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.
"First it is worth noting the two sided nature of the contracts (long one currency/short a second) make leverage in currencies over a diverse set of clients generally less of a problem.  In equities, since most margin investors are long ""equities"" making it more likely that large margin calls will all be made at the same time. Also, it's worth noting that high-frequency traders often highly levered make up a large portion of all volume in all liquid markets ~70% in equity markets for instance.  Would you call that grossly artificial?  What is that volume number really telling us anyway in that case? The major players holding long-term positions in the FX markets are large banks (non-investment arm), central banks and corporations and unlike equity markets which can nearly slow to a trickle currency markets need to keep trading just for many of those corporations/banks to do business.  This kind of depth allows these brokers to even consider offering 400-to-1 leverage.  I'm not suggesting that it is a good idea for these brokers, but the liquidity in currency markets is much deeper than their costumers." 1) Yes, both of your scenarios would lead to earning $10 on the transaction, at the strike date. If you purchased both of them (call it Scenario 3), you would make $20. 2) As to why this transaction may not be possible, consider the following: The Call and Put pricing you describe may not be available. What you have actually created is called 'arbitrage' - 2 identical assets can be bought and sold at different prices, leading to a zero-risk gain for the investor. In the real marketplace, if an option to buy asset X in January cost $90, would an option to sell asset X in January provide $110?  Without adding additional complexity about the features of asset x or the features of the options, buying a Call option is the same as selling a Put option [well, when selling a Put option you don't have the ability to choose whether the option is exercised, meaning buying options has value that selling options does not, but ignore that for a moment]. That means that you have arranged a marketplace where you would buy a Call option for only $90, but the seller of that same option would somehow receive $110.  For added clarity, consider the following: What if, in your example, the future price ended up being $200? Then, you could exercise your call option, buying a share for $90, selling it for $200, making $110 profit. You would not exercise your put option, making your total profit $110. Now consider: What if, in your example, the future price ended up being $10? You would buy for $10, exercise your put option and sell for $110, making a profit of $100. You would not exercise your call option, making your total profit $100. This highlights that if your initial assumptions existed, you would earn money (at least $20, and at most, unlimited based on a skyrocketing price compared to your $90 put option) regardless of the future price. Therefore such a scenario would not exist in the initial pricing of the options. Now perhaps there is an initial fee involved with the options, where the buyer or seller pays extra money up-front, regardless of the future price. That is a different scenario, and gets into the actual nature of options, where investors will arrange multiple simultaneous transactions in order to limit risk and retain reward within a certain band of future prices.  As pointed out by @Nick R, this fee would be very significant, for a call option which had a price set below the current price. Typically, options are sold 'out of the money' initially, which means that at the current share price (at the time the option is purchased), executing the option would lose you money. If you purchase an 'in the money' option, the transaction cost initially would by higher than any apparent gain you might have by immediately executing the option. For a more realistic Options example, assume that it costs $15 initially to buy either the Call option, or the Put option. In that case, after buying both options as listed in your scenarios you would earn a profit if the share price exceeded $120 [The $120 sale price less the $90 call option = $30, which is your total fee initially], or dropped below $80 [The $110 Put price less the $80 purchase price = $30]. This type of transaction implies that you expect the price to either swing up, or swing down, but not fall within the band between $80-$120. Perhaps you might do this if there was an upcoming election or other known event, which might be a failure or success, and you think the market has not properly accounted for either scenario in advance. I will leave further discussion on that topic [arranging options of different prices to create specific bands of profitability / loss] to another answer (or other questions which likely already exist on this site, or in fact, other resources), because it gets more complicated after that point, and is outside the root of your question. If you're into math, do this thought experiment: Consider the outcome X of a random walk process (a stock doesn't behave this way, but for understanding the question you asked, this is useful): On the first day, X=some integer X1. On each subsequent day, X goes up or down by 1 with probability 1/2. Let's think of buying a call option on X. A European option with a strike price of S that expires on day N, if held until that day and then exercised if profitable, would yield a value Y = min(X[N]-S, 0). This has an expected value E[Y] that you could actually calculate. (should be related to the binomial distribution, but my probability & statistics hat isn't working too well today) The market value V[k] of that option on day #k, where 1 < k < N, should be V[k] = E[Y]|X[k], which you can also actually calculate. On day #N, V[N] = Y. (the value is known) An American option, if held until day #k and then exercised if profitable, would yield a value Y[k] = min(X[k]-S, 0).  