CBOE announced today that they are launching derivatives on GVZ  Gold VIX index that is based on implied volatility of GLD ETF. What is surprising that only half of a year ago CBOE licensed to CME the right to develop their own volatility indexes (crude, and gold  GVX based on implied volatility of GC futures options), and CME did already launch futures and options on them. While as far as I know there has been no trading activity in these two products on CME (ok, gold futures traded a 4lot, options none, oil none for both futures and options) it is really a surprising move for CBOE to move directly into CME space, and also to try to revive a dead product. I would love to see this product gain liquidity, but experience suggests that the product is likely to fail.
Futures contracts specs, options contracts specs  all in parallel to the VIX contracts.
See my previous posts about CME indexes here, and here.
CBOE SKEW Index, Part 3
SKEW  2 Std. Dev  3 Std. Dev. 
100  2.30%  0.15% 
105  3.65%  0.45% 
110  5.00%  0.74% 
115  6.35%  1.04% 
120  7.70%  1.33% 
125  9.05%  1.63% 
130  10.40%  1.92% 
135  11.75%  2.22% 
140  13.10%  2.51% 
145  14.45%  2.81% 
Since SKEW index is "adjusted" as SKEW Index = 100  10 * implied skew, SKEW Index value of 100 is skew of 0, SKEW Index value of 105 is skew of 0.5, etc.
The table is based on GramCharlier expansion of normal distribution, for various skew levels with zero excess kurtosis, however the paper that is referenced provides the formula for probability distribution function, and not cumulative density function (see Wikipedia):
PDF(z) = n(z)*[1+skew/6*(z^{3}3z)+kurtosis/12*(z^{4} − 6z^{2} + 3)],
where n(z) is the normal probability distribution function.
Since kurtosis = 0, the expression becomes F(z) = n(z)*[1+skew/6*(z^{3}3z)]
The formula for CDF is obtained by integration
CDF(z) = N(z)  skew/6*n(z)*(z^{2}1),
where N(z) is the normal cumulative density function. In excel this formula would read:
NORM.DIST(Z,0,1,TRUE)  SKEW/6*NORM.DIST(Z,0,1,FALSE)*(Z*Z1),
where Z and SKEW are variables, Z is the Zscore e.g. 2 for negative 2 standard deviations move, and SKEW is implied skew, calculated from SKEW index. The results are not exactly the same, but sufficiently close to the ones in CBOE paper. I suspect the difference is due to weird rounding on CBOE's part. I do realize it may sound arrogant for me to assume CBOE's error rather than mine, however CBOE's numbers don't quite match standard results in the case of normal distribution (where skew is zero): e.g. for 2 stds the number should be 2.27501 to the 5 significant digits, where CBOE rounds it to 2.30, and for 3 stds the number should be 0.13499 to the 5 significant digits, where CBOE rounds it to 0.15, so I confidently stand by my numbers.
However there is a different problem that I would really like to point out  the GramCharlier approximation is a rather weak approximation. In some cases it produces rather strange numbers, for example in the case of Z=1 (down 1 standard deviation) probabilities become independent of the skew parameter, which obviously makes no sense.
SKEW  0.5 Std. Dev  1 Std. Dev.  1.5 Std. Dev. 
100  30.85%  15.87%  6.68% 
105  28.65%  15.87%  8.03% 
110  26.45%  15.87%  9.38% 
115  24.25%  15.87%  10.73% 
120  22.05%  15.87%  12.08% 
125  19.85%  15.87%  13.43% 
130  17.65%  15.87%  14.78% 
135  15.45%  15.87%  16.12% 
140  13.25%  15.87%  17.47% 
145  11.05%  15.87%  18.82% 
So, if you want to calculate riskneutral probabilities now you have the same formula CBOE used in the white paper, however know that the formula is only an approximation, and clearly does not work in some cases. I hope in the near future I'll blog about better formula, as well as other uses for SKEW index.
