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I have a question regarding the usage of European vs American Options. According to Professional Risk Mgr Handbook 2010, American-style options are used mostly on equities whereas European-style options are used on equity index options like Eurostoxx 50. Why is this the case?

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It is an attempt to make a general statement that is not entirely correct, and certainly will become increasingly incorrect as new products are introduced. It is true that individual stock options traded in the US are American exercise. And the index options that are traded on the CBOE are European type, however there are also index options traded on the CME which are American. Also, I am not familiar with the situation in other countries, but it is unlikely that this pattern fits everywhere.

So it is just a generalization valid for the US in 2010 but with some exceptions (the CME options) even in that case.

The reasons are historical (choices that were made by option exchanges long ago) rather than anything substantial.

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    $\begingroup$ From my knowledge there are American Index Options, but only very small percentage and like 99% of Index Options are European. $\endgroup$ – emcor Jul 23 '15 at 9:16
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You asked genuine question.

Remember one thing always, volatility is considered good by derivative players but not by the market as whole. More volatile is market, more riskier it is.

Since American option can be exercised at any time, whereas European options can only be exercised at the maturity only, so American options leads to excess volatility that would be otherwise either without the options or American options.

Regulator always aim to keep the volatility within a specific bound, since excess volatility would discourage investor for investing into the market, so they prefer European style option for both i.e. for index and individual stock. But American type is the first preference of speculator always. What is chosen at the end, believe me, depend on the bargaining power of both group i.e. regulator and speculator.

Since Index is the broad indicator of market performance it is the first thing seen by the investor before investing into the market. So regulators keep Index option as European and while Individual stock options as American.

Some countries might have American style option for both but now can understand why it is so.

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