Suppose we are in the BS framework. If we replace the Brownian Motion with a more general fractional Brownian motion therein, how can it be interpreted?

That is what is a financial interpretation of fractional brownian motion, what can it be understood to represent?


You can replace BM with FBM.

However, in finance, fBm is not a semi-martingale, the general results of mathematical finance in Delbaen and Schachermayer (1994) already imply that it allows a certain kind of arbitrage.

For example, Rogers (1997); Sottinen (2001); Cheridito et al. (2003); Bender and Elliott (2004); Bj¨ork and Hult (2005) have shown that the Black-Scholes model driven by fBm allows arbitrage in a number of ways.

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