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Free Bitcoin/Bitcoin Futures Quotes, Charts, & Historical Data

 
Thursday, December 14th, 2017 | Vance Harwood
 

Finding quotes and historical data for Bitcoin and Bitcoin futures can be an adventure.  Below I’ve assembled links to the online resources that I’ve been able to find.

In many cases, data is available from multiple sources.  I did not attempt to list all of them.

BTC Quotes

BTC Charts

 BTC Historical Prices

BTC Futures

  • CBOE/CFE  Symbol: XTB
    • Quotes
      • Spot: Gemini exchange
      • Cboe (including bid/ask)
        • Use “Enter Symbol” Field
        • Ticker construction:  XBT/ followed by month-year code (e.g, XBT/F8 = January 2018 expiration)
          • F=Jan, G=Feb, H=Mar, J=April, K=May, M=June, N=July, Q=Aug, U=Sept, V=Oct, X=Nov, Z=Dec
      • Cboe/CFE  (all months)
    • Historical Data  CBOE
    • Term Structure  Chart:  VIX Central/bitcoin
    • Reference exchange:  Gemini
    • Contract Size:  1 Bitcoin, cash settled  (Contract Specifications)
    • Initial customer margin 44%
      • Brokers may require much more margin ( e.g., Interactive Brokers is requiring $40K per contract–around 130%–on short contracts)
    • Trading Hours (USA Central Time)
      Type of Trading Hours Monday Tuesday – Friday
      Extended 5:00 p.m. (Sunday) to 8:30 a.m. 3:30 p.m. (previous day) to 8:30 a.m.
      Regular 8:30 a.m. to 3:15 p.m. 8:30 a.m. to 3:15 p.m.
    • Future settlement quote (once per day)
    • Option availability:  Earliest probably around March 2018

 

  • CME  Symbol: BTC
    • Quotes
    • Reference exchanges:  Bitstamp, GDAX, itBit, Kraken (combined into a composite quote via BRTI & BRR)
    • Contract Size:  5 Bitcoins, cash settled  (Contract Specifications)
    • Initial customer margin 35%
      • Brokers may ask for much more than this, especial for short contracts
    • Trading Hours:  Scheduled to start trading 18-Dec-2017
      CME Globex: Sunday – Friday 6:00 p.m. – 5:00 p.m. (5:00 p.m. – 4:00 p.m. CT) with a 60-minute break each day beginning at 5:00 p.m. (4:00 p.m. CT)
      CME ClearPort: Sunday – Friday 6:00 p.m. – 5:00 p.m. (5:00 p.m. – 4:00 p.m. CT) with a 60-minute break each day beginning at 5:00 p.m. (4:00 p.m. CT
    • Future settlement quote: BRR (once per day)  methodology) )   Historical Data

 

A Better Way to Model the VIX

 
Tuesday, November 28th, 2017 | Vance Harwood
 

Models are useful. They help us understand the world around us and aid us in predicting what will happen next. But it’s important to remember that models don’t necessarily reflect the underlying reality of the thing we’re modeling. The Ptolemaic model of the solar system assumed the Earth was the center of everything but in spite of that spectacular error, it did a good job of predicting the motions of the stars, planets, moon, and sun. It was the best model available for over a thousand years. But new data (e.g., phases of Venus as revealed by Galileo’s telescope) and errors in predicting the motions of the planets demonstrated that the sun-centric Copernican/Kepler models were superior.

There are a lot of models for the Cboe’s VIX. None of them are particularly good at predicting what the VIX will do tomorrow but they can be useful in predicting general behaviors of the VIX. The most popular model for the VIX (although people might not recognize it as a model) is simple mean reversion.

 Simple Mean Reversion

Car gas mileage is a good example of a simple mean reverting process.

Over time your car’s gas mileage will exhibit an average value, e.g., 28 miles per gallon. You don’t expect to get the same mileage with every tank because you know that there are factors that make a difference with your mileage (e.g., city vs highway driving, tire air pressure, and wind direction) but over time you expect your mileage to cluster around that average value. If you get 32 miles per gallon on one tank of gas you reasonably expect that next time you check it will likely be closer to 28. If the values start varying significantly from the average you start wondering if something has changed with the car itself (e.g., needs a tune-up)

A mean-reverting random walk is a relatively simple model and fits some of the basic behaviors of the VIX. Specifically, over time the mean value of the VIX has stayed stable at around 20 and the VIX exhibits range bound behavior—with all-time lows around 9 and all-time highs around 80.

However, there are many aspects of the VIX that aren’t well explained by a simple mean-reverting model. For example, a simple mean reverting process will have its mode value (the most frequently occurring values) close to its mean. This is not the case of the VIX; its mode is around 12.4—a long way away from its mean. The histograms below show that difference visually.

