The main component of that option premium is (forward-looking) volatility $\sigma$. The very simplest formula you could use for ATM options is the Bachelier model
\begin{equation}
\text{Call}_T = \sigma S \sqrt{\frac{T}{2\pi}}
\end{equation}
where the time to expiration is $T$ and $S$ is the current underlying price. This formula is "wrong" strictly speaking, but only by a factor of $\sigma^3T^{\frac32}$ which in your case will be around 5%. You'll also be ignoring a somewhat smaller error due to nonzero interest rates.
To obtain $\sigma$ you can work with your available historical data to get a historical volatility. Historical volatility is not always the very best choice but it is far better here than your current constant price assumption, and it is very simple to calculate:
\begin{equation}
\sigma_{\text{Hist}} = \sqrt{\frac1{N-1}\sum_{i=1}^N{(r_i-\bar{r})^2}}
\end{equation}
where the $r_i$ are the periodic returns
\begin{equation}
r_i = \frac{\frac{S_{i+1}}{S_i}-1}{\Delta t_i}
\end{equation}
taken of the underlying $S_i$ at times $t_i$, $\Delta t_i=(t_{i+1}-t_i)$ and $\bar{r}$ is their mean. (The Black-Scholes model would have used log returns instead.)
If you are happy with a crude estimate, you may assume $\bar{r}$ is zero rather than bothering to calculate it. And for a very crude estimate of historical volatility, you can instead use
\begin{equation}
\sigma_\text{Inaccurate} = \text{Mean}\left[|r_i|\right] \frac1{\sqrt{\text{Mean}\left[\Delta t_i\right]}}
\end{equation}
For maximum accuracy, you would of course want to use the Black-Scholes model. But frankly you would have an easier time finding the requisite historical option prices than you would finding a historical time series of forward-looking (implied) Black-Scholes volatilities.
