The "Hidden Figures" of VIX: Interview with Dr Catherine Shalen

If you trade anything volatility-related - VIX futures, VXX ETFs, watching SKEW or VVIX indexes you should know a significant contribution of one of the analysts at CBOE 20 years ago. Here is my interview with Dr Catherine Shalen where we talk about the real secret reason for changing the VIX formula, introduction of VIX trading, and what the future holds for volatility trading.


OnlyVIX: How did you come to work at CBOE?

Dr Catherine Shalen: I was in CBOT research dept. and after completing a global survey on the need for futures on individual stocks and a study of conversion factors for Treasuries, there seemed to be  no interesting projects forthcoming. So I decided to cross the street and switch to CBOE Research. That was in November 2002.

OV: What was the motivation for Goldman Sachs to list futures? Why did GS not want to keep the market OTC?

CS: As I heard it after starting at CBOE, Goldman Sachs  was offering its clients in the credit some OTC products and they wanted to hedge this exposure with listed futures on VIX. GS had written up a new interpretation of the VIX index based directly  on the work of Neuberger (Log Contract, 1994) and Carr and Madan (Towards a Theory of Volatility Trading 2008).  Credit spreads are well correlated with equity returns which in turn link to equity volatility. If stock prices tumble, it is likely that credit spreads widen, and also likely that equity volatility increases.  Hence volatility is a viable credit hedge.

OV: Why did they insist on the methodology change?

CS: The old VIX was a weighted average of eight  Black Scholes implied volatilities at and near the money, It is some measure of expected volatility over the next month, but it  cannot really  be replicated with securities.  Goldman Sachs wanted futures on a VIX that market makers could hedge. In other words market makers would be able to assume an option portfolio that would hedge a position in VIX futures.

This is precisely what the new VIX yielded. The new VIX is a new measure of expected volatility over the next 30 calendar days.  It is an interpolation of weighted sums of the mid-quote prices of at and out of the money S&P 500 put and call options at different strikes at two different expirations that bracket 30 days (that’s an interpolation, sometimes, an extrapolation may have to be used ). The new VIX incorporates the prices at  nearly all the listed S&P 500 strikes, whereas Goldman Sachs had envisaged only eight strikes.  In a telephone call, I suggested to them to use all the strikes because it was closer to the theoretical formula that came out of Carr and Madan’s work.

Example: today it’s Columbus day, October 10, 2022. Let us derive an expectation of 30 day volatility implicit in S&P 500 options.  Back then S&P options expired only monthly, on the third Friday of the month. The VIX calculation would fetch the prices of options that expire on October 22 and November 18, 2022 options, weigh them according to the prescribed formula, add them and that would yield VIX?  Well not quite. It would be expected variance, and to extract VIX, one must take the square root, annualize the number and express it in percentage terms.

As usual, there are more pesky details, because the strikes used should be fairly liquid. CBOE Research devised a method to screen out illiquid options. It discarded puts and calls at strikes below or above strikes with successive quoted bid prices of zero. In certain circumstances, that’s a lot of information lost, and furthermore, it makes the number more unstable. Bondarenko at UIC, and Andersen at Northwestern criticized this method.

Also note that nowadays, CBOE has deployed S&P 500 option expirations every day. Hence there is a rich menu of expiration combinations that will interpolate or extrapolate to 30 days.

Well that was  just the VIX spot index. A futures contract on the VIX is a leap forward.  On October 10, 2022, futures on VIX that expire at the open on November 16, 2022 will settle to the uncertain value of VIX at that open. At that open, VIX will be based on the prices of S&P 500 options with expirations that best bracket 30 days past November 16, 2022.  The final settlement price of the futures  is not based on quotes, it is generated by a “rotating” auction traveling through different strikes and the crossing price of the option at each strike feeds into the calculation.

Prior to November 16, 2022, market makers with positions in these November VIX futures can buy or sell (depending on whether they short or long) the portfolio of S&P 500 options approximately predestined to enter the VIX calculation on November 16, 2022. And voila, le tour est joue, the trick is done. The final settlement price of market makers' position in VIX futures matches the value of their hedging portfolio of S&P 500 options. Pretty neat replication.


OV: There was yet another reason why the VIX methodology had to be updated :)

CS: When Goldman Sachs proposed the new VIX, one reason CBOE Research VP warmly embraced it is, that way, there was no need to discuss and have to publicly correct an embarrassing feature of the old VIX. Bob Whaley who did the formula for the old VIX made a mistake in the annualizing factor. I saw it when I came to CBOE Research, but they were already painfully aware of it.


OV: Wow, I bet most people had no idea. So, what were your contributions to getting VIX futures listed?

CS: My first project upon arrival at CBOE was to write a business proposal for a futures exchange at CBOE where VIX  futures could be traded. That took a few rounds of editing, but the exchange was finally created, most probably independent of my little business plan:)

Second was the index formula itself. I was busy deepening my knowledge of volatility, specifically the new robust replication of variance coming from the Carr & Madan team. It was totally fascinating. After parsing the Goldsman Sachs formula, and comparing it to the Carr-Madan formula,  I suggested to Goldman Sachs in a telephone call  to use all the option strikes, not just the eight initially proposed by Goldman Sachs. They agreed.

