Black-Scholes

What makes an option priceable is not a forecast but a replication. A seller who holds the right quantity of the underlying, adjusts that holding continuously as the underlying moves, and funds the position with borrowing, ends up with the option's payoff. The option must therefore cost what running that hedge costs, otherwise a risk free profit exists. Black-Scholes is the closed form answer for the simplest version of that problem: a European option on a share paying no dividends, with constant volatility and a constant risk free rate, in a market that trades continuously and without costs.

The consequence most worth carrying into an interview is that your view on the expected return of the underlying never enters the price. Two investors with opposite opinions about direction must still agree on the option's value. That is why volatility, which governs how much the hedge has to be adjusted, matters far more to an option's price than direction does.

The model's own volatility assumption is the place it breaks. If it held exactly, every option on one share would imply the same volatility whatever its strike. They do not: equity index options show a persistent skew, with strikes below the market implying higher volatility, because investors pay up for downside protection. Practitioners do not treat this as a defect so much as evidence that the formula is a quoting convention rather than a description of reality.

Bound it correctly. Anything with early exercise, path dependence or an embedded credit component, which covers most convertibles, is valued on a binomial tree or by simulation instead. And in a banking interview you are asked what the model is, what goes into it and which way each input pushes. You are not asked to derive it, and if you are, the conversation has drifted onto a quantitative desk.