For the moment, forget about selling the option on the market. (so, the choices are either exercise it on some day #k, or letting it expire) Let's say it's day k=N-1.  If X[N-1] >= S+1 (in the money), then you have two choices: exercise today, or exercise tomorrow if profitable. The expected value is the same. (Both are equal to X[N-1]-S). So you might as well exercise it and make use of your money elsewhere. If X[N-1] <= S-1 (out of the money), the expected value is 0, whether you exercise today, when you know it's worthless, or if you wait until tomorrow, when the best case is if X[N-1]=S-1 and X[N] goes up to S, so the option is still worthless. But if X[N-1] = S (at the money), here's where it gets interesting. If you exercise today, it's worth 0. If wait until tomorrow, there's a 1/2 chance it's worth 0 (X[N]=S-1), and a 1/2 chance it's worth 1 (X[N]=S+1). Aha! So the expected value is 1/2. Therefore you should wait until tomorrow. Now let's say it's day k=N-2.  Similar situation, but more choices: If X[N-2] >= S+2, you can either sell it today, in which case you know the value = X[N-2]-S, or you can wait until tomorrow, when the expected value is also X[N-2]-S. Again, you might as well exercise it now. If X[N-2] <= S-2, you know the option is worthless. If X[N-2] = S-1, it's worth 0 today, whereas if you wait until tomorrow, it's either worth an expected value of 1/2 if it goes up (X[N-1]=S), or 0 if it goes down, for a net expected value of 1/4, so you should wait. If X[N-2] = S, it's worth 0 today, whereas tomorrow it's either worth an expected value of 1 if it goes up, or 0 if it goes down -> net expected value of 1/2, so you should wait. If X[N-2] = S+1, it's worth 1 today, whereas tomorrow it's either worth an expected value of 2 if it goes up, or 1/2 if it goes down (X[N-1]=S) -> net expected value of 1.25, so you should wait. If it's day k=N-3, and X[N-3] >= S+3 then E[Y] = X[N-3]-S and you should exercise it now; or if X[N-3] <= S-3 then E[Y]=0.  But if X[N-3] = S+2 then there's an expected value E[Y] of (3+1.25)/2 = 2.125 if you wait until tomorrow, vs. exercising it now with a value of 2; if X[N-3] = S+1 then E[Y] = (2+0.5)/2 = 1.25, vs. exercise value of 1; if X[N-3] = S then E[Y] = (1+0.5)/2 = 0.75 vs. exercise value of 0; if X[N-3] = S-1 then E[Y] = (0.5 + 0)/2 = 0.25, vs. exercise value of 0; if X[N-3] = S-2 then E[Y] = (0.25 + 0)/2 = 0.125, vs. exercise value of 0. (In all 5 cases, wait until tomorrow.) You can keep this up; the recursion formula is E[Y]|X[k]=S+d = {(E[Y]|X[k+1]=S+d+1)/2 + (E[Y]|X[k+1]=S+d-1) for N-k > d > -(N-k), when you should wait and see} or {0 for d <= -(N-k), when it doesn't matter and the option is worthless} or {d for d >= N-k, when you should exercise the option now}. The market value of the option on day #k should be the same as the expected value to someone who can either exercise it or wait. It should be possible to show that the expected value of an American option on X is greater than the expected value of a European option on X. The intuitive reason is that if the option is in the money by a large enough amount that it is not possible to be out of the money, the option should be exercised early  (or sold), something a European option doesn't allow, whereas if it is nearly at the money, the option should be held, whereas if it is out of the money by a large enough amount that it is not possible to be in the money, the option is definitely worthless. As far as real securities go, they're not random walks (or at least, the probabilities are time-varying and more complex), but there should be analogous situations. And if there's ever a high probability a stock will go down, it's time to exercise/sell an in-the-money American option, whereas you can't do that with a European option. edit: ...what do you know: the computation I gave above for the random walk isn't too different conceptually from the Binomial options pricing model. "According to the book of Hull, american and european calls on non-dividend paying stocks should have the same value. American puts, however, should be equals to, or more valuable than, european puts. The reason for this is the time value of money. In a put, you get the option to sell a stock at a given strike price. If you exercise this option at t=0, you receive the strike price at t=0 and can invest it at the risk-free rate. Lets imagine the rf rate is 10% and the strike price is 10$. this means at t=1, you would get 11.0517$. If, on the other hand, you did'nt exercise the option early, at t=1 you would simply receive the strike price (10$). Basically, the strike price, which is your payoff for a put option, doesn't earn interest. Another way to look at this is that an option is composed of two elements: The ""insurance"" element and the time value of the option. The insurance element is what you pay in order to have the option to buy a stock at a certain price. For put options, it is equals to the payout= max(K-S, 0) where K=Strike Price and St= Stock price.  