• Corpus ID: 59937451

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

  title={An extremal fractional Gaussian with a possible application to option-pricing with skew and smile},
  author={Alexander Jurisch},
  journal={arXiv: Pricing of Securities},
  • A. Jurisch
  • Published 8 April 2018
  • Mathematics
  • arXiv: Pricing of Securities
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. 

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