Week in Volatility
This week saw a lot of action  a strong rise in VIX and subsequent decline. VXX had a drawup of 20% ~log(34.01/27.73) with some large intraday volatility. Although this drawup seems significant, I think it is a good time to remember that average drawup for SPVIXSTR (the index that underlies VXX) for the last 5 years is 49% !, and that most of 2008 the index was making new highs.
For those who want to know about risks of being short VXX I recommend my previous post on the topic, as well as recent analysis on MarketSci blog (link).
For those who want to know about risks of being short VXX I recommend my previous post on the topic, as well as recent analysis on MarketSci blog (link).
XXV  IVO trade
I've written before about XXV and its price connection to VXX. The formula for historical relationship between two ETFs is
XXV ≈ $20 * (1  (VXX108.03)/108.03 ) = $40  VXX * (20/108.03)
That relationship has changed slightly, probably because of accrued fees / transaction costs. As I pointed out, it VXX falls to zero that provides a maximum for theoretical value of the ETF of $40. Having risen 70% since its inception (using base value of $20) in 7 months XXV does not provide much of an upside to investors, and will probably spend the rest of its existence going slowly to $40. Apparently in response to this iPath launched IVO  an identical fund, but with a more recent start date. Now that IVO has been trading for a few weeks, I provide a similar formula for IVO:
IVO ≈ $20 * (1  (VXX32.99)/32.99 ) = $40  VXX * (20/32.99)
The maximum value is still $40, but return upside is greater.
It is clear that arbitrage is possible among all three ETFs. For example the following relationship holds between IVO and XXV
IVO ≈ $40  (40XXV)*108.03/32.99
Good luck, traders!
XXV ≈ $20 * (1  (VXX108.03)/108.03 ) = $40  VXX * (20/108.03)
That relationship has changed slightly, probably because of accrued fees / transaction costs. As I pointed out, it VXX falls to zero that provides a maximum for theoretical value of the ETF of $40. Having risen 70% since its inception (using base value of $20) in 7 months XXV does not provide much of an upside to investors, and will probably spend the rest of its existence going slowly to $40. Apparently in response to this iPath launched IVO  an identical fund, but with a more recent start date. Now that IVO has been trading for a few weeks, I provide a similar formula for IVO:
IVO ≈ $20 * (1  (VXX32.99)/32.99 ) = $40  VXX * (20/32.99)
The maximum value is still $40, but return upside is greater.
It is clear that arbitrage is possible among all three ETFs. For example the following relationship holds between IVO and XXV
IVO ≈ $40  (40XXV)*108.03/32.99
Good luck, traders!
VIX Tuesday Open
It's Presidents Day in the US, a national and exchange holiday, and markets are closed. But in Asia and Europe markets were down by over 1% with volatility indexes up across the board:
VSTOXX +2.45
VDAX +1.99
VSMI +1.32
Asian volatility indexes (the ones that I know of) are up as well, and at the time of writing Asia opened lower, and S&P Eminis are down 1.17%. I guesstimate that VIX will open tomorrow at about 18, and probably will be volatile throughout the day.
VSTOXX +2.45
VDAX +1.99
VSMI +1.32
Asian volatility indexes (the ones that I know of) are up as well, and at the time of writing Asia opened lower, and S&P Eminis are down 1.17%. I guesstimate that VIX will open tomorrow at about 18, and probably will be volatile throughout the day.
Week in Volatility
From the volatility view it was a decidedly mixed week  VIX up, VSTOXX down.
While the volatility did its own thing I was watching the skew on VIX and VXX, and while I cannot point to any quantitative measures I have a strong feeling that something unusual was taking place this week. ATM vols on the VIX were up, but that is the usual pattern with VIX vols, and nothing out of the ordinary.
While the volatility did its own thing I was watching the skew on VIX and VXX, and while I cannot point to any quantitative measures I have a strong feeling that something unusual was taking place this week. ATM vols on the VIX were up, but that is the usual pattern with VIX vols, and nothing out of the ordinary.
VIX Expiration
Today VIX expired at 16.49, up 0.11 since last expiration. My prediction made on Jan 20, 2011 was for 18.42 at the time when futures were trading at 18.80. While the forecast is slightly closer than the futures, it is considerably off this month.
