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Arbitrage with Fractional Brownian Motion
Author(s) -
Rogers L. C. G.
Publication year - 1997
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.00025
Subject(s) - arbitrage , fractional brownian motion , economics , brownian motion , range (aeronautics) , econometrics , geometric brownian motion , financial economics , mathematics , diffusion process , statistics , economy , service (business) , materials science , composite material
Fractional Brownian motion has been suggested as a model for the movement of log share prices which would allow long–range dependence between returns on different days. While this is true, it also allows arbitrage opportunities, which we demonstrate both indirectly and by constructing such an arbitrage. Nonetheless, it is possible by looking at a process similar to the fractional Brownian motion to model long–range dependence of returns while avoiding arbitrage.