Economic Foundations of Energy Investments - Green Energy and Efficiency: An Economic Perspective - page 67

2.5 The Samuelson Effect

Energy futures contracts usually show decreasing volatility as a function of the
remaining lifetime of the contract T t , in what is known as the Samuelson effect.
As T t decreases, volatility increases and the spot price converges with the futures
contract price so that FðT ; TÞ ¼ S T .

2.6 Characteristics of the Models

The behavior of commodity prices may have certain characteristics that must be
incorporated into the corresponding stochastic models, depending on the purpose
for which they are to be used. Those characteristics include volatility, seasonality,
asymmetry, spikes, fat tails and even stochastic volatility.
The model must have a large enough number of parameters but not so many that
it acquires a level of additional complexity that is not justi ed in terms of signi cant

additional descriptive capability.
There is sometimes seasonality in demand, e.g., in the cases of heating oil,
natural gas, gasoline and electricity.

2.7 Volatility and Correlations

Volatility is a manifestation of uncertainty. It plays a determinant role in valuing
real options. It is usually calculated as the standard deviation of the log of the
yields:

S t
S t 1

R t ¼ ln ð 9 Þ

This gives the value of r d to obtain the annualized volatility r the following is

used:

p

252 r ¼ r d ð 10 Þ

where 252 is the number of trading days. Using spot price data from 12/31/2009 to
08/27/2013 9 this method can be used to calculate the data shown in the second
column of Table 1 (without drift). However, it is also possible to work with the
residues from the estimate provided by the differential equation. For a case of mean

9

Source of the original data: http://www.eia.gov/dnav/pet/pet_pri_spt_s1_d.htm .