TL;DR
The Volatility Smile and Skew: A canonical quantitative trading interview question at olympiad difficulty. Commonly asked at Optiver, SIG, IMC, Citadel Securities, Jane Street, Akuna Capital.
By Valenke Exam Prep Team·Last updated 2026-06-01
olympiadGame Theory & Strategy
The Volatility Smile and Skew
Asked at: Optiver, SIG, IMC, Citadel Securities, Jane Street, Akuna Capital
Problem
The Black-Scholes model assumes constant volatility, but in practice, implied volatility varies with strike price.
(a) Define implied volatility. Why is it quoted instead of option prices?
(b) For equity index options (e.g., S&P 500), the implied volatility of out-of-the-money puts is typically higher than for ATM options. Explain why.
(c) A 1-month ATM call on the S&P 500 has implied vol of 18%. A 1-month 90% strike put has implied vol of 25%. Explain the economic meaning of this 7-point skew.
(d) How does this relate to risk-neutral vs. physical probability distributions?
Related concepts
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