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Pricing derivatives with fractional volatility

International Journal of Financial Engineering, 2016
This paper studies the effect of fractional volatility on path-dependent options, which are highly sensitive to the volatility structure of a targeted underlying asset process. To this end, we propose an approximation formula for average and barrier options when volatility follows a fractional Brownian motion. Furthermore, using the analytical formula,
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The Causal Fractional Derivatives

2011
The fractional calculus is a 300 years old mathematical discipline. In fact and some time after the publication of the studies on Differential Calculus, where he introduced the notation \( {\frac{{{\text{d}}^{n} y}}{{{\text{d}}x^{n} }}} ,\) Leibnitz received a letter from Bernoulli putting him a question about the meaning of a non-integer derivative ...
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ON FRACTIONAL INTEGRALS AND DERIVATIVES

The Quarterly Journal of Mathematics, 1940
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