Option Time Premium Decay, Another Dimension of Theta

When I first began mentoring option traders one thing struck me.  The insistence that theta is non-linear almost all of an options decay took place inside the final 30 days of its life.  This statement is only half true.  We have all seen the chart.  It’s a chart that shows option decay sloping downward in the final 30 days of its life, with the decay getting greater and great each day.  If you haven't seen the chart, here it is:

There is only one problem; this chart only applies to a very small portion of options the chart above applies only to ATM options.  While it is true theta is non-linear in the rate of decay, the actual price points where the theta is at its highest is also non-linear.  While decay does continue to increase for all strikes, the rapid acceleration show above does not happen on the outer strikes.  I will show a real world example of this, then I will explain why this is so important.

This is a chart of the greeks taken from the October weekly options that will expire on Friday. The chart was cut at end of day on 10-1-10, when the SPY closed 114.61.  Notice the greeks of the 116 calls and the 110 put.  Then take a look at the 113, 114, and 115 strikes.

This is a chart from the following Monday on 10-4-10, the SPY closed 113.75.  Take a look at the same strikes, what does one notice about how the greeks have moved from strike to strike?

It is quite obvious that the ATM's saw their Theta's increase dramatically from Friday close to Monday close, while the outer strikes did not.  Those strikes barely budged.  This is because theta decay should really be show more with a graph that looks like this:

Notice, that at the end of the options' life, they converge, with the ATM's having a lot more lose.  This is something many traders do not understand or have knowledge of.

If one has this knowledge, how would one take advantage of it?  One point would be that this clearly makes is that butterflies might perform better closer to expiration instead of further out.  This could explain the success of weekly butterflies beyond that of the simple pin. It is long the cheap option that is has a slow demise and short 2 options that are quickly losing their value.  It is taking advantage of Theta convergence.

It is also a reason not to be short weekly condors.  While the likelihood of being hit is low, the need of the trader to stay in the trade to closer expiration makes the risk/reward very suspect.  I think after a move like today, or heck the NDX over the last few weeks’ traders have seen why they can be such a problem.

There are many other types of uses for this type of knowledge while public, is not well known or understood.  That is where a trader can find edge.  It’s also another example of how many traders can be misled by some of our competitors.

Want to know more about the dimensions of decay, and how to use them?  We talk a little bit about these things during the AM Pit Report.  During the Pit Report and of course our option mentoring programs we get into this little known function of option decay along with many others that to the best of my knowledge are not discussed anywhere.

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graphs from the bovespa, option trading tips, and TOS