Theta

Options become more expensive the more time that remains until their expiration date, and conversely, all options become less valuable the longer they are held. This decay of an option’s value due to the passage of time is known as Theta or Time Decay, and it works in favour of short positions in options and against long option positions.

The calculation of Theta for an option or portfolio of options requires evaluating the option or portfolio tomorrow versus today and determining the difference between the two valuations with all other factors remaining equal as follows: 

Theta = Option Value Tomorrow – Option Value Today.

Bought options have negative Thetas, while sold options have positive Thetas. Generally, a portfolio with a positive Theta will gain in value as time passes provided that nothing else changes, whereas a portfolio with a negative Theta will decay in value over time if nothing changes. Also, as its expiry date comes closer, the value of an option falls, all other price factors being equal.

This makes intuitive sense because less time is available for a favourable price movement to occur. Also, the rate of this time decay generally increases as the option approaches its maturity date and decreases as the underlying rate and the option’s strike price are moved farther apart.

Since an option has maximum time value when it is at-the-money, options struck close to the money will have more influence on a portfolio’s Theta than options struck far from the money. Also, since most time decay occurs close to expiration, this is this time during which a positive theta seem most attractive, provided that the strategy can he kept Delta- hedged without incurring excessive losses due to volatile movements in the underlying instrument.

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