Implied volatility varying with strike

Question

What is meant by the volatility smile?

Short answer

It is the pattern that implied volatility, plotted against strike for one expiry, is not flat but curved, often higher for out-of-the-money options. Equity markets mostly show a skew, with low strikes having higher implied volatility (crash fear); currencies show a more symmetric smile. Its existence contradicts constant-volatility Black-Scholes and is modelled with local volatility, stochastic volatility or jumps.

Adapted from Wilmott, Frequently Asked Questions in Quantitative Finance, FAQ 34, p.157; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

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

Start with a free lesson: Options is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free