### Triple Expiration

Next time, for the first time in SPX history, we will have 3 expirations in one week: on Monday Feb 29 month-end options will expire, newly listed Wednesday weeklys will expire on Wednesday Mar 2, and "regular" weeklys on Friday Mar 4. All of the options expire in the PM. And I have positions in all 3.

Speaking of Wednesday weeklys, the launch was a clear success. On the first day of trading - this past Tuesday, quotes width was somewhat sporadic, but the last few days I see that the width is pretty much like a regular weekly expiration, with volume and open interest also at quite respectable levels.

### Old VIX vs New VIX - Simple Explanation

CBOE started disseminating VIX index in 1993. At that time the index was based on OEX (S&P100) options, that were most liquid index options at the time, and was calculated using weighted average of Black-Scholes implied volatility of ATM options. Ten years later CBOE changed the calculating, moving from OEX to more liquid SPX options, and also, most importantly, completely changing the calculation formula.

This formula for new VIX is not intuitive, and is quite complicated, but I will explain both old VIX formula and new VIX formula in simple geometric terms. Let's create a chart of options prices, calls and puts, vs their strikes. You will end up with a chart that looks something like this -

If options are relatively expensive the lines would be higher; if options are relatively cheaper the the lines would be lower. At one point, these lines will intersect, and the strike where they intersect will be very close to where the underlying index is trading. And the height of the point where these lines intersect is (approximately) proportional to the old VIX value. If volatility is high, then options are expensive, and the height of intersection point will be higher. If volatility is low, the height will be proportionally lower.

The math behind this is based on approximation for the price of ATM straddle ≈ 0.8  * index price * volatility * √ time to expiration  In our case, volatility ≈ height of the intersection point (0.4 * index price * √ time to expiration  )

New VIX is calculated in a very different way, but also has the place on the chart. Take the area under the call and put curves, that looks like a curved pyramid.

The area under the curve is (approximately) proportional to the square of the new VIX! This is something that I covered in a previous post, so for the sake of not repeating myself I will just summarize:

old VIX is proportional to the height of the pyramid, new VIX is proportional to the square of the area of the pyramid.

This connects two ideas, and also shows how new VIX uses information from all options, as opposed to the original VIX that uses only ATM options.

### CBOE to List SPX Wednesday-Expiring Weeklys Options

CBOE announced yesterday that they will start listing SPX weekly options series with the same expiration time as VIX options. While it is not clear from the press-release, the circular clearly states that new options will be PM-settled, adding half-day of basis risk for traders. Overall I think this contract specification is somewhat surprising, but let's go over the history of VIX to understand CBOE's position.

Original VIX, as introduced by CBOE in 1993 was based on OEX (S&P100) options, most liquid index options at the time, and calculated by interpolating Back-Scholes implied volatililities of ATM options; OTM options did not figure in the calculation. VIX was already in use for 10 years, when in 2003 CBOE updated VIX methodology in two ways - first, moving from OEX to SPX, more liquid index options market, and changing the calculation to be in line with a formula for a variance swap - an OTC instrument that allowed for a pure (as in no delta, no rebalancing required) bet on variance.

While not exactly the same (VIX is a square root of var-swap, a non-linear transformation which makes static replication impossible) VIX futures and options became a class of its own. The original foundation of VIX vs basket of 30 day SPX options became less important as VIX complex became the dominant market leading the price discovery in volatility.

However that led to some inconvenience for traders - if you have two correlated markets like SPX and VIX, and you treat them as observable (as opposed to some model based latent quantity) you would want to naturally trade one against the other. However with Wednesday vs Friday expiration this adds significantly to residual risk. But current solution (Wednesday PM) begs a question - why PM? Trading VIX vs SPX Wedensday options still leaves half-day of difference?

I called CBOE (so you don't have to) asking for a comment. After being transferred from one person to another I received an answer that can be summarized as "we cannot comment on product design decisions" . Basically what it means is that CBOE decided to add another day for expirations, and designed the product to be similar to existing weeklys (PM). They were not meant to perfectly align with VIX complex, despite what it says in the press-release.

FWIW I think this is actually an unfortunate decision, and lost opportunity for CBOE.

### Weekly market report

Wall st delivered a mixed bag of news with VIX, VNKY, and VSTOXX and their underlying markets almost unchanged. VXD - volatility index based...