Hey all,I've been playing around with regime switching pde's as an alternative to stochastic volatility models, but I'm stuck trying to replicate the heston like stock-vol correlation. Essentially a regime switching model has n black scholes pde where each pde has a different vol diffusion parameter. At each stage in backwards recursion one mixes between the states as an additional term in the pde. One can create skew by having jumps in the stock between state movements, but there isn't any obvious approximation for the spot-vol correlation term in heston.The benefit of the regime switching is the simplicity of approximating any vol diffusion pde with a few states (as long as the transition matrix is set up correctly). I figure that since at any point in time I have a vector of prices corresponding to each vol state, there may be a way to approximate the correlation term and incorporate a heston like stock-vol correlation.My understanding of heston models is that the cross term is the largest challenge, so I would not be surprised if this wasn't possible without many states (so that the difference between a given state is small and the dPrice/dvol approximation is accurate).Does anyone have any thoughts or references on such an idea?On page 3 one can find an example of a specification for a standard regime switching pde.https://cs.uwaterloo.ca/~paforsyt/regim ... .pdfThanks for your thoughts in advance.