# A volatility analysis on EUR/USD currency pair from 2000 to 2015

When the price of the EUR/USD cross is more volatile?

The EUR/USD, like all other currency pairs on Earth, shows different volatility ranges depending on the hour of the day. In the present article you may find some experiments I made on historical data, in order to understand if there are any temporal, intra-day patterns. My main question: are there any differences in volatility between each hour of the day?

## Data sources and algorithms

First of all I downloaded prices from HistData.com, a place where free forex historical data is published daily. As the "About Us" section reports, they are "a group of traders and strategy developers that also need to use historical forex data to develop [their] own trading strategies and EA’s". While I've focused on EUR/USD only, prices seem to be quite reliable, with some easily negligible temporal gaps here and there.

Then I started churning out that data. The task consisted in computing, for each hour of the day (each hour made of 60 minutes of data points), the prices' standard deviation, a numerical value that indicates how widely the elements of a set vary from the mean. If the standard deviation is large, it means that we are facing high volatility. Standard deviation is always computed on a set of values, which in this case is the set of prices that EUR/USD pair takes on in a hour.

At this point I had a histogram with 24 bins showing the hourly volatility for one day. Then I repeated the process for all days in a year, averaging the standard deviations and coming up with another histogram: the average, hourly price volatility in a year.

### Technical notes

The timezone of all data is Eastern Standard Time (EST) time-zone without Day Light Savings adjustments. I also normalized the standard deviations in a range from 0 to 1, so that the histograms have vertical bars that go from 0 to 1. Absolute numbers might be irrelevant here, my interest is to highlight the possible differences in volatility between each hour.

## EUR/USD average hourly volatility plots

1. EUR/USD hourly volatility, year 2000.
2. EUR/USD hourly volatility, year 2001.
3. EUR/USD hourly volatility, year 2002.
4. EUR/USD hourly volatility, year 2003.
5. EUR/USD hourly volatility, year 2004.
6. EUR/USD hourly volatility, year 2005.
7. EUR/USD hourly volatility, year 2006.
8. EUR/USD hourly volatility, year 2007.
9. EUR/USD hourly volatility, year 2008.
10. EUR/USD hourly volatility, year 2009.
11. EUR/USD hourly volatility, year 2010.
12. EUR/USD hourly volatility, year 2011.
13. EUR/USD hourly volatility, year 2012.
14. EUR/USD hourly volatility, year 2013.
15. EUR/USD hourly volatility, year 2014.
16. EUR/USD hourly volatility, year 2015.

## Final thoughts

I clearly see a pattern, here. Actually, year 2001 shows a strange glitch in data — that big spike that occurs on hour 20, but if you mentally omit it, you may see that even in 2001 the overal pattern persists.

Volatility starts quite low from hour 0 (midnight EST) to 3, then roughly doubles its value around hours 3, 4 and 5. A calm moment follows, spanning from hour 5 to hour 8. The greatest burst occurs at hour 9 and continues to hour 11 and 12, preceding a slow decay toward a "relaxed" zone until hour 19. The day closes with a final small peak around hour 20-21.

I don't have an explanation for such behavior, yet. I will update this article as soon as I have gathered enough information.