We give an approximation to geometric fractional Brownian motion. The approximation is a simple corollary to a ‘teletraffic’ functional central limit theorem by Gaigalas and Kaj in (Bernoulli 9:671–703, 2003). We analyze the central limit theorem of Gaigalas and Kaj from the point of view of semimartingale limit theorems to have a better understanding of the arbitrage in the limit model. With this approximation we associate the corresponding pricing model sequence, which has the no-arbitrage property and which is complete.