## Sep 28, 2011

### Nikkei Volatility Futures / VNKY Futures On The Way

Yesterday Nikkei Inc announced that starting January they are going to start real-time calculation of Nikkei Volatility Index and today Osaka Securities Exchange announced plans to launch volatility futures on the main Japanese index. Links: announcement, futures introduction document, proposed contract specifications, index guidebook (calculation methodology). Right now the futures are under month-long public comment period, and are expected to launch sometime in the winter and trade on J-Gate platform. No word on Nikkei VI options yet.

P.S. See my updated post on Nikkei volatility futures here.

### Basket of Volatility: Koop Eens Een Mandje Volatiliteit

Readers from Netherlands, or anyone who speaks Dutch can enjoy this concise yet informative introduction from DB analyst Knut Huy to US and European volatility derivatives and how they can act as an insurance for equity portfolios.
Koop Eens Een Mandje Volatiliteit
Nameer dan een decennium van kommer en kwel op de markten vinden veel beleggers het nog te vroeg om in dit barre beursklimaat volop de kaart van de aandelen te trekken. Alternatieven lijken schaars: staatspapier en cash brengen weinig op en grondstoffen worden steeds meer de speelbal van speculanten. Investeren in volatiliteit kan een uitweg biede.
One things I could add is to be weary of backtested VSTOXX futures performance which (as I have written before) is unrealistic, and is probably based on theoretical marks, and not on actual trades.

As we are talking about VSTOXX I think one things is worth mentioning: Since Monday Sep 26 CBOE extended trading hours for VIX futures. Now they start trading at 8 AM EST. Since VSTOXX futures close at 18:30 Zurich time (12:30 EST), this brings total overlap between contracts to four and a half hours. The contracts are highly correlated, and although exchange rate remains a risk I think there are interesting opportunities for statistical arbitrage between the contracts. I am doing research on such possible strategy, and will blog about it once I get some results.

## Sep 24, 2011

### Volatility Indexes & Exchange Traded Products

I created a new page that I believe has the most complete list of implied volatility indexes including all international VIX-like indexes, commodity volatility indexes, and currency volatility indexes, and listed ETFs and ETNs all over the world including all that are based on the VIX and VSTOXX futures. I will try to keep the list up to date as much as I can and update prices on a weekly basis.

## Sep 22, 2011

### Variance Risk Premium In VIX Options

I just came across a very interesting research paper: Quantifying the Variance Risk Premium in VIX Options by Reed M. Hogan. Even though the work is a college senior thesis, it is a quality research and I believe one of the first papers on the subject!

If you have read Jared Woodard's Options and the Volatility Risk Premium you know about volatility risk premiums for different asset classes like equities and commodities. Now with proliferation of trading products on VIX and VSTOXX, it is important to measure the risk premium embedded in VIX options. The author explains the methodology developed by Peter Carr and Liuren Wu to create synthetic var-swap on VIX options (please note, there is a plus sign missing in the formula [1]), but uses a different formula that is developed by Gatheral. Realized volatility is computed from corresponding futures contract that has at least 12 days until expiration. The author then tests simple call and put writing strategies on the VIX.

Abstract:
This thesis uses synthetically created variance swaps on VIX futures to quantify the variance risk premium in VIX options. The results of this methodology suggest that the average premium is -3.26%, meaning that the realized variance on VIX futures is on average less than the variance implied by the swap rate. This premium does not vary with time or the level of the swap rate as much as premiums in other asset classes.  A negative risk premium should mean that VIX option strategies that are net credit should be profitable.  This thesis tests two simple net credit strategies with puts and calls, and finds that the call strategy is profitable while the put strategy is not.

## Sep 21, 2011

### VIX Expiration

Over the last month we continued to see higher volatility in the market, but since last expiration volatility indexes were pretty much unchanged: VIX expired at 33.72, up 0.99 from 32.73, and VSTOXX closed on 44.14, up 9.10 from 35.04. It is clear that the debt crisis in Europe is adding upward pressure on VSTOXX. While VIX fell from the August highs, VSTOXX rose higher.

While my forecasts were quite off, they were accurate on the signal - both indexes were forecasted to go higher, and both did expire significantly higher than market predicted. For complete history of my forecasts see forecasts tracker page. For the next expiration, October 19 2011 my forecasts are:

VIX to close at 31.99 vs 35.70 in futures
VSTOXX to close at 41.97 vs 40.70 in futures

This is unusual, since the forecast is for VIX futures to finish lower, while for VSTOXX futures to finish higher. While it can make sense from the economic point of view, in the past my forecasts did not perform very well when signs for VIX and VSTOXX were different. Good luck traders, and hedge your deltas!

