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Why are American-style options worth more than European-style options?
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.