Long
A long or a long position is the buying of securities such as stocks, bonds, currency etc. If a trader is long a security then it means that the trader owns the security. An investor takes a long position, with the expectation to sell a security at a higher price in order to realize a profit. For example, suppose you bought 100 shares of Microsoft stock, it can be said that you are long 100 shares.
In the context of options, it is the buying of an options contract that is considered as long position. Buying of an option contract gives you the right but not the obligation, to buy or sell the underlying for a specified period of time at a specified date.
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