 

Another VIX behavior that departs from a simple mean-reverting process is the abrupt cessation of values below 9—almost a wall. For a normal mean reverting process you would not expect such a sharp cut off at the low end.

The Acid Test:  How good is the model for predicting the future?

Having a good model for a process is useful because it can help us predict at least some aspects of the future. For example, we can use our average gas mileage to decide whether we need to gas up before entering a long stretch of highway without gas stations.

A simple mean-reverting model is not particularly good at predicting the future moves of the VIX. If the VIX is low (e.g., 12 or below) a simple mean-reverting model predicts that since the VIX is far from its mean that will likely increase soon. But history shows this is usually not the case. Often the VIX can be quite content to hang around 12. This leads to news stories quoting various pundits stating “The VIX is broken” –when in reality they are just using an inferior model.

 As I said earlier there are VIX models out there that address some of these deficiencies. Unfortunately, the ones I know of are complex and not very intuitive. I believe the model that I describe below can improve our intuition considerably without adding too much complexity.

A Better VIX Model

A better way to view the VIX is that it behaves like the combination of two interacting processes: a specialized mean reverting process and a “jump” process. The jump process captures the behavior that all VIX watchers know—its propensity to occasionally have large percentage moves up and down. Since 1990 there’ve been over 86 times where the VIX has increased 30% or more in a 10 day period. The occurrence of these spikes is effectively random with a probability of happening on any given day of around 1.28%. It’s like a roulette table with 78 slots, 77 of them black and one red. If the ball lands on a black the normal reigns—if red then things get crazy. The graph below shows a histogram of the number of days between these 30% spikes in the VIX since 1990.

There’s nothing that prevents reds on consecutive spins nor is there some rule that reds become really likely if you haven’t had a red in a while. The roulette ball has no memory of where it landed on previous spins.

VIX jumps are generally not just one-day events; subjectively it looks like it takes around two weeks before the market reverts to more typical behavior. The model assumes that when a jump occurs it essentially drives the behavior of the VIX for 10 trading days.

The other process, the specialized mean reverting process, addresses the non-jump mode of the VIX—which is historically around 85% of the time. One of the key behaviors it needs to address is the slow relaxation in the mean value of the VIX after a big volatility spike rekindles a generally fearful attitude in the market. This decay process continues (unless interrupted by another VIX jump) until the average monthly VIX values drop into the 11-12 range.

The chart below illustrates this relaxation process.

 

This characteristic can be modeled by expecting the short term mean of the VIX (when it’s not jumping) to decay exponentially until it reaches its “quiet” mean of around 11.75. It works well to quantify this decay as having a time constant of 150 days.

With this approach, sans jumps, the difference between the current VIX value and its long-term quiet value will decay by 50% in 104 days. So if the VIX is at 30 the model predicts the mean will decline to 20.75 in 104 days [30- (30-11.5)*0.5=20.75].  If there are no jumps for the next 104 days the VIX’s mean would decline to 16.13. If a jump occurs in the interim the short term mean is reset to the VIX’s value at the end of the jump.

The other part of the specialized mean reverting process mimics the day-to-day volatility of the VIX. I used a formal mean reverting diffusion process (Ornstein-Uhlenbeck) to accomplish this. Despite its scary name, you can think of it as a random walk with the thing “walking” being attached to the mean with a spring—similar to walking a dog with a springy leash. The further the dog gets from you the larger the force pulling the dog back to you.

Unlike the simple mean-reverting model often used for the VIX, this process has a much tighter distribution, with the extreme values effectively limited to around +-20% from the mean. When the VIX is quiet this process replicates the firm lower limit on the VIX, a VIX of 9 is -21.74% lower than a quiet mean of 11.75.

Simulating the Model

 To implement/validate this model I estimated the key input variables and then used Excel to simulate 20-year volatility sequences. I then compared these time series to the actual VIX history and tuned the model’s parameters such that the key characteristics (e.g., volatility, mean, mode, decay rates) were similar to the VIX’s historic values.

Resulting histogram of historic VIX values vs the simulated combined process

 

The next chart shows an example 20 year time series of the simulated VIX combined process compared to the historic VIX. The two series aren’t time synchronized; my intent is to show how the simulated VIX time series has the same visual feel as the real VIX.

 

Conclusion

This improved model is not a path to riches. It isn’t any better than other models at predicting when VIX jumps will occur. However, this model does help us understand how the VIX behaves over longer time spans. In particular, during times of sustained low volatility, it predicts that the VIX will tend to stay low until the next significant VIX spike and not trend up like the simple mean-reverting model demands.

