Why are american call options more valuable than european options ONLY if the underlying asset pays cash flows?
Really all you need to know is that American style can be exercised at any point, European options cannot be exercised early. Read on if you want more detail.  The American style Call is worth more because it can be exercised at any point. And when the company pays a dividend, and your option is in the money, if the extrinsic value is worth less than the dividend you can be exercised early. This is not the case for a European call. You cannot be exercised until expiration. I trade a lot of options, you wont be exercised early unless the dividend scenario I mentioned happens. Or unless the extrinsic value is nothing, but even then, unless the investor really wants that position, he is more likely to just sell the call for an equivalent gain on 100 shares of stock.
"There are two reasons why most options aren't exercised.  The first is obvious, and the second, less so. The obvious: An option that's practically worthless doesn't get exercised. Options that reach expiry and remain unexercised are almost always worthless bets that simply didn't pay off. This includes calls with strikes above the current underlying price, and puts with strikes below it. A heck of a lot of options. If an option with value was somehow left to expire, it was probably a mistake, or else the transaction costs outweighed the value remaining; not quite worthless, but not ""worth it"" either. The less obvious: An option with value can be cancelled any time before expiration. A trader that buys an option may at some point show a gain sooner than anticipated, or a loss in excess of his tolerance. If a gain, he may want to sell before expiry to realize the gain sooner. Similarly, if a loss, he may want to take the loss sooner. In both cases, his capital is freed up and he can take another position. And — this is the key part — the other end matched up with that option sale is often a buyer that had created (written) exactly such an option contract in the first place – the option writer – and who is looking to get out of his position. Option writers are the traders responsible, in the first place, for creating options and increasing the ""open interest.""  Anybody with the right kind and level of options trading account can do this. A trader that writes an option does so by instructing his broker to ""sell to open"" a new instance of the option. The trader then has a short position (negative quantity) in that option, and all the while may be subject to the obligations that match the option's exercise rights. The only way for the option writer to get out of that short position and its obligations are these: Not by choice:  To get assigned. That is to say: a buyer exercised the option. The writer has to fulfill his obligation by delivering the underlying (if a call) to the option holder, or buying the underlying (if a put) from the option holder. Not by choice: The option expires worthless. This is the ideal scenario for a writer because 100% of the premium received (less transaction costs) is profit. By choice: The writer is free to buy back exactly the same kind of option before expiry using a ""buy to close"" order with their broker. Once the option has been purchased with a ""buy to close"", it eliminates the short position and obligation.  The option is cancelled.  The open interest declines. Options thus cancelled just don't live long enough to either expire or be exercised." "Yes, if it's an American style option. American style options may be exercised at any time prior to expiration (even if they're not in-the-money). Generally, you are required to deliver or accept delivery of the underlying by the beginning of the next trading day. If you are short, you may be chosen by the clearinghouse to fulfill the exercise (a process called ""assignment""). Because the clearinghouse is the counter-party to every options trade, you can be assigned even if the specific person who purchased the option you wrote didn't exercise, but someone else who holds a long position did. Similarly, you might not be assigned if that person did exercise. The clearinghouse randomly chooses a brokerage to fulfill an assignment, and the brokerage will randomly choose an individual account. If you're going to be writing options, especially using spreads, you need to have a plan ahead of time on what to do if one of your legs gets assigned. This is more likely to happen just before a dividend payment, if the payment is more than the remaining time value." When you can exercie your option depends on your trading style. In the american options trading style (the most popular) you're allowed to exercice your options and make profit (if any) whenever you want before the expiration date. Thus, the decision of  exercising your option and make a profit out of it does not rely only on the asset price. The reason is, you already paid for the premium to get the option. So, if taken into account the underlying price AND your premium, your investment is profitable then you can exercice your contract anytime. I agree that high volatility just means the underlying stock price fluctuates more, and it does not imply if the stock is going up or down. But a high volatility in the price of an underlying also means that there is a higher chance that the underlying price could reach extreme prices (albeit in either direction). However, if you purchased a call option then if the underlying price reached an extremely high value, then you will be richly rewarded. But if the underlying price reached an extremely low value, you won't lose any more than the initial premium that you paid. There is no additional risk on your side, it's capped to the premium that you paid for the call option. It's this asymmetric outcome (Heads - I win, Tails - I don't lose) combined with high volatility that means that call options will increase in value when the underlying price becomes more volatile. If the optionality wasn't there then the price wouldn't be related to the volatility of the underlying. But that would be called a Future or a Forward :-) "No, there are neither advantages nor disadvantages. I'll take on this question from an accounting standpoint.   Financial statements, the tools at which the market determines (amongst other things) the value of a stock, are converted at year end to the home currency (see 1.1.3).If Company A has revenue of 100,000 USD and the conversion to EUR is .89, revenue in the European market will be reported as 89,000 EUR. These valuations, along with ratios, analysis, and ""expert"" opinions determine if a person should own shares in Company A.  Now, if we're talking about comparing markets this is a entirely different question.  Example:  Should I buy stock of Company A, who is in the American market (as an European)?  Should I buy stock of Company B, who is in the European market (as an American)? I would recommend this as additional level of diversification of your portfolio to inlcude possible large inflation of either the currency. The possible gains of this foreign exchange may be greater if one or the other currency becomes weak." The short term bond fund, which you are pretty certain to have as an option, functions in this capacity.  Its return will be low, but positive, in all but the most dramatic of rising rate scenarios. I recall a year in the 90's when rates rose enough that the bond fund return was zero or very slightly negative. It's not likely that you'd have access to simple money market or cash option. There are a few situations in which it may be advantageous to exercise early. Wikipedia actually has a good explanation: Option Style, Difference in value To account for the American's higher value there must be some   situations in which it is optimal to exercise the American option   before the expiration date. This can arise in several ways, such as: An in the money (ITM) call option on a stock is often exercised just   before the stock pays a dividend that would lower its value by more   than the option's remaining time value.  A put option will usually be   exercised early if the underlying asset files for bankruptcy.[3]  A deep ITM currency option (FX option) where the strike currency has a   lower interest rate than the currency to be received will often be   exercised early because the time value sacrificed is less valuable   than the expected depreciation of the received currency against the   strike.  An American bond option on the dirty price of a bond (such as   some convertible bonds) may be exercised immediately if ITM and a   coupon is due.  A put option on gold will be exercised early when deep   ITM, because gold tends to hold its value whereas the currency used as   the strike is often expected to lose value through inflation if the   holder waits until final maturity to exercise the option (they will   almost certainly exercise a contract deep ITM, minimizing its time   value).[citation needed] Options can have a negligible time premium. For American1 calls the time premium is never negative. If it had a negative premium it would be profitable to exercise it immediately. A deep in the money call has a delta of exactly one. That is, it's price movements completely mirror the price movements of the underlying stock. That means an option seller can buy stock and completely hedge his short option position. The seller of the option may be in an position to buy with very little margin and take your money and invest it. For example, consider a stock trading at $7.50, with its January 2014   $4 call option trading at $3.50. For one option, representing 100 shares, a trader could take your 350 dollars and invest it, and only use a small portion of the money to buy the stock on margin. Market-makers can typically borrow money at very low interest rates. If you have high borrowing costs, or are unable to buy on margin, then buying deep in the money calls can be a good strategy. Long story short, option sellers are making money off selling these deep in the money calls even with almost zero time premium. So, in general, there's no way to make money by buying them. 1. An American call is a call that can be exercised at any time up to and including its expiration date.