Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10527152 | Stochastic Processes and their Applications | 2016 | 22 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Fernando Cordero, Irene Klein, Lavinia Perez-Ostafe,