Volatility smile

Quantitative Finance Glossary

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 = tfrac12(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).

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