The scientific debate of recent years about option pricing with respect to fractional Brownian
motion was focused on the feasibility of the no arbitrage pricing approach. As the unrestricted
fractional market setting allows for arbitrage the conventional reasoning is that fractional
Brownian motion does not qualify for modeling price process. In this book the author points
out that arbitrage can only be excluded in case that market prices move at least slightly
faster than any market participant can react. He clarifies that continuous tradability always
eliminates the risk of the fractional price process irrespective of the interpretation of the
stochastic integral as an integral of Stratonovich or Itô type. Being left with an incomplete
market setting the author shows that option valuation with respect to fractional Brownian
motion may be solved by applying a risk preference based approach. The latter provides us with
an intuitive closed-form solution for European options within the fractional context.
