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

Alexander Jurisch

Papers from arXiv.org

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.

Date: 2018-04, Revised 2019-02
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1804.02689

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