Implied volatility and the shape of the smile

Question

What is implied volatility, and what do practitioners mean by the volatility smile or skew?

Short answer

Implied vol is the volatility that makes Black-Scholes reproduce an option's market price; the smile or skew is how it varies with strike. If Black-Scholes were true, all strikes would imply the same vol. In practice equity index vols are higher for low strikes (a skew, reflecting crash risk and leverage effects), while FX vols often rise on both sides (a smile, reflecting fat tails). Together with maturity this forms the implied volatility surface.

Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q2.58, p.22; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Reading the Implied Vol Surface — Moneyness, Term Structure, and Quoting Conventions

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