimating the dimension of factors of diffusion processes
- Ranking of populations in parameter′s modulus
Articles in the same Issue
- On arbitrage and replication in the fractional Black–Scholes pricing model
- On the construction of efficient estimators in semiparametric models
- The Bahadur risk in probability density estimation
- On preferences of general two-sided tests with applications to Kolmogorov–Smirnov-type tests
- Estimating the dimension of factors of diffusion processes
- Ranking of populations in parameter′s modulus
