I’ve read a few option books.
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Monday, April 6, 2009

Option’s TIME VALUE – Putting It Together – Part 4: Behavior

The Behavior of Time Value
As mentioned in Part 3, the Time Value component of an option price will decline or “erode” as expiration is nearing (i.e. Time Decay).

The rate of decline of option’s time-value resulting from the passage of time (i.e. rate of Time Decay) is known as THETA, which is one of the Options Greeks.

Comparing Theta at a certain point of time between ATM (At-The-Money), ITM (In-The-Money) & OTM (Out-of-The-Money) options, Theta is typically highest for ATM options, and gradually decreases as options move towards ITM and OTM.
This is understandable because ATM options have the highest time value component, so they have more time value to lose over time than an ITM or OTM option.

Comparing Theta over time, there are different behaviors between ATM and ITM / OTM options:
For ATM options, as the Time Value component of an option price decreases when the option is approaching expiration, the rate of time value decrease is accelerating (i.e. Theta is increasing) as it is getting closer to expiration.
This means that the amount of time value disappearing from the option price per day gets bigger with each passing day. For ATM option, time value decreases sharply particularly in the last 30 days before expiration.

On the other hand, for both ITM & OTM options, Time Value actually decreases at a decelerating rate as expiration nears. In other words, Theta decreases as the option is approaching expiration.
This means that the amount of time value disappearing from the option price per day gets smaller with each passing day.

This Time Value behavior can be seen in the following graphs:

1) Time Value of ATM Option:






2) Time Value of OTM Option:




Note: Both pictures courtesy of Sigma Options

Therefore, based on the above, we can summarize as follow:

For ATM options, Theta (i.e. the rate of time value decline as the time passes) is typically the highest (as compared to ITM & OTM options), and will be increasing (i.e. the rate of time value decrease is accelerating) as the option is nearing expiration.

For both ITM & OTM options, Theta is relatively lower (than ATM options), and will be decreasing (i.e. the rate of time value decrease is decelerating) as the option is nearing expiration.

The Impact of Implied Volatility (IV) on THETA
When Implied Volatility (IV) decreases, Theta will be lower, especially when it is approaching expiration.
On the other hand, when IV increases, Theta would be higher.

Why is it so?
As discussed earlier in this post, time value as the price that people are willing to pay for the chance / uncertainty as to whether or not an option will finish ITM.
The more uncertain, the higher the time value will be.

When IV decreases, such uncertainty will be lower, particularly when the option is nearing to expiration. This lower uncertainty will then be reflected in lower time value. Since Theta is the decrease of time value due to the passage of time, Theta will naturally be lower because it has less time value to lose over the remaining time to expiration.

Related Topics:
* FREE Trading Educational Videos You Should NOT Miss
* Options Trading Basic – Part 1
* Options Trading Basic – Part 2
* Understanding Implied Volatility (IV)
* Option Greeks

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