Why does BSM price options by replication instead of just discounting the expected payoff?

Excellent question. The short answer: you cannot compute the expected option payoff under the real-world probability measure without knowing the expected return of the stock — and that number is famously hard to estimate. The replication trick lets BSM sidestep that estimation problem entirely.

The naive approach (and why it fails):

If a call pays $\max(S_T - K, 0)$, then a naive valuer would write:

But $E[S_T]$ depends on the expected return $\mu$ of the stock, which is unobservable, controversial, and varies across investors. Two analysts disagreeing about $\mu$ would disagree about the option price — yet the option trades at a single market price. So the naive formula cannot be right.

The replication approach:

Once you can replicate the payoff, no-arbitrage forces the option to trade at the cost of the replication. The stock's drift ($\mu$) drops out because the replication is dynamic — you continuously rebalance, so whatever direction the stock drifts, the hedge tracks it.

The deep insight (risk-neutral pricing):

You can recover a formula that looks like discounting an expected payoff, but under a transformed probability measure called the risk-neutral measure $Q$. Under $Q$, every asset has expected return $= r$ (the risk-free rate), so the formula becomes:

This is mathematically equivalent to the replication argument. It is the cleanest way to express the result and the form most quants use day-to-day.

Why this generalises: the replication / risk-neutral trick works for ANY derivative whose payoff is a function of tradable assets. That is why the same machinery prices forwards, swaps, exotic options, even some credit derivatives. The replication argument is the conceptual gift — the formula is just one consequence.