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We develop a highly efficient approach to compute the volatility of the Fractional Brownian Motion (FBM) implied by American options. To this aim, the theoretical values of American option prices under the FBM are calculated using a finite difference scheme enhanced by a space-time Richardson extrapolation procedure. Such an approach, which is coupled with a suitable optimization algorithm, turns out to be very accurate and fast. The practical performances of the method proposed aredoi:10.12732/ijam.v26i2.7 fatcat:j66lpcefirachakaof2zq52xoy