BINARY MARKETS UNDER TRANSACTION COSTS

Fernando Cordero (), Irene Klein () and Lavinia Perez-Ostafe ()
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Fernando Cordero: Faculty of Technology, University of Bielefeld, Universitätsstrasse 25, U4-151, Bielefeld 33615, Germany
Irene Klein: Department of Statistics and Operations Research, University of Vienna, Oskar-Morgerstern-Platz 1, Vienna 1090, Austria
Lavinia Perez-Ostafe: Department of Mathematics, ETH Zurich, Rämistrasse 101, Zurich 8092, Switzerland

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 05, 1-27

Abstract: The goal of this work is to study binary market models with transaction costs, and to characterize their arbitrage opportunities. It has been already shown that the absence of arbitrage is related to the existence of λ-consistent price systems (λ-CPS), and, for this reason, we aim to provide conditions under which such systems exist. More precisely, we give a characterization for the smallest transaction cost λc (called "critical" λ) starting from which one can construct a λ-CPS. We also provide an expression for the set $\mathcal{M}(\lambda)$ of all probability measures inducing λ-CPS. We show in particular that in the transition phase "λ = λc" these sets are empty if and only if the frictionless market admits arbitrage opportunities. As an application, we obtain an explicit formula for λc depending only on the parameters of the model for homogeneous and also for some semi-homogeneous binary markets.

Keywords: Binary market; transaction costs; consistent price system; arbitrage (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024914500307

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