# An extremal fractional Gaussian with a possible application to option-pricing with skew and smile

@article{Jurisch2018AnEF, title={An extremal fractional Gaussian with a possible application to option-pricing with skew and smile}, author={Alexander Jurisch}, journal={arXiv: Pricing of Securities}, year={2018} }

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.

## One Citation

Statistical mechanics and time-series analysis by L\'evy-parameters with the possibility of real-time application

- Mathematics
- 2019

We develop a method that relates the truncated cumulant-function of the fourth order with the Levian cumulant-function. This gives us explicit formulas for the Levy-parameters, which allow a…

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