I also spent time discussing and interpreting the Goldman Sachs formula with my colleagues in CBOE research. How the formula discretized the Carr-Madan formula, how expected volatility sprung from a portfolio of options. Also, there was the mystery of the remainder term in the Goldman Sachs formula. Where did it come from? I showed the team that it was a term compensating for the fact that  there is usually no listed strike exactly at the money. The Carr-Madan formula expands call and put options from the theoretical at the money price. The remainder is generated from a Taylor expansion.  I wrote the derivation of the remainder on a page for a colleague, and I presume he used it to  talk to clients, or something like that.  The colleague kept losing my write up and so I gave him new copies. 😊

I also wrote the VIX white paper with a colleague, the VIX futures primer, and  published articles on VIX and variance in magazine (Swiss Derivatives) and book (Izzy Nelken editor for Volatility as an Asset Class) I also developed several volatility-related indexes: SKEW which won the invited address at Quant congress, VIXVIX, VXTH (has an ETF) , STRGL, and option overlays: 2% OTM BXM, PUT, CLL, SMILE.


OV: Development of VIX as a tradable product allowed for other similar indexes to be developed around the world, and many ETFs/ETNs to be built on top of VIX success. What do you expect from volatility derivatives in 5 years from now? Where do you see the future of the industry?

CS: I see a limit to the use of VIX analogs. The volume in VIX derivatives perks up during crises but it  is not growing at same pace as S&P 500 volume. It should if it was an effective hedging instrument. MIAX has listed SPIKE, a VIX wannabe, and volume there is small. It is pretty difficult to dislodge a first mover, especially in what is ultimately a niche market, even with zero trading cost.  It is possible that some variations of VIX could be successful.

AUM in volatility ETFs is growing, on and off. Perhaps they are attracting a new clientele If I were to work for an exchange, I would propose different types of volatility based derivatives. If I worked for an ETF provider, I would propose new types of option overlays.  


OV: Would you like to add something from yourself - maybe promote your consulting services, a book you’re working on?

CS: I welcome all job opportunities. I am forever brewing new ideas about derivatives, It is my natural habitat. My PhD thesis was on silver futures, and I love to write about derivatives. But I am also very well versed in most financial markets and try to keep up with new themes in financial theory, e.g. signature of time series, application of machine learning and neural networks to finance and economic problems.


OV: Thank you very much for the interview; thank you for your contributions to volatility trading!

CS:  Thank you for letting me respond to this interview. I thoroughly enjoyed it.

Volatility and Price of a Straddle, Are They The Same?

Yesterday I found another piece of ignorance on Medium: Stop Watching The VIX, Just Make Your Own

tl;dr : Just use ATM straddles 🤦

This is of course not correct. As I have written before on this blog that (skipping mathematical rigor) the value of ATM straddle is

or about 80% of the expected volatility. So if SPY = $400 and VIX = 20, the expected volatility is $400 * 20/100 = $80,  then 1 year ATM straddle would be about 80% of $80 ~ $64

Alternatively, if you see a straddle, you can approximate expected volatility dividing by 80%. For example SPY ATM straddle for 2022/11/18 expiration is about $25 . The expected volatility for November expiration is $25/0.8 ~ $31.25

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Volatility and Expected Range ( High - Low ), Are They The Same?



This is not a post to correct some abstract mathematical technicality, or a semantic point. Rather I hope to shed some light on widespread mis-estimation of important risk metric that I often see on the internet. For example this double-decker of ignorance popped up on my twitter feed today.

VIX as you know is an annualized measure and in order to calculate an expected daily move - that is from one trading day to another, one should use trading day count convention, and sqrt(1/252) - not 365 - as a factor. 

sqrt(2/pi) ~ 0.8 is the multiplier to get the average absolute daily return, and here the author is correct.

However the range of a random walk is double that amount, 2 * sqrt(2/pi) ~ 1.6 , and in our case over 3%

Lower than 5% range we saw in S&P today, but the difference is far less dramatic than the tweet suggests.

Traders, pay attention to numbers and formulas you use in your trading. Mistakes can costs you money!

Natural Clustering in VIX Futures Data

 If you take all available VIX futures data and create a scatterplot of daily settlement prices as a function of time to expiration you will see a curious pattern:

Yes, there are clear clusters in prices. But what do these clusters mean? The simple explanation is that the VIX term structure passes from one regime to another and there is noise around these regimes. There is a low-volatility flat, regular volatility backwardation, and high volatility contango regimes.
To estimate a model like this from historical data one would need to run some sort of HMM - honestly I am not sure how to do this. But what I did instead is to create daily fits to a basic 3-parameter model, applied k-means to the fitted parameters (n_clusters = 3) 
These 3 term-structures are pretty much what I expected. The fit would probably be better in log-space, but that is something I will work on for next time. For now I want to conclude that - completely unsurprisingly three regimes are correlated with S&P returns, with low-volatility regime having high returns, and sharpe ratio, and high volatility having negative returns and low sharpe. Since 2004 we had mostly bull market, so it would be interesting to repeat this study with synthetically constructed VIX futures for 1990 and on. How would you construct synthetic VIX futures? Well - take S&P options data, calculate VIX for that expiration, and apply historical estimates for vol-of-vol premium. 

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