  We derive an extremal fractional Gaussian by employing the L\'evy-Khintchine
theorem and L\'evian noise. With the fractional Gaussian we then generalize the
Black-Scholes-Merton option-pricing formula. We obtain an easily applicable and
exponentially convergent option-pricing formula for fractional markets. We also
carry out an analysis of the structure of the implied volatility in this
system.
