# Last edited on 2014-12-01 01:08:27 by stolfilocal


[b]Comparing prices among some exchanges[/b]

The goal of this exercise was to compare the prices on major exchanges over time, trying to filter out daily variations.

For this goal, I collected from the ste bitcoincharts.com the daily prices at six major exchanges available there:[pre]
  MGOX 2010-07-17 -- 2014-02-25 MtGOX     
  BTCE 2011-08-14 -- 2014-11-27 BTC-e     
  BSTP 2011-09-13 -- 2014-11-27 Bitstamp  
  BFNX 2013-03-31 -- 2014-11-27 Bitfinex  
  BTCC 2011-06-13 -- 2014-11-27 BTC-China 
  OKCO 2013-06-12 -- 2014-11-27 OKCoin.cn[/pre] 
Specifically, for each exchange, I used the average of the trade prices within each UTC day, weighted by the trade volumes. These prices were smoothed with a 29-day Hahn window, and interpolated over small gaps by weighted linear regression in that window. See the plot below.

[url=http://www.ic.unicamp.br/~stolfi/temp/2014-11-29-01d-gox-full-2010-07-17--2014-11-29-join.png][img]http://www.ic.unicamp.br/~stolfi/temp/2014-11-29-01d-gox-full-2010-07-17--2014-11-29-join.jpg[/img][/url]
[ click on the image for a full-size version. ]



In this plot, for easier comparison, the prices at BTC-China and OKCoin were divided by 6.18, the mean CNY:USD currency rate since April 2014.

[b]Initial inflation[/b]

Note that, when each of those exchanges opened, its price was significantly above the others for some time.  A possible explanation is that their initial clients include many enthusiastic but novice traders, who had not yet learned to compare prices among exchanges.  The only exception is BTC-e, which has been somewaht lower than the others, most of the time.

[b]Reference price[/b]

To compare the prices of those six exchanges, I had to pick a reference price.  None of those exchanges existed over the complete time interval spanend by the data, from 2010-07-17 to 2014-11-27.  Moreover, every one of them was clearly "deviant" at some time or another. 

For example, it is well-known that MtGOX's price was well above market  A visual comparison of the plots show that the discrepancy started around 2013-04-01:  

[url=http://www.ic.unicamp.br/~stolfi/temp/2014-11-29-01d-gox-full-2013-03-01--2014-03-31-join.png][img]http://www.ic.unicamp.br/~stolfi/temp/2014-11-29-01d-gox-full-2013-03-01--2014-03-31-join.jpg[/img][/url]
[ click on the image for a full-size version ]

It turns out that, between May/2012 and Jan/2013, the prices of MtGOX and Bitstamp are fairly close.   Therefore, I decided to set the (smoothed) reference price as being the (smoothed) MtGOX price before 2012-05-01 and the (smoothed) Bitstamp price after 2013-01-31, with a gradual transition between the two (a weighted mean of the two, with shifted-sine weight).

[b]Relative prices[/b]

The following plot shows the ratios of the (smoothed) price at each exchange to the (smoothed) reference price defined as above:

[url=http://www.ic.unicamp.br/~stolfi/temp/2014-11-29-01d-gox-full-2010-07-17--2014-11-29-ccf.png][img]http://www.ic.unicamp.br/~stolfi/temp/2014-11-29-01d-gox-full-2010-07-17--2014-11-29-ccf.jpg[/img][/url]
[ click on the image for a full-size version ]

[b]Comments[/b]

Note that BTC-e was below the MtGOX/Bitstamp reference most of the time. Also, except at the opening in April 2013, Bitfinex has always been
always almost identical to Bitstamp. 

The BTC:CNY prices in BTC-China and OKCoin were quite close, except for a couple of weeks after OKCoin opened on 2013-06-12.  However, both varied significantly relative to the MtGOX/Bitstamp reference.

Specifically, the price in China was significantly higher than normal during the ascending phases of the bubbles that peaked on 2012-06-01,
2012-10-01, 2013-04-09, 2013-11-29.  The Chinese prices sharply dropped in the descending phases of those bubbles, particularly around 2013-06-01 and 2013-12-20. This behavior is consistent with the theory that those bubbles were created by the opening of markets in China, and markets outside China struggled to follow.

On the other hand, the price at BTC-China were higher than normal also from 2011-07-01 to 201112-01, and around 2013-06-15, when the price was falling. That may indicate that those drops of the price were due to loss of demand (or increased offer) outside China, and BTC-China lagged behind.

[b]Data files[/b]

[url=http://www.ic.unicamp.br/~stolfi/temp/2014-11-29-01d-gox-full-join.txt]Raw volumes and smoothed prices[/url]. The data fields (ignoring the "|" separators) are the UTC date and the start UTC hour of the sampling interval (always "00:00:00" hour), and then, for each of the six exchanges: the day's traded volume in the national currency, the day's traded volume in BTC, and the smoothed mean trade price. Zero values are missing data.

[url=http://www.ic.unicamp.br/~stolfi/temp/2014-11-29-01d-gox-full-ccf.txt]Relative smoothed prices[/url]. The data fields are the date and time as above, the smoothed reference price (smooth splice of MtGOX and Bitstamp prices), and then, for each exchange, the ratio of its smoothed mean price to the smoothed reference price.  Zero relative prices indicate missing data.