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arXiv · 1804.02689

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

Alexander Jurisch
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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.

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Alexander Jurisch. 2018-04-08. An extremal fractional Gaussian with a possible application to option-pricing with skew and smile. https://arxiv.org/abs/1804.02689

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