An extremal fractional Gaussian with a possible application to option-pricing with skew and smile
arXiv:1804.02689
Abstract
We derive an extremal fractional Gaussian by employing the Lévy-Khintchine theorem and Lévian 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.
6 pages, 3 figures