The idea that an american option on forwards/futures is worth the same as a european option is just patently false. If you are int he money now, but think the position will move against you, you can excercise an american option, but not a european option, the idea that there is no advantage to that is beyond reproach.
I cannot reconcile this with the text. Thoughts?
You can sell an American option 999 times out of 1000 for a higher price than the intrinsic value. It’s never optimum to exercise; it’s optimum to just sell your position to someone else.
Hotchner covered why its never optimal to excersize. And then under the one example you’ve given where you’re in the money now, but you want to excersize. Say you have a euro call with a strike of 80 that’s trading at 84, you just short the underlying and you will lock in your profit, or you just sell it to someone else. Selling it to someone else is obviously still better because there’s no short cost and there should be a premium for future volatility.
This paper covers the premium for early exercise pretty well. http://69.175.2.130/~finman/Prague/Papers/AmericanPutIndexOptionsEarlyExercisePremiumEstimation.pdf
I thought the text just siad that an american option was worth AT LEAST a european option but likely more since you have more options where did you see that it siad they were worth the same?
“If you are int he money now, but think the position will move against you, you can excercise an american option, but not a european option”
Your prediction of the direction of stock movements is not relevant to the “time value” that you lose if you exercise the American option. When you buy an option, you buy volatility risk in addition to delta risk. If you have a view on stock price movements, you can express that by trading the stock itself, thus retaining the time value of your option.