Does Theta Accelerate Faster for American or European Options?
Theta generally accelerates at a similar rate for both American and European options, as time decay is a function of the remaining time to expiration and volatility. However, the American option's early exercise feature complicates the pure decay calculation.
The European option's price is a smoother function of time, making its theta more predictable.
Glossar
Early Exercise Feature
Feature ⎊ The Early Exercise Feature is the defining characteristic of American style options, permitting the holder to execute their contractual right to buy or sell the underlying asset before the official expiration date.
Early Exercise Boundary
Threshold ⎊ The specific price level at which it becomes mathematically optimal to exercise an American style option before its expiration date defines this limit.