In the mean-reverting Vasicek model (17.47) with \(b>0\), compute:

i) The asymptotic bond yield, or exponential long rate of interest

\[r_{\infty}:=-\lim _{T \rightarrow \infty} \frac{\log P(t, T)}{T-t}\]

ii) The long-bond return \[L_{t}:=\lim _{T \rightarrow \infty} \frac{P(t, T)}{P(0, T)}\]
Start from \(\log (P(t, T) / P(0, T))\).