At the time the forecast was made the index, futures and my forecast were around the same level of about 1819. While lower forecast certainly made sense my model did not anticipate the unrest in Egypt, or susequent volatility decline. Since about Feb 4th VIX remained unchanged at around 16, and futures slowly declined to that level.
My forecast for March VIX is 17.44 vs 18.05 (yesterday's settlement) and VSTOXX at 21.39 vs 22.35 in the futures market. Question for the readers: is there an official settlement for VSTOXX, like VRO for the VIX?
At the time the forecast was made the index, futures and my forecast were around the same level of about 1819. While lower forecast certainly made sense my model did not anticipate the unrest in Egypt, or susequent volatility decline. Since about Feb 4th VIX remained unchanged at around 16, and futures slowly declined to that level.
My forecast for March VIX is 17.44 vs 18.05 (yesterday's settlement) and VSTOXX at 21.39 vs 22.35 in the futures market. Question for the readers: is there an official settlement for VSTOXX, like VRO for the VIX?
Week in Volatility
CBOE SKEW Index, Part 2
If we apply SKEW in combination with VIX to market analysis (for example using it as technical indicator) we can see some interesting patterns. I separate SPX returns into 4 categories and calculate annualized returns (I assume everyone knows the importance of using geometric average returns for evaluation of longterm strategies)
Regime  Arithmetic average  Geometric average  Sharpe ratio 
Low VIX Low SKEW  1.9%  1.3%  0.18 
High VIX Low SKEW  12.3%  9.5%  0.49 
Low VIX High SKEW  11.3%  11.3%  1.07 
High VIX High SKEW  5.2%  2.7%  0.23 
Right now we're in the Low VIX High SKEW regime, which can be considered a bullish signal. This is just the basic way of using SKEW index, more complicated indicators can be developed. For example Bollinger bands indicators seem to work reasonable well. In the next skew post I'll examine what SKEW means for option traders.
CBOE SKEW Index, Part 1
White paper, FAQ, and time series in Excel are now available from CBOE website.
EDIT: The dataset is missing 9/20/2000 to 9/29/2000 and a few other random days for some reason.
EDIT: Here is a combined dataset of SPX, VIX, and SKEW indexes. Missing days are left as blanks. Data from CBOE and Yahoo! Finance.
Week in Volatility
Equity indexes were up this week with S&P up 2.7% and Stoxx up 1.6%. VIX index sank more than four points from 20 to just below 16. Long term futures declined by about 1.5, with the longest expiration now trading at 23.30. VStoxx fall was more modest, with longterm volatility still above 26%.
While uncertainly in Egypt may have been an excuse for volatility rise last week, we see that market discounted it as a nonevent. Even now with more recent news about gas pipeline explosion, would probably not be a catalyst for higher volatility. Longterm futures tell us unambiguously that we're still in the lowvolatility regime.
One of the reasons for such fall in volatility can be falling correlations. After the crisis in 2008 we've seen a spike in correlation among all asset classes, what became colloquially known as risk on / risk off. Lately that pattern started to wane. For example KCJ implied correlation index closed near a 6month low (chart) Looking at historical charts of ICJ, JCJ, KCJ it looks like implied correlation will likely not to go much lower, and that is probably going to have a negative effect on VIX skew.
While uncertainly in Egypt may have been an excuse for volatility rise last week, we see that market discounted it as a nonevent. Even now with more recent news about gas pipeline explosion, would probably not be a catalyst for higher volatility. Longterm futures tell us unambiguously that we're still in the lowvolatility regime.
One of the reasons for such fall in volatility can be falling correlations. After the crisis in 2008 we've seen a spike in correlation among all asset classes, what became colloquially known as risk on / risk off. Lately that pattern started to wane. For example KCJ implied correlation index closed near a 6month low (chart) Looking at historical charts of ICJ, JCJ, KCJ it looks like implied correlation will likely not to go much lower, and that is probably going to have a negative effect on VIX skew.
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