Lognormal approximation and SDF


I am trying to make risk-free rates under the assumption that SDF is lognormal.

That is,

r_f=-E_t(logM_t+1))-1/2Var_t(logM_t+1) where M is SDF.

My problem is that I do not know how to make the second term “1/2Var_t(logM_t+1)” in dynare. This term seems to be time varyng risk premia and is very crucial to express the expected exchage rate risk premium in Verdelhan (2010).

Please let me know if it is possible to make dynare code for the second term in the current version. Also please let me know if the third order approximation can help or how it can help.

Thank you in advance.