Why are American-style options worth more than European-style options?
"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." I'm sorry, but your math is wrong.  You are not equally likely to make as much money by waiting for expiration. Share prices are moving constantly in both directions.  Very rarely does any stock go either straight up or straight down.  Consider a stock with a share price of $12 today.  Perhaps that stock is a bad buy, and in 1 month's time it will be down to $10.  But the market hasn't quite wised up to this yet, and over the next week it rallies up to $15. If you bought a European option (let's say an at-the-money call, expiring in 1 month, at $12 on our start date), then you lost.  Your option expired worthless. If you bought an American option, you could have exercised it when the share price was at $15 and made a nice profit. Keep in mind we are talking about exactly the same stock, with exactly the same history, over exactly the same time period.  The only difference is the option contract.  The American option could have made you money, if you exercised it at any time during the rally, but not the European option - you would have been forced to hold onto it for a month and finally let it expire worthless. (Of course that's not strictly true, since the European option itself can be sold while it is in the money - but eventually, somebody is going to end up holding the bag, nobody can exercise it until expiration.) The difference between an American and European option is the difference between getting N chances to get it right (N being the number of days 'til expiration) and getting just one chance.  It should be easy to see why you're more likely to profit with the former, even if you can't accurately predict price movement. OK, my fault for not doing more research. Wikipedia explains this well: http://en.wikipedia.org/wiki/Option_style#Difference_in_value Basically, there are some cases where it's advantageous to exercise an American option early.  For non-gold currency options, this is only when the carrying cost (interest rate differential aka swap rate or rollover rate) is high. The slight probability that this may occur makes an American option worth slightly more. "An option is an instrument that gives you the ""right"" (but not the obligation) to do something (if you are long). An American option gives you more ""rights"" (to exercise on more days) than a European option. The more ""rights,"" the greater the (theoretical) value of the option, all other things being equal, of course. That's just how options work.  You could point to an ex post result, and and say that's not the case. But it is true ex ante." Differences in liquidity explain why American-style options are generally worth more than their European-style counterparts. As far as I can tell, no one mentioned liquidity in their answer to this question, they just introduced needlessly complex math and logic while ignoring basic economic principles. That's not to say the previous answers are all wrong - they just deal with periphery factors instead of the central cause.  Liquidity is a key determinant of pricing/valuation in financial markets. Liquidity simply describes the ease with which an asset can be bought and sold (converted to cash). Without going into the reasons why, treasury bills are one of the most liquid securities - they can be bought or sold almost instantly at any time for an exact price. The near-perfect liquidity of treasuries is one of the major reasons why the price (yield) of a t-bill will always be higher (lower yield) than that of an otherwise identical corporate or municipal bond. Stated in general terms, a relatively liquid asset is always worth more than an relatively illiquid asset, all else being equal.  The value of liquidity is easy to understand - we experience it everyday in real life. If you're buying a house or car, the ability to resell it if needed is an important component of the decision. It's the same for investors - most people would prefer an asset that they can quickly and easily liquidate if the need for cash arises.  It's no different with options. American-style options allow the holder to exercise (liquidate) at any time, whereas the buyer of a European option has his cash tied up until a specific date. Obviously, it rarely makes sense to exercise an option early in terms of net returns, but sometimes an investor has a desperate need for cash and this need outweighs the reduction in net profits from early exercise.  It could be argued that this liquidity advantage is eliminated by the fact that you can trade (sell) either type of option without restriction before expiration, thus closing the long position. This is a valid point, but it ignores the fact that there's always a buyer on the other side of an option trade, meaning the long position, and the right/restriction of early exercise, is never eliminated, it simply changes hands. It follows that the American-style liquidity advantage increases an options market value regardless of one's position (call/put or short/long). Without putting an exact number on it, the general interest rate (time value of money) could be used to approximate the additional cost of an American-style option over a similar European-style contract. An option gives you an option.  That is, you aren't buying any security - you are simply buying an option to buy a security.  The sole value of what you buy is the option to buy something. An American option offers more flexibility - i.e. it offers you more options on buying the stock.  Since you have more options, the cost of the option is higher. Of course, a good example makes sense why this is the case.  Consider the VIX.  Options on the VIX are European style.  Sometimes the VIX spikes like crazy - tripling in value in days.  It usually comes back down pretty quick though - within a couple of weeks.  So far out options on the VIX aren't worth just a whole lot more, because the VIX will probably  be back to normal.  However, if the person could have excercised them right when it got to the top, they would have made a fortune many times what their option was worth.  Since they are Euroopean style, though, they would have to wait till their option was redeemable, right when the VIX would be about back to normal.  