The observation
Black-Scholes assumes returns are lognormal with a single constant volatility. If that were true, every strike on the same expiry would imply the same volatility.
Plot implied volatility against strike and you do not get a flat line. You get a smile (both wings elevated) or, in equity markets, a skew where downside puts trade at substantially higher implied vol than upside calls.
What it means
The market is pricing a distribution with fatter tails than lognormal, and in equities an asymmetric one.
Out-of-the-money puts being expensive says the market assigns more probability to a large fall than a lognormal model would - and that participants will pay a premium for protection against it beyond the actuarially fair price.
Why equities skew rather than smile
Several reinforcing explanations, and a good answer names more than one:
- Crash risk. Equity markets fall faster than they rise, so the left tail genuinely is fatter.
- Leverage effect. As equity value falls, a company's leverage rises, which raises volatility - so price and volatility are negatively correlated.
- Demand for protection. Institutional hedging demand for downside puts is structurally one-sided, pushing their price up.
The historical marker
The skew was much flatter before October 1987. The crash demonstrated that lognormal tails were badly wrong, and the pricing of downside protection changed permanently. That date is a useful thing to know.
Consequences for trading
Quoting in a single vol number is insufficient - desks maintain a surface across strike and expiry. Relative value between points on that surface, rather than outright direction, is a large part of options trading.
It also means Black-Scholes is used as a quoting convention rather than as a belief. Everyone knows the model is wrong; it survives because it maps prices to a comparable number invertibly.
In the interview
"If Black-Scholes is wrong, why does everyone use it?" Because it is a bijection between price and a single interpretable parameter, which makes options comparable and quotable. The wrongness is handled by letting the parameter vary by strike.
Practise in finance and derivatives.