There is a funny thing that I've come across while trying to build a volatility model. According to my estimations the VIX is usually higher than the actual volatility (RV) realized for that same period. Just take a look at the following chart:

In the top chart I've plotted the VIX (IV) and RV estimate for a 3-year period. The bottom chart is the difference between the IV & RV . To estimate the RV I've used a function from tradingwithmatlab blog. It uses several common estimators for RV (I've used the average value for RV ).

It looks like IV on average is 7% higher than the RV. So one could just sell volatility and get a steady profit, right? Knowing that there is no free lunch in trading, it seems that I'm missing out something. Is my estimation of RV incorrect? Is it unjustified to compare VIX and SP500 volatility? All feedback is very welcome...

Your value of implied volatility completely depends on the fair value model for option prices you use.

ReplyDeleteIf there's a systemic bias, either the market is perpetually inefficient, or it uses a different model to invert implied volatility with.

My money is on your implied vol calculation being inferior to that of the market's.

Have you tried to backtest an implementation? That may shed some light on the situation. Specifically, what contracts would you trade to capitalize on the bias you see? Sell VIX futures and buy straddles on SPX? Roll cost on futures and on straddles may be a factor as well.

ReplyDelete@The Sanch: I don't estimate IV, but RV. IV is given by the VIX. My observation is that there is a consistent bias between the IV and RV.

ReplyDeleteThis is backed by more sources if you google for 'volatility premium'.

You can go ahead of do this, collect the volatility prem., however you face significant tail risk. If I'm not mistake the equity curve for this strategy has a nice monster DD in 08.

ReplyDeleteThe thing is there is basically no arbitrage for VIX due to lack of underlying, I could think of something but too complicated to be practical.

ReplyDeleteLike Jen said, you need to backtest this.

ReplyDeleteIf there's a true volatility premium, then a (theoretical) arbitrage should show historical profits.

If there's no historical arb profit to be made, then there's something incorrect in the calculation of IV, because it should in principle be an unbiased estimator of RV.

VIX is calculated based on the mid market of SPX option strips. For arb, you need to constantly adjust the positions. The bid-ask spread, where you can actually trade, explains a no-arb zone.

ReplyDelete@The Sanch: there has been some work on volatility premium, take a look at this one: http://www.marginalq.com/eraker/volPremiumPaperJune08.pdf

ReplyDeleteMy conclusion from this is that IV is in fact a *biased* estimator of RV. This does not mean that this bias can be turned into profit however.

Very interesting, although as you point out, the divergence between IV and various other estimators of RV has been noted.

ReplyDeleteEven if you can't make any money with the strategy you mentioned, you might want to look at the difference between IV and your RV-estimate. Can you use the difference to predict something else? What happens to the market when the difference is very large vs when it is very small?

@JCF, indeed, the IV-RV divergence could be used as a sentiment indicator. I assume that it is already being widely used by volatility traders. I'll certainly try to use it in my own trading.

ReplyDeleteImplied being higher than realized is expected. The difference is due to the anticipation of unknown future events. As a previous comment indicates, you will make money with this strategy, but there will be fat tails. If your money is 'slow' and prepared to wait out the tails then it will make money. If your money is 'fast' and will cut losses on fat tails then it will lose money.

ReplyDeleteCheck out the tikcer in bloomber web site SPARBV:IND.

ReplyDeleteIn genelat selling implied vol vs historical vol works grate, until it doesn't. (2008)

The volatility premium has been around for a very long time and is very well researched (see Bakshi and Kapadia 2003, which also has a brief literature review).

ReplyDeleteCurrent theory suggests the volatility premium is a rational response to the skewness preference of investors. The premium also exists in the cross section of options returns when looking at the expected skew of an option's payoff (see Boyer and Vorkink 2011). I believe the premium is also generally greater in individual equity options than indices.

Hi,

ReplyDeleteVIX is just the weighted BS-implied volatility of a couple of options (different maturities and strikes) on the index. Since IV is always different from RV (at least since the 1987 crash, as E. Derman has showed), this shouldn't come as a surprise.

What you see is the volatility smile in another form - equity RV is below IV, unless you're pricing ATM, mid-short maturity options.

If you want to build a strategy from this, you would have to make an assumption about how the spread between IV and RV evolves, i.e. estimate the skew of the vola.

Cheers

@Anonymous, thanks for the tip, already working on it ;-)

ReplyDeleteit has to be this way, if implied was at realized on average, who would ever sell volatility? Basically the premium seller needs to collect and build equity so they'll survive when realized spikes.

ReplyDeleteIV has to be higher than IV. If IV priced in was on average less than RV then traders who sell options would loose money. Options are essentially insurance , so IV priced in has to be greater than RV for option sellers to make. And VIX is derived from options.

ReplyDeleteShort IV is a classic example of collecting pennies in front of a steamroller. It works most of the time. If it doesn't, you're dead. So go sell insurance, my friend ;)

ReplyDeleteHave been doing this for quite some time now, with profit. The trick is to hedge the vol position so you don't get kicked by the broker on a volatility spike. And respect the term structure of course.

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