In this case, an American style option would be far more valuable - especially for something that is difficult to predict, like the VIX. The value of an option has 2 components, the extrinsic or time value element and the intrinsic value from the difference in the strike price and the underlying asset price. With either an American or European option the intrinsic value of a call option can be 'locked in' any time by selling the same amount of the underlying asset (whether that be a stock, a future etc).  Further, the time value of any option can be monitised by delta hedging the option, i.e. buying or selling an amount of the underlying asset weighted by the measure of certainty (delta) of the option being in the money at expiry. Instead, the extra value of the American option comes from the financial benefit of being able to realise the value of the underlying asset early. For a dividend paying stock this will predominantly be the dividend. But for non-dividend paying stocks or futures, the buyer of an in-the-money option can realise their intrinsic gains on the option early and earn interest on the profits today. But what they sacrifice is the timevalue of the option.  However when an option becomes very in the money and the delta approaches 1 or -1, the discounting of the intrinsic value (i.e. the extra amount a future cash flow is worth each day as we draw closer to payment) becomes larger than the 'theta' or time value decay of the option. Then it becomes optimal to early exercise, abandon the optionality and realise the monetary gains upfront. For a non-dividend paying stock, the value of the American call option is actually the same as the European. The spot price of the stock will be lower than the forward price at expiry discounted by the risk free rate (or your cost of funding). This will exactly offset the monetary gain by exercising early and banking the proceeds. However for an option on a future, the value today of the underlying asset (the future) is the same as at expiry and its possible to fully realise the interest earned on the money received today. Hence the American call option is worth more. For both examples the American put option is worth more, slightly more so for the stock. As the stock's spot price is lower than the forward price, the owner of the put option realises a higher (undiscounted) intrinsic profit from selling the stock at the higher strike price today than waiting till expiry, as well as realising the interest earned. Liquidity may influence the perceived value of being able to exercise early but its not a tangible factor that is added to the commonly used maths of the option valuation, and isn't really a consideration for most of the assets that have tradeable option markets. It's also important to remember at any point in the life of the option, you don't know the future price path. You're only modelling the distribution of probable outcomes. What subsequently happens after you early exercise an American option no longer has any bearing on its value; this is now zero! Whether the stock subsequently crashes in price is irrelevent. What is relevant is that when you early exercise a call you 'give up' all potential upside protected by the limit to your downside from the strike price. Think of it this way, if you traveled back through time one month - with perfect knowledge of AAPL's stock price over that period - which happens to peak viciously then return to its old price at the end of the period - wouldn't you pay more for an American option? Another way to think about options is as an insurance policy.  Wouldn't you pay more for a policy that covered fire and earthquake losses as opposed to just losses from earthquakes? Lastly - and perhaps most directly - one of the more common reasons people exercise (as opposed to sell) an American option before expiration is if an unexpected dividend (larger than remaining time value of the option) was just announced that's going to be paid before the option contract expires.  Because only actual stockholders get the dividends, not options holders.  A holder of an American option has the ability to exercise in time to grab that dividend - a European option holder doesn't have that ability. Less flexibility (what you're paying for really) = lower option premium. 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.
I think what you will see is Amazon turning into a Sams/costco style where they have warehouse shopping centers to directly compete with other club memberships. If they get buildings added to the shopping package they offer, prime memberships will skyrocket and then the days might be numbered for Costco and Sams. How do you compete with a company that offers shipping at a loss to them and can now compete with all your in store options. I have held an in the money long position on an option into expiration, on etrade, and nothing happened.   (Scalping expiring options - high risk) The option expired a penny or two ITM, and was not worth exercising, nor did I have the purchasing power to exercise it. (AAPL) From etrade's website: Here are a few things to keep in mind about exercises and assignments: Equity options $0.01 or more in the money will be automatically   exercised for you unless you instruct us not to exercise them. For   example, a September $25 call will be automatically exercised if the   underlying security's closing price is $25.01 or higher at expiration.   If the closing price is below $25.01, you would need to call an   E*TRADE Securities broker at 1-800-ETRADE-1 with specific instructions   for exercising the option. You would also need to call an E*TRADE   Securities broker if the closing price is higher than $25.01 at   expiration and you do not wish to exercise the call option. Index   options $0.01 or more in the money will be automatically exercised for   you unless you instruct us not to exercise them. Options that are out   of the money will expire worthless. You may request to exercise   American style options anytime prior to expiration. A request not to   exercise options may be made only on the last trading day prior to   expiration. If you'd like to exercise options or submit   do-not-exercise instructions, call an E*TRADE Securities broker at   1-800-ETRADE-1. You won't be charged our normal fee for   broker-assisted trades, but the regular options commission will apply.   Requests are processed on a best-efforts basis.  When equity options are exercised or assigned, you'll receive a Smart   Alert message letting you know. You can also check View Orders to see   which stock you bought or sold, the number of shares, and the strike   price.  