Illustrative article · Sample editorial content and publication date, prepared for this website. Not a disclosure of proprietary research.
A price is a distribution
An option price implies a view of how far the underlying might move before expiry. Under a simple lognormal model, that range is set by two numbers: implied volatility and time. The same index, priced at a higher implied volatility, is priced for a wider spread of outcomes.
Time compresses the range
The spread of outcomes grows with the square root of time, not with time itself. An option with a quarter of the time to expiry is priced for roughly half the range. This is why short-dated options are so sensitive to a change in implied volatility close to expiry.
A model is a reference
Real returns have fatter tails than a lognormal model assumes, and implied volatility differs by strike. Treating the model as a reference, and studying where market prices depart from it, is more informative than treating it as a forecast.