Hi folks,I heard there is a method called "alpha-parameterization" to define vol/vol and stock/vol. correlations for mulit underlying Heston model.Let S = stock, V= volatilityCorr( S(i) V(j) ) = Corr( S(j) V(j) ) * Corr( S(i) S(j) ) ******************************** (1)Corr( V(i) V(j) ) = Corr( S(i) V(i) ) * Corr( S(j) V(j) ) * Corr( S(i) S(j) ) + sqrt ( 1 - Corr( S(i) V(i) ) ^ 2) * sqrt ( 1 - Corr( S(j) V(j) ) ^ 2) ************************************* (2)May I know how to derive these 2 equations above ? Any good ref. papers appreciated as well.thx,

The formula for the Spot(i)Vol(j) calculation really gives you just an expected value (by multiplying SABR RHO(1) into the spot correlation)As for the Vol_Vol correlation: have a look at this Durrleman paper: math.stanford.edu/~valdo/papers/coupling-fx.pdf

Hello,thx for the explanation. but i really can't understand....In the paper you refer, which page can i find the vol_vol correlation derivation ? thx,

if I assume dS1 = r1 dt + sig1 dX1dS2 = r2 dt + sig2 dX2Similarly for sig1 and sig2 we have brownian motions dX3, dX4. then E[dX1dX2] = rho1 dt(or correlation between two stocks]E[dX2 dX4] = rho3 dt (correlation between stock and vol of other stock)E[dX1 dX4] => What you need to calculate ....Multiplying we get...E[dX1dX2] x E[dX2 dX4] = rho1 rho3 (dt)^2since...E[dX^2] = dtWhich proves ur first formula.

Hi,thx for the explanation but i don't see it...>>>E[dX1 dX4] => What you need to calculate ....>>>Multiplying we get...>>>E[dX1dX2] x E[dX2 dX4] = rho1 rho3 (dt)^2>>>since...E[dX^2] = dt(1) Why is E[dX1dX2] x E[dX2 dX4] = E[dX1 dX4] X E[dX2 ^ 2] ?(2) Even if yes, we should get E[dX1 dX4] x dt = rho1 rho3 (dt) ^ 2=> E[dX1 dX4] = rho1 rho3 * dt (there is a dt term!!!)(3) How about the other one ? Corr( V(i) V(j) ) thx

1. I am just regrouping the expectations. Brownian motions have independent increments. 2. of course there will be a dt term coz I am calculating instantaneous correlation. You can relate that to instantaneous volatility & implied volatility. Next formula is also simple.....it's just another way of generating correlated random numbers. if X and Y are two independent brownian motions, how do I convert them to correlated brownian motions with correlation (instantenous) rho dt?Some simplifications will give you the second formula...

Thanks, mateIn this slide:-http://www.cmap.polytechnique.fr/~euros ... ixis.pdfIt is mentioned that Vol-vol correlation is a trader's input. So this formula Corr( V(i) V(j) ) = Corr( S(i) V(i) ) * Corr( S(j) V(j) ) * Corr( S(i) S(j) ) + sqrt ( 1 - Corr( S(i) V(i) ) ^ 2) * sqrt ( 1 - Corr( S(j) V(j) ) ^ 2) is of no practical use ?