Notes: If you do not have sufficient purchasing power in your account   to accept the assignment or exercise, your expiring options positions   may be closed, without notification, on the last trading day for the   specific options series. Additionally, if your expiring position is   not closed and you do not have sufficient purchasing power, E*TRADE   Securities may submit do-not-exercise instructions without   notification. Find out more about options expiration dates. Conceptually, yes, you need to worry about it.  As a practical matter, it's less likely to be exercised until expiry or shortly prior. The way to think about paying a European option is: [Odds of paying out] = [odds that strike is in the money at expiry] Whereas the American option can be thought of as: [Odds of paying out] = [odds that strike price is in the money at expiry] + ( [odds that strike price is in the money prior to expiry] * [odds that other party will exercise early] ). This is just a heuristic, not a formal financial tool.  But the point is that you need to consider the odds that it will go into the money early, for how long (maybe over multiple periods), and how likely the counterparty is to exercise early. Important considerations for whether they will exercise early are the strategy of the other side (long, straddle, quick turnaround), the length of time the option is in the money early, and the anticipated future movement. A quick buck strategy might exercise immediately before the stock turns around.  But that could leave further gains on the table, so it's usually best to wait unless the expectation is that the stock will quickly reverse its movement.  This sort of counter-market strategy is generally unlikely from someone who bought the option at a certain strike, and is equivalent to betting against their original purchase of the option.  So most of these people will wait because they expect the possibility of a bigger payoff. A long strategy is usually in no hurry to exercise, and in fact they would prefer to wait until the end to hold the time value of the option (the choice to get out of the option, if it goes back to being unprofitable).  So it usually makes little sense for these people to exercise early.  The same goes for a straddle, if someone is buying an option for insurance or to economically exit a position. So you're really just concerned that people will exercise early and forgo the time value of the American option.  That may include people who really want to close a position, take their money, and move on.  In some cases, it may include people who have become overextended or need liquidity, so they close positions.  But for the most part, it's less likely to happen until the expiration approaches because it leaves potential value on the table.  The time value of an option dwindles at the end because the implicit option becomes less likely, especially if the option is fairly deep in the money (the implicit option is then fairly deep out of the money). So early exercise becomes more meaningful concern as the expiration approaches.  Otherwise, it's usually less worrisome but more than a nonzero proposition. /u/NotMyRealFaceBook  As a sniff test, I threw the following assumptions into a Black-Scholes options pricing calculator:  * Stock Price and Strike Price = $200  * Valuation date = 10/31/2017  * Expiration date = 10/29/2027 (European style - no early exercise)  * Volatility = 20% (on the low end for a tech. company - but again see the non-log-normal assumption point above)  * Interest rate = 4% (on the high end - which means the option seller is over-charging you)  * Dividend yield = 0%  The calculator's theoretical call option price results in $82.  Unless the company in question has a materially skewed upside given today's starting valuation, my opinion is the options you are offered are being priced via a Black-Scholes model and are over-priced. Cultural aspects aside, there are a lot of American universities throughout Europe. Reinsertion into the US market would be my #1 concern but besides that it beats the tons of debt you get in the US while being able to expand your horizons. I just find it very weird more people don't at least consider it and rather make the mistake of paying 60k a year. Or at least go to community College... "Black-Scholes is ""close enough"" for American options since there aren't usually reasons to exercise early, so the ability to do so doesn't matter. Which is good since it's tough to model mathematically, I've read. Early exercise would usually be caused by a weird mispricing for some technical / market-action reason where the theoretical option valuations are messed up. If you sell a call that's far in the money and don't get any time value (after the spread), for example, you probably sold the call to an arbitrageur who's just going to exercise it. But unusual stuff like this doesn't change the big picture much." "Suddenly its not just comparing the current price to the price of the contract, or is it? Sure it is.  Suppose you bought 100 option contracts (each for 100 shares) and paid a $1 per share premium ($10,000 total).  Now those options are trading for $1.50 per share.  You have an unrealized $0.50 gain per share, or $5,000. The $10,000 in options you bought are now worth $15,000.  It holds whether they were bought to open or close a position, or whether they are puts or calls.  The only difference is whether you bought or sold the options (the arithmetic is just reversed for selling an option). But lets say we have an Option, where the payoff is max(St-K, c0) where ct is the market price. What do you do then? Your current, unrealized P&L is different than the payoff.  The payoff only happens at maturity.  The current P&L is based on current market prices, just like stock.  Option prices all have a ""time premium"" making them worth more than their payoff (intrinsic) value prior to maturity." "You've described the process fairly well.  It's tough to answer a question that ultimately is 'how is this fair?' It's fair in that it's part of the known risk. And for the fact that it applies to all, pretty equally. In general, this is not very common. (No, I don't have percents handy, I'm just suggesting from decades of trading it's probably occurring less than 10% of the time). Why? Because there's usually more value to the buyer in simply selling the option and using the proceeds to buy the stock. The option will have 2 components,  its intrinsic value (""in the money"") and the time premium. It takes the odd combination of low-to-no time premium, but desire of the buyer to own the stock that makes the exercise desirable."