The time value of the option can be thought of as a risk-premium. It's difference between the value of the option and the insurance element. If the benefits of exercising a put option early (i.e- earning the risk free rate on the proceeds) outweighs the time value of the put option, it should be exercised early. Yet another way to look at this is by looking at the upper bounds of put options. For a european put, today's value of the option can never be worth more than the present value of the strike price discounted at the risk-free rate. If this rule isn't respected, there would be an arbitrage opportunity by simply investing at the risk-free rate. For an american put, since it can be exercised at any time, the maximum value it can take today is simply equals to the strike price. Therefore, since the PV of the strike price is smaller than the strike price, the american put can have a bigger value. Bear in mind this is for a non-dividend paying stock. As previously mentioned, if a stock pays a dividend it might also be optimal to exercise just before these are paid." You made 94$ on an investment of 554.80 *100 = 55480$ for an approx holding period of 1 year. So the % return is ~0.16%, which is not much better than the short term us treasury rate. The current 1 year treasury rate is 0.27%: http://ycharts.com/indicators/1_year_treasury_rate So yes, you have a risk free portfolio, so you make the risk free rate. Remember this is an European option, so you are stuck for 1 year. if you found the same mispricing in an American option, then you found an arbitrage. On NYSE it isn't the equity which is listed but is an ADR(American Depositary Receipt). Source A negotiable certificate issued by a U.S. bank representing a specified number of shares (or one share) in a foreign stock that is traded on a U.S. exchange. ADRs are denominated in U.S. dollars, with the underlying security held by a U.S. financial institution overseas. ADRs help to reduce administration and duty costs that would otherwise be levied on each transaction. Else people would make a killing on the arbitrage opportunity. Frankly speaking arbitrage opportunities are more or less non existent. They occur for maybe seconds or milliseconds and the HFT firms and banks trade on it to remove the arbitrage. as no advantage from exerting American call option early,we can use Black schole formula to evaluate the option.However, American put option is more likely to be exercised early which mean Black schole does not apply for this style of option "Look, as my final comment.  You're overthinking this.  Companies routinely have waaaay more cash on their books than they ""need"" because they keep a rainy day fund.  Yes, there are extreme examples like Apple that has about 60 billion more than they need but practically all companies are going to maintain excess cash for emergencies, acquisitions, etc.  As I said in another comment, the common theme between a DCF and an EV multiple is that they are both capital structure independent.    Even here there are going to be differences, companies with a really shitty capital structure (read: too much debt) will trade publicly at a lower enterprise value multiple because of the risk that they go bankrupt.  In an acquisition, this (probably) would not be the case.  In the case of a DCF, you would probably raise your discount rate to account for the risk of bankruptcy." You can think of a free cash flow as dividends from operations. FCF = cash from operations - investment in operations. The present value of these cash flows into the future is the value of the firm (DCF is very much like the dividend discount model).   Now why does a DCF produce enterprise value and not equity value? Because a DCF values the firm's operating assets. To find the equity value, you use the accounting relation: assets = liabilities + equity (or in financial terms net operating assets = net financial obligations + common stockholders equity). This means you take away net debt from the value produced by the DCF to find equity.  Now all your excess cash is netted off against your financial obligations (debt) to find the net debt. Cash used for day to day operations is an operating asset and should be treated as such, operating cash should not deducted from value of assets when finding the value of equity.  