Lessons in Greek: Theta

by Bill Burton on July 9, 2011

Ancient Greek WomenMy previous article introduced the concept of “the Greeks” and their applicability to characterizing the response of an option position to changes in both price of the underlying and implied volatility- delta and vega.  There remains one additional major Greek used to help understand the impact of the passage of time on an option position; this Greek is theta.

I need to remind readers of the structure of an option price.  We discussed this anatomy in detail in last week’s posting in the discussion of vega.  Similar to vega, theta is a factor which only impacts the extrinsic (time) portion of option premium.

Theta is reflective of a unique characteristic of options.  Time, at least in our present universe, only moves in one direction.  Tomorrow there will exist one less day until expiration as compared to today.  Since the time to expiration represents one of the major inputs to the option pricing model, each day less that exists in an option contract is reflected in a lower time premium.  Harnessing the power of this “theta decay” of option prices represents a major point of advantage for option traders.

Theta measures the reaction of an individual option or multi-legged option position to the passage of time. The concept of theta is particularly helpful in more complex option positions consisting of combinations of several individual positions.  In such positions, the response to passage of time is often not intuitively obvious.  This “position theta” is calculated by simply adding the theta values of each individual option position.

For a given long option position, theta is always a negative number regardless of whether the option is a put or call.  The trader who wants to construct positive theta positions, structures that benefit from the passage of time, must include short options for at least a portion of his total position.

In order to help understand the impact of theta on a position, let us consider the AMZN July 200 call.  AMZN is currently trading around $200; the 200 strike would be the current at-the-money series.  This option is currently priced at $5.30 and has a theta of -14.2.

If price and implied volatility both remained constant until tomorrow, this option would decrease in value 14.2¢ as simply the result of passage of time.  As you begin to become familiar with these concepts, I find it easy to think in terms of options being an insurance contract.  In the case of owning a call, you have bought insurance to protect you against the risk of AMZN stock moving upwards beyond $200.  The daily premium cost for this insurance policy is the 14.2¢ that the value of the call erodes if all other factors remain static.

The sensitivity of an option’s price to theta is greatest in the at-the-money strike within an individual expiration cycle because this strike always contains the maximum dollar amount of time premium.  In addition, shorter dated options have greater rates of theta decay than longer dated options.

Theta decay is not linear, especially when considered in the framework of at-the-money options.  The classic pattern is to see relentlessly accelerating theta decay as options expiration is approached.  During the last month of an at-the-money option, time decay goes from a gentle green ski slope to a double black diamond slope in the last week of the option’s life.

The relentless and inescapable impact of “theta decay” of option positions represents a major “tailwind” for a variety of options positions and a secret advantage for the educated trader. Learning to capitalize on the relentless decay of option premium gives the knowledgeable trader a huge competitive advantage.

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{ 2 comments… read them below or add one }

John July 30, 2011 at 7:25 am

1. ” In the case of owning a call, you have bought insurance to protect you against the risk of AMZN stock moving upwards beyond $200. The daily premium cost for this insurance policy is the 14.2¢ that the value of the call erodes if all other factors remain static.”

2. ” In addition, shorter dated options have greater rates of theta decay than shorter dated options.”

Hi Daaan!
The excerpt #1 from your notes on theta. Is hard to understand. Because when you buy a call you want the call option to go up in value.
excerpt #2
I thought the theta of shorter dated option is greater than longer dated options.

I always enjoy hearing your amusingly understandable videos and webinars

John

Bill Burton July 31, 2011 at 1:50 pm

John:

Thanks for the comments and finding my typo in your point #2. You are absolutely correct and I have fixed the typo. I am sure it was very confusing since I said shorter dated options decay faster than shorter dated options.

As regards your point #1, I was just trying to make the point that the passage of time negatively impacts your position if you are long a call.

Thanks again.

Bill Burton

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