[extropy-chat] Peak Oil news

Hal Finney hal at finney.org
Tue Mar 7 08:18:54 UTC 2006

Neil H. writes:
> A slightly off-topic question: Is there a way to quickly plot the sigmas for
> futures markets?

There's an easy way and a harder way, so I'll tell you the easy way.
According to this article by James D. Hamilton on his Econbrowser blog:


oil has had a volatility of 32% per year for many years.  This means
that we can compute the k-sigma range by the following formula.  Let k
be the number of standard deviations; let t be the number of years in the
future; and let P be the price of oil futures for that date in the future.
Then the k-sigma range is P / (1.32^(k*t)) to P * (1.32^(k*t)).  Here,
^ means exponentiation.  A good site for oil futures prices is:


For example, to get the 2-sigma range for the end of 2007, k = 2,
t = 1.75 (roughly), and P from the page above is $67.85 (the sixth
column on the row for December 2007).  1.32^(2*1.75) is 2.64, so the
price range is 67.85/2.64 to 67.85*2.64, or 25.7 to 179.  This is a
2-sigma range so we can say there is a 95% probability that oil price
will be in that range at the end of 07.

As I said, this is the easy way because we assumed the volatility as
fixed.  A more complex method involves first estimating the volatility
using options prices.  Hamilton has a posting that discusses how to do
this, as well as much valuable information about futures market pricing,



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