Option Pricing in Fractional Brownian Markets - Rostek, Stefan (Lecture Notes in Economics and Mathematical Systems, 2009)
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.