# Estimating instantaneous forward rate without continuous formula

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?