Hello,

Let’s consider the Forward-Backward SDE composed of one Forward SDE:

dx = a(x, y) * dt + b(x, y) * dW

and one Backward SDE:

dy = c(x, y) * dt + z * dW

where a, b and c are some functionals. Thanks to Dynare, I can solve this FBSDE using a second order approximation near its steady state using

```
dt = 1/12;
model;
x - x(-1) = a(x(-1), y) * dt + b(x(-1), y) * dWt;
y(+1) - y = c(x(-1), y) * dt;
end;
shocks;
var dWt = dt;
end;
```

Let’s assume now the more general case where a, b and c depend on z. I would need to define z as an endogenous variable, but what equation should be associated with it?

In other words, how can I access the volatility of an endogenous forward-looking variable?

Thanks a lot for your help!

Best regards,

Thibaut