The volatility smile, skew and surface

In a perfect Black-Scholes world, every option on the same underlying would share one implied volatility. In the real market they do not — and the pattern of how IV varies across strikes and expiries is rich information.

The smile and the skew

If you plot implied volatility against strike price, you rarely get a flat line:

• Volatility smile — IV is higher for deep OTM and deep ITM strikes than for ATM, forming a U-shape. Common in currencies.

• Volatility skew (smirk) — in equities, IV is typically higher for lower strikes (puts) than higher strikes. The market charges more for downside protection because crashes are sharper and more feared than rallies.

  Equity index IV by strike: strike 80 -> IV 30% (downside puts - expensive) strike 100 -> IV 20% (ATM) strike 120 -> IV 18% (upside calls - cheaper)

Why the skew exists

Crashes happen faster than rallies, and demand for portfolio insurance (puts) is structurally high. That persistent demand bids up downside IV. The skew is the market's memory of 1987 and every crash since.

The volatility surface

Add the expiry dimension and you get a 3-D volatility surface: IV as a function of both strike and time. Professional desks model and trade this entire surface, because it encodes the market's full view of risk across prices and horizons.

Why it matters to you

The skew tells you that a naive single-volatility model misprices the wings. It also explains why protective puts feel expensive (you are buying into the high-IV part of the skew) and why some strategies sell the rich downside IV. You do not need to model the surface, but you should know that "one volatility per stock" is a simplification reality contradicts every day.