American option – option that can be exercised at any time prior to expiration. American options allow their holders to exercise the option at any time, thereby increasing their value relative to European options that can only be exercised on the expiration date. Most options traded on the exchanges are American options.
Since investors are free to choose when to exercise their right to buy/sell the underlying asset, American options are of greater value than European options.
Let us take an example: A trader holds a call option for shares in Google with an expiry date of March 2022. Thus, the trader is entitled to exercise the option until March 2022. If the option on Google was European, the trader would be able to exercise the option only on the expiry date. However, perhaps, the most optimal entry point to buy Google shares was January 2022, but trader would have to wait until March 2022.
The name of the option has nothing to do with geographical location.
European Option - an option that can be used to buy/sell the underlying asset only at the time of expiry. European options are usually traded below the value of American options because American options provide more variability to the holder.
Traders who specialize in options trading will generally not exercise options until the expiration date. Option trading itself involves trading volatility, not direction, in the case of stocks or futures. Therefore, the exercise of an option before the expiration date can be replaced by selling it.
Asian option - a type of option, the profit/loss on which depends not on the price at the moment of expiry, but is defined as the difference between the average price of the underlying contract for a certain period of time and the strike price. Averaging the price of the underlying significantly reduces the value of an Asian option compared to that of an ordinary European or American option contract.
Asian options are highly dependent on the price trajectory of the underlying asset (have a path dependence property). Asian options are traded exclusively in the over-the-counter market between major investment funds and bulge bracket banks.