Heston multiasset

Posted by PinkLizard on
URL: http://quantlib.414.s1.nabble.com/Heston-multiasset-tp7414.html

Hi all,

I'm a new guest..

I'm working on Heston model.  I'd like to know how quantlib manage heston multiassets or how can one implement it.

In an object logic, we just have the process for the single underlyings each one with specified correlation between price-vol.
So one has to incorporate the correlation between two assets returns vol-vol, price-vol.

Think about 2 underlyings.
1)To specify the dynamic of asset 1 I throw a random "object" w1=(w_price1  w_vol1), where corr(w_price1  w_vol_1)=rho1.
2)For the 2nd asset  I throw an other random "object" w1=(w_price2  w_vol2), where corr(w_price2  w_vol_2)=rho2.

Now the points where I'm in difficult.
Let's define a product "x" between random "object" to be a matrix in this way:
w1 x w_2= w1=(w_price1*w_price_2      w_price_1*w_vol_2;
                       w_price_1*w_vol_2       w_vol1 *w_vol2).
where * is the standard produtc.
 
                   
3) The main idea, following black scholes framework, is that now:
corr(w_1,w2)= matrix_rho= =(corr(w_price1*w_price_2)      corr(w_price_1*w_vol_2);
                                        corr(w_price_1*w_vol_2)       corr(w_vol1 *w_vol2)).


To generate such random "objects" w_1 e w_2 with that correlation matrix,I throw two indipendent
random "object" z_1 and z_2 and then set:

w_1 = z1
w2 = sqrt(1-rhomatrix^2)Z2+rho_matrix Z1.

The engine isn't correct cause with that definition of product we haven't that corr(Z2,Z2)=corr(Z1,Z1)=identity_matrix.

Any solution or suggestion?