# Rough Volatility Prediction - Gatheral, Jaisson, Rosenbaum Paper

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.

## 1 Answer

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.

• Thank you skoestlmiere. I'm wondering if you could guide me on how to write formulas/equations. I did not see an option to "insert formula" when writing my response. Thank you – DangerousMouse Aug 11 '19 at 9:17