At least that's what they're teaching at university now (i'm a uni student who's just finished my business valuation subject). "Both models understand that the value of a company is the sum total of all cashflows in the future, discounted back to the present. They vary in their definition of ""cash"". The Gordon Growth model uses dividends as a proxy for cashflow, under the assumption that this is the only true cash received by shareholders. (In theory, counting cash is meaningless if there's no eventual end-game where the accumulated cash is divvied up amongst the owners.) The Gordon model is best used to value companies that have an established, reliable dividend. The company should be stable, and the payout ratio high. GG will underestimate the value of firms that consistently maintain a low payout ratio, and instead accumulate cash. There are multiple DCF models. A firm valuation measures all cash available to both equity and debt holders. A traditional equity valuation measures all cash that can be claimed by shareholders. While the latter seems most intuitive and pertinent to a shareholder, the former is very good at showing what a company can do regardless of their choice of capital structure. A small add-on to a firm valuation is the concept of EVA, or economic value add, where the return on capital (all capital -- both debt and equity) is compared to the blended cost of capital. The DCF model is more flexible (optimistic?) than the Gordon in its approach to cash. The approach can be applied to many types of companies, at every stage in their maturity, even if they don't pay a dividend. A simplistic, or single-stage DCF is similar to the Gordon. The assumption is that the company is fully mature, growing at a rate perhaps just slightly above inflation, forever. For younger companies a multi-stage DCF can be employed, where you forecast fairly confident numbers for the next 3-5 years, then 3-5 years beyond that the forecast is less certain, but assumed to be slowing growth, and a generally maturing, stabilizing company. And then the steady-state stage is tacked on to the end. You'll want to check out Professor Aswath Damodaran's website: http://pages.stern.nyu.edu/~adamodar/ . He addresses all this and so much more, and has a big pile of spreadsheets freely downloadable to get you started. I also highly recommend his book ""Investment Valuation"". It's the bible on the topic." "The term ""stock"" here refers to a static number as contrasted to flows, e.g. population vs. population growth. Stock, in this context, is not at all related to an equity instrument.  Yes, annual refinance costs, interest rate payments etc. are what we should be looking at when assessing debt burden. Those are flows. That was my point when cautioning against naive debt GDP comparisons.  Also, keep in mind that by borrowing in it's sovereign currency, the US has an enormous amount of monetary tools to handle the debt if it ever became a problem. Greece, by comparison, is at the mercy of the ECB, so they only have fiscal levers to pull. The interest expense does not strike me as especially concerning, but I'd be happy to verify BIS or IMF reports if you would like." "For sake of simplicity, say the Euro is trading at $1.25. You have leveraged control of $100,000 given the 100x leverage. If you are bullish on the Euro, you are long 80,000 euros. For every 1% it rises, you gain $1000. If it drops by the same 1%, you are wiped out, you lost your $1000. With the contracts I am familiar with, there is a minimum margin, and your account is ""marked to market"" each night. If your positive balance drops too low, you get the margin call. It's a zero sum game, for every dollar you make, there's a guy on the other side of the trade. Odds are he's doing this full time and is smarter than you." "I don't know how much finance you know, but a fundamental idea is that something's value is the present value of all its future cash flows. Basically what those cash flows are worth today. So if we can predict the cash flows the equity holders will get in the future (not easy), and determine at what rate to discount the cash flows (not easy), we can value the equity.   So a company will have cash flows coming in. But not all go to the equity holders. Some will go to debt holders, if any (interest payments). Some will go to preferred equity holders (dividends), if any. What's left over is what the equity holders will get. If there's no debt, preferred equity or other things like that, then the equity holders get all the cash flows.  This doesn't mean the equity holders literally receive the cash - they'll get whatever is given out via dividends. But, they ""own"" the cash and it may be reinvested in the business to generate more cash in the future." Yes. If I own a call, an American call option can be exercised at my wish. A European call can only be exercised at expiration, by the way.  Your broker doesn't give you anything but a current quote for a given strike price. There are a number of good option related questions here. A bit of searching and reading will help you understand the process. if you don't intent to touch the money for 10 years or longer, then dumping 100% into a low-expense-ratio index fund seems like a perfectly reasonable thing to do. it is simple, low maintenance and fairly mindless. just remember to reinvest the dividends occasionally (e.g. every 6 months).  however, if you are the kind of person who is going to lose their nerve when the market goes down 30%, then putting some of your money into a bond index fund or even a treasury note fund would be better than selling stock in a down market. just figure out how much of your portfolio you are comfortable losing, and put that in stocks.  then put the rest in some stable value fund and watch it's value get slowly washed away by inflation while your stock investments rise through violent swings.