Yesterday in class someone asked about "Bermuda options," This occurred during the discussion of the difference between European options, which can be exercised only on the expiration date, and American options, which may be exercised at any time before expiration. Bermuda lies between America and Europe, and so, too, with Bermuda options, which may be exercised at certain fixed times before expiration (on the first of each month, for instance).
Bermuda options are generally not traded on exchanges. They are traded in the Over-the-Counter Market, wherein buyers and sellers can negotiate any terms of the contracts (such as which days the option can be exercised).
Other categories of over the counter options include Asian options, digital options (also called binary options or all-or-nothing options) and lookback options.
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