What is a Brownian motion? State the assumptions of the Black-Scholes model of an asset price, and derive the time- 0 price of a European call option struck at $K$, and expiring at $T$.

Find the time- 0 price of a European call option expiring at $T$, but struck at $S_{t}$, where $t \in(0, T)$, and $S_{t}$ is the price of the underlying asset at time $t$.