How Does the Volatility of the Underlying Asset Influence the Difference in Premium between American and European Options?

Higher volatility increases the value of both American and European options because there is a greater chance of a large price movement, increasing the option's intrinsic value. However, the value of the early exercise feature in the American option is less affected by volatility than the overall option price.

The difference in premium is generally smaller for higher volatility options, as the European option already captures a lot of potential profit from the wide range of possible future prices.