Estimate parameters of two correlated processes

[Marion2025]

Hi Marek,

I’ve had similar challenges implementing a multivariate SDE, where the two processes are correlated. See my latest post on this thread below. I ended up using theano.scan to update the volatility process (which depends on previous values) , but I think in general having a Multivariate SDE class would handle these types of problems would be incredibly valuable.

Marek, it looks like you are estimating two correlated geometric Brownian motions (Black model). I’m very interested in your solution as I am trying to solve a very similar problem

Help with Multivariate SDE Timeseries

Here’s a possible workaround…though I still prefer the type of solution involving a new multivariate class… is it possible to define a Deterministic that’s a recursive function? this would be similar to the vol-update function in the GARCH class. Consider the model again: Y_t=\sqrt{V_{t-1}}\epsilon_t^s log(V_t)=\alpha_v+\beta_vlog(V_{t-1})+\sigma_v\epsilon_t^v \epsilon_t^s and \epsilon_t^v have correlation \rho Set \epsilon^s=\rho\epsilon_t^v+\sqrt{1-\rho^2}\epsilon_t^n so that \epsilon_t^…