## Sep 17, 2011

Equity markets rose, and volatility indexes fell this week - $SPX finished low last Friday, and gained 5% over the week, while Euro Stoxx 50 closed on a multi-month low on Monday, but gained almost 4% for the week. Implied volatility ETFs - VXX and VSXX made new multi-month highs. On Friday VIX futures entered a slight contango, while VSTOXX remains in backwardation, showing lingering concerns about European economic recovery. Implied volatility of VIX options fell, while VSTOXX remained unchanged. As I wrote before, liquidity in VSTOXX options is lower than the VIX, and combined with options expiration coming on Wednesday I don't think we can read much into the numbers. ## Sep 15, 2011 ### Intuitive Understanding Of VIX Formula Many investors are looking at VIX and VSTOXX indexes as a leading indicators of volatility in equity markets, however many are confused by the formula. According to CBOE VIX white paper or VSTOXX Index guide (page 23) volatility index is calculated using the formula below: $\dpi{150} \bg_black \dpi{150} \\* \\ \sigma^2 = \frac{2}{T}\sum{\frac{\Delta K}{K^2}e^{rT}Q(K)} - \frac{1}{T}[\frac{F}{K_0}-1]^2 \\* \\$ The square root of this number multiplied by 100 gives you the volatility index. This formula is a discrete version of the formula for "fair" strike of variance swap: $\dpi{150} \bg_black \dpi{150} \dpi{150} K_{var} = \frac{2e^{rT}}{T}\ \left ( \int\limits_{0}^{F} \frac{1}{K^2}\ P(K)dK + \int\limits_{F}^{\infin} \frac{1}{K^2}\ C(K)dK \right )$ While this formula may look complicated it is actually really simple if viewed in a chart. Below are 3 charts that will illustrate step by step what the formula means, and I hope will provide intuitive understanding behind the formula. For the charts below I used simulated prices of calls and puts on a hypothetical stock with 36 days until expiration (tenth of a year) and 20% annualized volatility, so we should expect the volatility index in this theoretical example to be about 20. I plot prices of calls and puts vs strike. As expected puts increase with strike, and calls decline. The point at which they intersect is the forward price. Now let's consider the area below the two curves. The higher the volatility the higher are options prices, the greater the area under curves. Now the last step - multiply each value by 2*exp(r*T) and divide by T*K^2 . The adjusted curve will have almost the same shape, but will be different in height. So meaning of the curve does not change, just the scale - the higher the volatility, the greater the area under the curve. The area under the curve is sigma squared in the first equation. In my calculations the area is 0.040157. The square root of the number multiplied by 100 is 20.0392 which is very close to 20 as we expected. To summarize - VIX is approximately proportional to the area under call and put curves. Another property of volatility indexes is becomes apparent - ATM, or near ATM options have the greatest contribution to its value. This post is based on ideas from Simple Variance Swaps by Ian Martin (available here). ## Sep 10, 2011 ### Week in Volatility Stock indexes tumbled across the world on increasingly negative outlook on European debt crisis and prospects of US recovery. VIX futures rose 4.60 points, and VSTOXX rose 9.70. While VIX at 38 is 10 below its recent high, VSTOXX made a new high. Implied volatility ETNs VXX in the US and VSXX in Europe finished week on new highs as well. Implied volatility of VIX and VSTOXX was also higher than last week, but still lower than at the highs few weeks ago. VSTOXX long-term implied volatility was lower than last week, but I believe it is simply because of limited liquidity of those options, and does reflect true VSTOXX vol levels. ## Sep 7, 2011 ### Options Arbitrage In VXX While doing some analytics last week I realized that there is a pure (not statistical) arbitrage situation in VXX options. By the time I noticed it was too small of an edge to try to trade manually so I did not do anything, and since this is something that is very unlikely to happen again I'll disclose all the details that came up in my analysis. All data obtained from Nanex(nXCore) - a very high quality datafeed. This feed has all messages from exchanges, although to create the charts below I took 1 second snapshots. When VXX split in Nov 2010 OCC decided to leave the "old" unadjusted strikes, so one can trade both after-split VXX and before-split VXX which has quarter of its value. On August 30th some options were trading out of line with the others, I guess because some market-maker did not properly adjust volatility skews that day. Because options are so far OTM early exercise is not a consideration, and the mispricing is a pure arbitrage. For example (pre-split) VXX 21 Jan 2012 Call should trade at 1/4 value of VXX 84 Jan 2012 Call, and they do most of the time. The first chart plots bid of VXX 21 Jan 2012 Call times 4, versus ask of VXX 84 Jan 2012 Call. Around lunchtime bid exceeded ask, and traders had an opportunity to capture as much as 12 cents by selling four 21-strike contacts and buying one 84-strike contract. Using conservative estimates of costs for institutional trader this would give 0.12-5*0.01=0.07 profit on 5*0.25 haircut (margin), or 5.6%. Given that at that time there was 143 trading days until expiration, this translates into 5.6 %* (143/365) = 14.3% annualized of riskless profit. The volume on the quotes was sufficient run the spread at least 25 times (0.07 * 100 * 25 =$175) by the most conservative estimate.

Similar opportunity presented itself between (pre-split) VXX 22 Jan 2012 Call and VXX 87 Jan 2012 Call, which is the highest strike available for regular contracts. Because 22*4 = 88 > 87, 22-strike contract bid multiplied by four should be smaller than ask of 87 strike contract. Here the spread also widened as much as 12 cents. These are of course not common opportunities, but provide an interesting lesson. There were obviously no low-latency arbitrageurs that brought the spread in-line as mispricing persisted for many minutes.
Thanks to Jason S. Williams of Front Run the Delta for his invaluable feedback on this post.

## Sep 1, 2011

### Volatility Products For European Investors

There is an interesting article (in German) from Baader about volatility linked structured products available to European investors that I was not aware of. For example UBS issues a performance certificate on their Euro Volatility Arbitrage Index that is tied to performance of VSTOXX index (webpage, product info). From term sheet is looks like a variance swap with some adjustments. Another product mentioned is SGI Vol Premium (webpage, product info) which is also a var-swap but based on VIX index. Both products had losses in the recent volatility spike, but otherwise performed similar to other short-gamma strategies indexes like CBOE VIX Premium Strategy Index, CBOE Capped VIX Premium Strategy Index, or CBOE S&P 500 VARB-X Index.