How Does the Concept of Volatility Relate to the Square Root of Time in Option Pricing?

Volatility, in financial models, is typically measured as the standard deviation of the underlying asset's returns. Assuming returns are independent and identically distributed, the total volatility over a period of time is proportional to the square root of that time period.

This is because variance (volatility squared) is additive over time. Therefore, an option's value is more sensitive to volatility changes over longer time horizons, reflecting the greater uncertainty.