Calculating Option-Implied Expected Moves with a Lognormal Range
Summary
The document explains how an options chain can display an expected price range for each expiry, using the underlying price and at-the-money implied volatility. It interprets the range as an estimated one-standard-deviation move: under the assumed model, the expiry price falls within it roughly 68% of the time. Separate exponential formulas produce the upper and lower bounds, with time to expiry expressed in years and implied volatility interpolated when needed. The examples show that the range widens as volatility or time to expiry increases, and that lognormal bounds become asymmetric.
The article contrasts this approach with a symmetric normal-style move, which can imply impossible negative prices for high volatility and long horizons. It also explains how traders may use the range to compare strikes with market-implied movement. The estimate reflects option prices and a lognormal assumption; it is an implied market view, not a forecast of actual probabilities. Prices can finish outside the range, so the display is a reference rather than a standalone trading signal.
Key ideas
- ATM implied volatility and time to expiry determine the option-implied expected range.
- The range represents an estimated one-standard-deviation move, which corresponds to roughly 68% coverage under the model.
- Lognormal calculations create distinct upside and downside moves and prevent negative modeled prices.
- Higher volatility and longer time to expiry produce wider expected ranges.
- The range reflects market-implied expectations and can be wrong or fail to contain the expiry price.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.