Volatility smile
Quantitative Finance glossary · Derivatives Pricing & Volatility Surfaces
Definition
U-shaped pattern of implied volatility versus strike — the textbook FX-options shape, symmetric because both tails of the spot distribution are economically significant. Reflects fat-tailed (leptokurtic) return distributions inconsistent with Black-Scholes log-normality. Quoted in FX via the 25-delta butterfly BF = 1/2(σ_25Δ c + σ_25Δ p) - σ_ATM alongside the risk-reversal (skew). Smile vs skew distinction: smile is symmetric (FX), skew is monotone (equity indices).
Volatility smile in plain English
A volatility smile is what you see when out-of-the-money options on BOTH sides — big up moves and big down moves — are priced more expensively than calm middle-of-the-road ones, so a graph of the prices curves up at both ends like a grin. It shows up in currency markets, where a huge jump either way is genuinely worth worrying about. The reason is that real prices have 'fat tails' — extreme moves happen more often than the simple textbook bell-curve model predicts — so the market charges extra for insurance against both tails. The key contrast: a smile is symmetric (both sides pricey, typical of currencies), while a skew is lopsided (mostly the downside is pricey, typical of stocks).
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