According to the Black-Scholes-Merton formula, the value at time zero of a European call on a stock whose initial price is $S(0)=x$ is given by
$$
c(0, x)=x N\left(d_{+}(T, x)\right)-K e^{-r T} N\left(d_{-}(T, x)\right),
$$
where
$$
\begin{aligned}
& d_{+}(T, x)=\frac{1}{\sigma \sqrt{T}}\left[\log \frac{x}{K}+\left(r+\frac{1}{2} \sigma^2\right) T\right], \\
& d_{-}(T, x)=d_{+}(T, x)-\sigma \sqrt{T} .
\end{aligned}
$$
The stock is modeled as a geometric Brownian motion with constant volatility $\sigma>0$, the interest rate is constant $r$, the call strike is $K$, and the call expiration time is $T$. This formula is obtained by computing the discounted expected payoff of the call under the risk-neutral measure,
$$
\begin{aligned}
c(0, x) & =\widetilde{\mathbb{E}}\left[e^{-r T}(S(T)-K)^{+}\right] \\
& =\widetilde{\mathbb{E}}\left[e^{-r T}\left(x \exp \left\{\sigma \widetilde{W}(T)+\left(r-\frac{1}{2} \sigma^2\right) T\right\}-K\right)^{+}\right],
\end{aligned}
$$