 

 

 

Quant Corner

  • The mean-reverting diffusion process used is an Ornstein-Uhlenbeck mean reverting diffusion process using a log-normal distribution. The volatility was set at an annualized 112% and the return to mean strength parameter ETA set to 0.3. The mean of the process is determined by the previous day’s VIX value minus the exponential decay factor that will decay the mean down to 11.75 over time if there are no additional jumps (Tau of 150 days). If the mean has decayed down to 11.75 the process acts very similarly to the VIX’s low volatility regimes (e.g., 2004-2006, 2016-2017) with the “return to mean” factor effectively acting to keep the VIX  higher than 9.0
  • The Jump process used (with a few small tweaks) is a compound Poisson process where the probability of a jump sequence is random with a probability of a jump being 1.28% per day. The jump sequence and its daily amplitudes are determined using a technique borrowed from rappers called sampling. Instead of trying to recreate the decidedly non-Gaussian distribution of VIX jumps I reused historic VIX jumps by randomly selecting, and replaying one of the more than 85 jump sequences since 1990 where the VIX jumped more than 30% in 10 days. Each jump sequence is 10 days long, with the first 2 days being the behavior before the jump.

One Reason Why the New VIX Calculation is Better

 
Thursday, November 30th, 2017 | Vance Harwood
 

The CBOE changed the way the VIX® was calculated on October 6th, 2014—asserting the change would provide a more accurate assessment of expected volatility.  The new process does look better to me, but I’ve been surprised that the new VIX and the old VIX (listed as VIXMO) sometimes differ by as much as plus/minus 10 percent.

Disagreements between the two indexes are not due to only one factor, but clearly one improvement was to eliminate the week of the month where the VIX was calculated using extrapolation.

The VIX provides a 30 day estimate of volatility, but the S&P 500 options (SPX) used in the VIX calculation have fixed expiration dates.  The CBOE transforms the options’ data into the VIX by using volatility specific interpolation / extrapolation.  For example, if you have a volatility number for options that expire in 10 days and another for options that expire in 38 days you can reasonably assume that the VIX level should be between those two numbers.

One requirement with the old VIX calculation was that it couldn’t use options with less than 7 days to expire.  When the 7 day restriction was reached the calculation switched to using options that had more than 30 and 58 days until expiration.  The chart below shows the calculation right after that switch on January 12th, 2015.

VIX-Calc-12Jan15-extrapolation


The blue and red bars are the volatility numbers (VINMO & VIFMO) from the S&P options and the green bar is the VIX calculation extrapolated from those two numbers.  For details on that process see: Calculating the VIX Index—the Easy part

Normally this extrapolation was reasonable, but if the market is nervous the shorter term volatility values climb.  January 12th, 2015 was a case in point—notice how the light blue VXST bar (9 day volatility) is higher than the VIX estimate.

The next chart shows the new and old VIX calculations together.  The black dotted line shows the interpolation used for the new VIX calculation; the blue dotted line shows the old VIX extrapolation. The black vertical bar shows the VIX estimate.

VIX cacl-graph


Clearly the two calculations have a major difference of opinion —the new calculation’s result is 7.5% higher (19.60 vs. 18.15).

The CBOE’s new calculation always uses options that expire within a week of the VIX’s 30 days.  The red and orange triangles show their values on January 12th.

The old VIX calculation misses the fact that the shorter term volatility has ramped up.

The CBOE provides VIX style calculations on six different sets of options used in their VIX, VIXMO, and VXST calculations.  These calculations don’t need time extrapolations / interpolations so that source of potential errors is eliminated.   The chart below shows how they mapped out on January 12th, 2015 (click image to enlarge).

vix term c+m


The green dots on the top line represent the CBOE VIX style volatilities over time.  The vertical black bar shows the old VIX calculation and the purple outline above it shows the new VIX calculation.

In this case the new VIX calculation is more accurate, cleanly mapping into the overall volatility term structure.

 

Additional Resources:

Weekly Options Take Charge

 
Friday, March 10th, 2017 | Vance Harwood
 

The volume of CBOE’s Weeklyssm options has grown rapidly since they expanded their listings into equities and Exchange Traded Products in June 2010.  Now weekly options comprise almost 30% of the CBOE’s average daily option volume.  The list of available weekly options is available on the CBOE website.

http://www.cboe.com/micro/weeklys/introduction.aspx

http://www.cboe.com/micro/weeklys/introduction.aspx

Among other things option traders take advantage of the Weeklys to position themselves for earnings releases,  harvest rapid premium decay near expiration, and place low cost directional plays.

