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## THE RIGHT FRACTIONAL VOLATILITY MODEL?

After some struggle with the fractional Heston model, where proving positivity for the volatility process is a nontrivial problem, I came across the nice results with the exponential Ornstein-Uhlenbeck model which seems like a better model to fractionalize without worrying about positivity — perello-sircar-masoliver-2008

The fractional version should be, with correlated brownian motions $\langle dw_X, dw_Y \rangle = \rho dt$,

$dX/X = mu dt + m e^{Y(t)} dw_X(t)$

$Y(t) = T_{\alpha}(t) y_0 + \nu \int_0^t S_{\alpha}(s) dw_Y(s)$

I plan to spend more time analyzing this model on data.