Asymptotic proportion of arbitrage points in fractional binary markets

Fernando Cordero, Irene Klein and Lavinia Perez-Ostafe

Stochastic Processes and their Applications, 2016, vol. 126, issue 2, 315-336

Abstract: A fractional binary market is a binary model approximation for the fractional Black–Scholes model, which Sottinen constructed with the help of a Donsker-type theorem. In a binary market the non-arbitrage condition is expressed as a family of conditions on the nodes of a binary tree. We call “arbitrage points” the nodes which do not satisfy such a condition and “arbitrage paths” the paths which cross at least one arbitrage point. In this work, we provide an in-depth analysis of the asymptotic proportion of arbitrage points and arbitrage paths. Our results are obtained by studying an appropriate rescaled disturbed random walk.

Keywords: Fractional Brownian motion; Fractional binary markets; Binary markets; Arbitrage opportunities (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2015.09.002

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