Why Do Long Dated Options Have More Similar Term Structures?

Why Do Long Dated Options Have More Similar Term Structures?

I was recently working with a newer option mentoring student explaining term structure.  He pointed out to me this graph:

 

He wondered how it was possible that two options that are only one month apart, March and April (March is Green, April is Blue), could have a wider volatility term structure than two months that are about half a year apart, Dec 2011 and June 2012 (Dec is Purple, June is Orange).

I explained to him it had to do with only one thing: the function of decay.  We have all seen this chart:

 

 

Notice how that ATM decay takes off in the final few months.  Simply put, if we looked at the ATM decay going forward into the next 30 days in March and the Next 30 days in April, the March decay will be a lot higher.  As the days pass, the decay speeds up and speeds up.  This makes the March increasingly more price sensitive and less sensitive to volatility.   My thoughts are the lower IV is a result of March tracking closer to realized volatility.

Meanwhile, the time decay for the December and June options, options that have a very long time to decay, are very similar in speed, and rate of increase.  As time passes, the options continue to move in lock step.  Options are like a marriage: the Options that decay together stay together. 

Said another way, if options have similar Greeks, they will have similar volatility structures.  Notice how dissimilar the greeks for March and April are:

March Vega: 1.68, April Vega: 2.22

Notice how similar Dec 2011 and June 2012 are:

Dec 2011 Vega: 4.85, June 2012 Vega: 6.07

Notice that March has about 75% of the April's vega.  December, despite expiring six months sooner than June has 80% of June's vega.  This is the model's way of pointing out the similarities of back month options vs front dated terms.  This similarity also likely produces more similar volatilities.  Options with similar sensativities to changes in volatilities have similar volatilities

This explains why the implied volatility curve is more similar in the back months vs. front month options.  Just because we know why it is there, doesn't mean it should exist.  Just because the greeks and risk profile are different does tha mean the implied volatilities should be different?  My thoughts are no, which is why trader's that know how to weight the months have the ability to really take advantage of these differences.  Tomorrow, I will explore the market reasons for these vol differences and whether the arguements hold water..  

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About Mark Sebastian

Mark Sebastian is a former market maker on both the Chicago Board Options Exchange and the American Stock Exchange. Along with his role directing the path of education for Option Pit, Mark is currently the director of risk for a private hedge fund. He writes a daily blog, the Option Pit blog, formerly Option911. Sebastian has been published nationally on Yahoo Finance, Google finance, Financial Times Alphaville and is a featured contributor for TheStreet.com. He is also published regularly at SFO, the Options Insider, and is one of the Co-Hosts of The Option Block Podcast, a featured Podcast from Options Insider Radio. Mark is the managing editor for Expiring Monthly: The Option Traders Journal. Sebastian has a Bachelor's in Science from Villanova University. To learn more about Option Pit and their mentoring services, please visit: http://www.optionpit.com