How to set correlated wiener processes when constructing stochastic model?

Questions v3
1

I have stochastic price model with its volatility being stochastic too.
dS and dV (where S is price of stock and V is volatility of stock) both has dW term which follows normal distribution.
and the correlation between them is rho = dW_S * dW_V

Then how can I construct this stochastic model?

2

Hi KTX,

A Wiener process is just a continuous time gaussian random walk, and PyMC has this distribution built in as pm.GaussianRandomWalk. It also comes in a multivariate flavor. You will need to re-write your SDE in discrete time and solve it (or the other-way around I guess). That will give you a mean vector and covariance matrix that describes the price and volatility processes. You can plug these into the MvGaussianRandomWalk to actually implement the model.