Rough Volatility Prediction - Gatheral, Jaisson, Rosenbaum Paper

Question

I just read through the paper "Volatility Is Rough" by Gatheral, Jaisson and Rosenbaum. There is a website (link: http://tpq.io/p/rough_volatility_with_python.html) that details the simulations they have done in their paper which I found quite useful. There is one point, however, where I seem to miss something. They are approximating the prediction formula (5.1 in the paper) via its Riemann sum but they drop the term $\frac{cos(H\pi)}{\pi}$. Any reason why? Apologies if this is obvious.

Thanks.

Answer 1

1) They drop the
$$ \frac{\cos (H\pi)}{\pi} \cdot \Delta^{H + 1/2}$$

2) They divide by a normalization factor, which is the sum of the integrand (without the $\log v_s$).

If you integrate: $$ \frac{\cos (H\pi)}{\pi} \cdot \Delta^{H + 1/2} \cdot \frac{1}{(x + \Delta) \cdot x^{H + 1/2}}$$ from zero to infinity, you will get 1.