When the stockprice follows a GBM, the arbitrage-free value of an EU call is given by the Black Scholes model:
\begin{align}
C(S, t) &= N(d_1)S_0 - N(d_2) Ke^{-r(T - t)} \\
d_1 &= \frac{1}{\sigma\sqrt{T - t}}\left[\ln\left(\frac{S_0}{K}\right) + \left(r + \frac{\sigma^2}{2}\right)(T - t)\right] \\
d_2 &= d_1 - \sigma\sqrt{T - t}
\end{align}
The stockprice is given by
$$S_t=S_0e^{(r-\sigma^2/2)t+tW_t},\quad W_t\sim N(0,t)$$
$S_t$ is the only random term and log-normally distributed.
Its inverse function for the VaR quantile can only be calculated numerically as by MATLAB logninv function (assuming 250 trading days):
$$VaR_\alpha^S=\text{logninv}\left(\alpha,\mu_S=(r-\sigma^2)/2,\sigma_S=3/250\right)$$
As we know, the call option delta is positive, such that its value will always fall and increase with the stock price. Hence the Option VaR follows as:
$$VaR_\alpha^C=C(S_0,0)-C(VaR_\alpha^S, 3/250)$$
which corresponds to the loss at the $\alpha$ quantile.
The option value also falls deterministically with decreasing time to maturity, as represented by the theta Greek:
$$Theta(t)=\frac{\partial C}{\partial t}= -\frac{S_0 N'(d_1) \sigma}{2 \sqrt{T - t}} - rKe^{-r(T - t)}N(d_2)\, -\frac{S_0 N'(d_1) \sigma}{2 \sqrt{T - t}} + rKe^{-r(T - t)}N(-d_2)$$
That loss is however already included in calculating the difference $C(S_0,0)-C(VaR_\alpha^S, 3/250)$.