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I'm trying to use Hull-White - Vasicek extension short-rate model (1994a).

I need the market forward rate $f^{M}(t)$ which is used in $\theta(t)$, $A(t,T)$ and $B(t, T)$. But data is not continuous: list of pairs $\{t, r(t)\}$.

Is it OK to compute it with interpolation (If so which method?):

$f^{M}(t) = \frac{\frac{P_{inter}(t+dt, T)}{P_{inter}(t, T)}-1}{dt}$

Is it better to use a continuous function that fits the curve? If so, any recommended method?

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