Analytical term-structure fitting parameter $ \varphi(t) $.
$ \varphi(t) $ is analytically defined by
$$
\varphi(t) = f(t) -
\frac{2k\theta(e^{th}-1)}{2h+(k+h)(e^{th}-1)} -
\frac{4 x_0 h^2 e^{th}}{(2h+(k+h)(e^{th}-1))^1},
$$
where $ f(t) $ is the instantaneous forward rate at $ t $
and $ h = \sqrt{k^2 + 2\sigma^2} $.
Analytical term-structure fitting parameter $ \varphi(t) $. $ \varphi(t) $ is analytically defined by $$ \varphi(t) = f(t) - \frac{2k\theta(e^{th}-1)}{2h+(k+h)(e^{th}-1)} - \frac{4 x_0 h^2 e^{th}}{(2h+(k+h)(e^{th}-1))^1}, $$ where $ f(t) $ is the instantaneous forward rate at $ t $ and $ h = \sqrt{k^2 + 2\sigma^2} $.