I'm trying to understand which parameter controls the instantaneous correlation in the 2 F HW model. As in, correlation b/w 2 rates observed at the same time. My thinking is as follows:
Intuitively, if I know $Rate(1)$, more the correlation between short rates $x(t)$ and $y(t)$, the better I can predict $Rate(2)$, and thus correlation must be controlled by the correlation between the Brownian Motions.
However, correlation must also depend on the mean reversion difference, because we're back to perfect correlation (1F HW) if mean reversions of the 2 short rates are the same.
I am wondering if someone has the closed form expression for this correlation. I'd be very glad to see a reference.
For reference above, $P$ and $Q$ are some functions, $x(t)$ and $y(t)$ are the 2 constituent short rates in the model.
Edit: To clarify, I'm asking for the correlation between 2 rates in the same currenct, but of different tenors (say 3M LIBOR and 6M LIBOR)