HESTON and kappa

SPAAGG · June 2nd, 2004, 1:43 pm

Hi,I know that kappa is the speed of the mean reverting process (in the Heston model) : ds2 = kappa * (eta - s2) * dt + theta * sqrt(s2) * dWcould you give me an intuitive interpretation of this parameter, i.e if kappa 2, what does it meanThanks

Sofiane · June 2nd, 2004, 3:14 pm

Hey, The more kappa is high, the more volatility will converge rapidly to its long term mean and thus defined as follwing a mean reverting process. The impact of this parameter in the skew dynamic is relatively weak compared to the volvol or rho parameters.

SPAAGG · June 3rd, 2004, 4:43 am

I see,but if the kappa=2, I think this means that, the vol returns to the mean every 250 / 2 * 2 = 62 days. Is it correct ?Tx

granchio · June 3rd, 2004, 5:43 am

think of tau=1/kappa as the decay timescale.

Sofiane · June 3rd, 2004, 7:34 am

I would take the inverse of kappa and multiply by a factor that ajust for maturity (bring from calendar days to trading days).

GiacomoGalli · June 4th, 2004, 5:57 am

Hey Sofiane,what about the meaning of Rho and Vol of Vol (skew/smile parameters) in the calibration process?thanks

SPAAGG · June 4th, 2004, 6:02 am

rho is the correlation between the vol and the stock returns. Usually, this is negative (leverage - Black effect, check paper of Black, 1976 for an explanation)the vol of vol is simply the volatility of the volatilitythe remaining parameter, eta, is the long term variance

GiacomoGalli · June 4th, 2004, 6:04 am

thanks Spaagg