I am very new to stan, appreciate any help to code this model in rstan.
Sorry nobody responded, Mai, but we don’t really have time to formulate models for people. You can basically write this one down exactly as written, but rather than taking \eta_t to have a normal distribution, take h_{t+1} \sim \textrm{normal}(\mu + \textrm{diag}(\phi_{11}, \phi_{22})(h_t - \mu), \Sigma_\eta). Then you want to give y_t a lognormal distribution centered at \Omega_t.
The Stan user’s guide also has an example of a univariate SV model. Shouldn’t be too hard to adapt to bivariate using @Bob_Carpenter’s suggestion.