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

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  • Alexander Jurisch

Abstract

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.

Suggested Citation

  • Alexander Jurisch, 2018. "An extremal fractional Gaussian with a possible application to option-pricing with skew and smile," Papers 1804.02689, arXiv.org, revised Feb 2019.
    • Handle: RePEc:arx:papers:1804.02689
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