GREEKS: THETA
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Theta is the change of an option price per unit of time.
The time value of option premiums is non-negative at any point of time and zero at expiration.
It follows that the time value of an option is in constant decay as a function of time.
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There is two important rules of thumb to remember about option prices time decay:
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(I) THE AT THE MONEY OPTION PRICES TEND TO FALL WITH THE SQUARE ROOT OF TIME.
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(II) OUT OF THE MONEY OPTIONS LOOSE VALUE AT A FASTER PACE.
The graph above represents the expansion of a stock price, starting today on the left and moving towards the future on the right.
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The price of the stock today is known, but as it moves away into the future, it is increasingly uncertain. This results in a wider and wider tree - with more distance between the top and the bottom branches (115 and 85 prices to the right of the tree)
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The price of an at the money call option (100 strike for the example), is determined by the average branch on the top side of the expansion tree. It is the payout expected from the top side of the tree.
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The price of an out of the money call option is determined by the probability of reaching the highest branch,
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Intuitively, if the stock price has not increased as time goes by, the highest branch has less and less probability of happening. In the above example the highest branch is only reached if you have an increase in every branch division (or node).
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This intuition is behind why at the money option prices increase with the square root of time. They represent the average high branch, not the top (highest) branch of the tree.
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On the other hand the probability of reaching a top branch is similar to an out of the money option. Out of the money options loose money over time quicker than at the money options.