Three recent press releases suggest that the Options Clearing Corporation (OCC) and the CBOE are moving to the next phase—making up to 5 weeks of options available on popular securities and moving existing options to look more like the Weeklys.  The specific moves are:

  1. Five weeks of Weekly options for many securities (press release)
    •  Initially Weekly options were only made available 9 days before their expiration.  If you needed a later expiration date your only choices were monthly options with their 3rd Saturday of the month expiration, or in some cases quarterlies.    In 2013 the CBOE started making SPX options available with weekly expirations 5 weeks in advance.   Evidently encouraged, they rolled out additional weekly expirations for additional  indexes and stocks (e.g., SPY & AAPL).    Overall I think the advantages of a more regular set of dates will outweigh the  problems with spreading option volume across more option classes.
  2. Friday afternoon expiration for most monthly options
    • The OCC announced a plan to change the expiration date for monthly options—to align with the Weeklys.  Instead of expiring on Saturday, they would expire at the end of trading Friday.   The Saturday expiration always seemed awkward to me, causing confusion on theta calculations and exposing investors to weekend news events.  I suspect it’s a throwback to days when paper actually had to be shuffled to close things out.  This change, planned for February 2015, would render the 3rd Friday of the month options indestinguishable from Weeklys.
  3. Rationalizing ticker symbols with SPX options (press release)
    • There are  three different tickers for SPX options,  SPX, SPXW, and SPXPM. Unlike other options there are weekly options (PM settled) on the same week that the monthly (AM settled) expire.

In general the move to weekly options has been gradual and non-invasive.   One of the side benefits of the rise of the SPX weeklys is that now there are always options series that closely bracket the 30 day volatility window of the VIX calculation.  Using the monthly SPX options there were sometimes longish extrapolations required with suspect accuracy. In October 2014 the CBOE switched the VIX calculation methodology to take advantage of the SPX weeklys availability.   Ultimately this new VIX calculation was needed to support VIX Weekly futures and VIX Weekly options.

Possible XIV termination events

 
Sunday, October 15th, 2017 | Vance Harwood
 

In the prospectuses for  XIV, there are some disconcerting discussions about termination events. For XIV the termination event is triggered if the daily percentage drop exceeds 80%. I did some digging into these events to try and figure out how likely they are to occur.  If you’d like to read a more general discussion about this ETN you can read this post.

First of all  XIV provisions for termination/acceleration relate to VIX futures not the CBOE’s VIX index. The VIX relates to the instantaneous implied volatility of the S&P 500—which is a different thing. Volatility futures have contracts with different expiration dates. Typically the further out their expiration dates (e.g., 6 months from now), the slower they react to the day-to-day moves of the market. XIV is based on the two futures contracts that are closest to expiration, the administrators for these funds adjust their positions in these contracts daily to achieve an effective average time till expiration of 30 days.

VXX does the same thing, except it is trying to be long volatility, not short/daily inverse % of volatility. When trying to understand XIV you can view them as being a short position in VXX , or tracking the opposite daily percentage move of VXX (XIV).

VXX is not as volatile as the VIX index. On a day with sharp market moves VXX will typically move about half the percentage move of what VIX does. VXX can still make big moves however—one day during the May 2010 Flash Crash, it jumped almost 25%—the VIX on that day jumped 46%.

Now we can talk about termination / acceleration. I think it is reasonable to assume that the goals of the ETN providers in including these measures are to:

  • Prevent the ETN value from going negative (they specify in these prospectuses that the value will be greater than or equal to zero)
  • Protect the provider from undue market risk in hedging these products during volatile times

With XIV termination (or “acceleration” in marketing speak) relates to daily percentage moves. If VXX jumped more than 100% in a day, then if VelocityShares didn’t terminate XIV its notational value could go below zero.   They avoid this particular unhappy situation by terminating the fund if the daily move of VXX is 80% or more—although losing 80% in one day would still be plenty traumatic.

Just to be clear, this fund isn’t tied directly to VXX, but rather the underlying futures contracts, but I believe VXX is a good proxy for the situation.

The termination risk for XIV appears to be limited to market crashes worse than the Flash crash. Two examples that come to mind are the 2009 crash and the October 1987 crash. VXX didn’t exist for either of these. I have analyzed VIX data (or simulated data) since 1992—there were 20 days with VIX jumping over 30% (previous day close to intraday high) during that period. The highest percentage jump over that period was 70.5% on February 27, 2007. There were three days with VIX jumps over 30% in the 2008/2009 crash, and during the Flash Crash.

If VXX had existed during this time span and held to its typical behavior of 50% of VIX’s move it looks like the XIV termination event would not have occurred, but obviously it would have taken heavy losses on those days.

If you are investing significant amounts of money in these products it looks prudent to at least hold some OTM VIX or VXX  calls. These would provide some insurance against these infrequent, but dramatic events.

Thanks to Steve, who commented on the first version of this post pointing out that the ETN providers were probably not looking out for the investor, but rather for their own hides in incorporating these termination events.