The calendar spread refers to a family of spreads involving options of the same underlying stock, same strike prices, but different expiration months. They can be created with either all calls or all puts. Also known as time spread or horizontal spread.
Using calls, the calendar spread strategy can be setup by buying long term calls and simultaneously writing an equal number of near-month at-the-money or slightly out-of-the-money calls of the same underlying security with the same strike price.
The idea behind the calendar spread is to sell time, which is why calendar spreads are also known as time spreads. The options trader hopes that price of the underlying remains unchanged at expiration of the near month options so that they expire worthless. As the time decay of near month options is at a faster rate than longer term options, his long term options still retain much of their value. The options trader can then either own the longer term calls for less or write some more calls and repeat the process.
If the options trader is bullish for the long term and is selling the near month calls with the the intention to ride the long call for free, he is implementing the bull calendar spread strategy.
If the options trader is neutral on the underlying security and is selling the near month calls primarily to earn from time decay, then he is implementing the neutral calendar spread strategy.
The calendar spread can also be implemented using put options.
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