There was an interesting discussion about new research in The International Journal of Business and Finance Research that made the rounds in the blogosphere last week here and here. The study looked at the difference in implied volatilities of index options compared to the implied volatilities of the options on the corresponding ETFs.  For instance, the authors compared the implied volatility of NDX options to implied volatility to QQQ options.  They did the same thing for SPX to SPY and DJX to DIA.

The researchers found that, during the period from 2003 to 2006, the implied volatility of the ETF options had a tendency to be slightly higher than the corresponding index options.  Delving deeper, they found that the deep-in-the-money options had the greatest discrepancy.  They also noticed that the discrepancy was most pronounced in the NDX to QQQ relationship.  Based on these two facts, deep-in-the-money QQQ options are the most overpriced relative to their comparable index options.

The researchers listed some possible reasons for the difference, such as bid-ask spreads and the net buying pressure argument.  They also said it may be that ETF options are simply more attractive instruments for hedging and speculation.

What caught my eye, however, was the first sentence of the second paragraph in their conclusion: “Because the underlying return distributions are the same…”

That statement piqued my interest because, believe it or not, the investigation of return distributions and their discrepancies from theoretical expectations just so happens to be what I specialize in!

So I decided to take a look at the paper a bit more deeply, to see if I could find a reason why the ETF options were more expensive than their index counterparts during that 4-year time frame.  I just completed the analysis yesterday.

The first thing I noticed, which was obvious to others besides me, was that the time period was very limited: 2003 to 2006.  Anything can happen in such a small sample.  More important, during that four-year period, volatility — both realized and implied — went in one direction: down.  VIX fell from a peak of 35 to less than 10 with just a couple of blips up.

Another possible factor was and still is the inherent difference in the way cash-settled index options and ETF options are settled.  ETF options are physical delivery, meaning that if you have an in-the-money option at the close on expiration Friday, you’re going to get a long or short position in the ETF shares, depending on whether the type of option you traded was a call or put and whether you bought the option or sold it.

Index options are completely different.  Their settlement is in cash.

But there are two other very important differences:

1. Index options like those traded on the NASDAQ 100 Index stop trading the Thursday before expiration Friday.  Their settlement price is determined based on Friday’s open.  ETF options like those on the QQQ don’t stop trading till Friday’s close.  So ETF options have almost an entire extra day of action that index options don’t have.  Could that extra day be the source of the added volatility?
2. Another thing that is unusual about index options is the way the “open” is determined.  It’s not the opening print of the index itself.  Instead, tt’s a settlement value calculated based on the opening prints of the constituent securities in the index.  These settlement values have their own prices and ticker symbols.  For instance, the ticker symbol for the settlement value of NASDAQ 100 Index options is NDS, not NDX.

The net result of these differences indicate that, perhaps, comparing the return distribution of NDX to QQQ may not have been the proper comparison, at least on options expiration day.  It could be that the return distributions on expiration day are vastly different … different enough to explain the implied volatility discrepancies.

To investigate this, I checked to see if there was a significant difference in the return distributions of NDS to NDX on expiration Friday.  [Because the researchers found no significant difference between NDX and QQQ, I only compared NDS to NDX and did not compare NDS to QQQ.]  I used the period in which the implied volatilities were compared — from 2003 to 2006 — for the initial analysis.  You can see the distribution comparison below.

Notice any difference?  The biggest difference is that NDX has many more large moves than NDS on expiration Friday.  There are far fewer blue bars at the extreme left or right.  That tells us the return distributions are different — at least on expiration Fridays during that time period.

But what about a more complete data set?  After all, the analysis above is based on only 4 years of data during a period where realized volatility did nothing but drop.  To get a more complete data set, I added data going back to March 1999 through 2006.  This represents the entire time frame in which the study’s index data was measured.

As you can plainly see, at least on options expiration day, the return distributions show a very significant difference.  The close-to-close distribution (NDX) has far more large moves than the close-to-open distribution (NDS).  In fact, the NDX column to the extreme left is taller than any other NDX column.  Relative to NDS, NDX has extremely fat tails on expiration day.

Is that the source of the higher implied volatility for index options compared to ETF options?  I think so.  But it remains to be answered definitively.  The purpose of this post is not to provide a final answer.  Instead, I am posting this to generate ideas for future research.

For instance, one idea that popped into my mind this morning comes from a concept that I (along with nearly every professional options trader) was well aware of back in the 1980s and 1990s: when evaluating index options, you should never be using the index itself.  Instead, you should be using the device that traders use to hedge their options bets.  In the case of QQQ options, it’s the QQQ ETF.  For NDX options, however, you can’t hedge with the NDX index itself; you hedge with the NDX futures.  So perhaps investigators should look at the return distributions of NDX futures and NDS instead of NDX.

– Don

P.S. — Here’s the distribution with the complete dataset from April 1998 to current.

P.P.S. – One other note on future research.  Based on the graph above, I plan on looking at the current situation, rather than the way things were in 2003-2006.  My guess is that the implied volatility of the ETF options may not be as high relative to the implied volatility of the index options as it was in the past.