Economic Foundations of Energy Investments - Green Energy and Efficiency: An Economic Perspective - page 81

Table 8 Crude Oil (CL) and Fuel Oil (HO) parameters estimated with simulation
Parameter CL HO

σ 0.2821 0.2298

6 Conclusions

This chapter deals with issues that are signi cant for the valuation of investment in

energy assets when the Real Option Approach (ROA) method is used, combined
with stochastic differential equations for the prices of the commodities, the
parameters of which are estimated using market quotations. A description is given
of the conditions that must exist for this valuation technique to be able to be used
correctly. An analysis is also given of the characteristics of the prices of the
commodities traded on energy markets, with particular emphasis on mean rever-
sion, the convenience yield and seasonality.
A simple method is also presented for estimating the parameters of the corre-
sponding stochastic differential equations using real market data and the 3:2:1 crack
spread is examined. The data obtained are used in some simple, illustrative

examples.
The chapter ends with an appendix that gives more details of the properties of
the stochastic processes used.

Acknowledgments I gratefully acknowledge the Spanish Ministry of Science and Innovation for
nancial support through the research project ECO2011-25064, the Basque Government (IT-799-
13), and Fundaci n Repsol through the Low Carbon Programme joint initiative, http://www.

lowcarbonprogramme.org .

ó

Appendix: Stochastic Models for Energy Investments

Stochastic models for valuing energy assets must take into account the most sig-
ni cant characteristics of each commodity, i.e. volatility, asymmetry, spikes, fat

tails and stochastic volatility among others. However models should have suf cient

parameters but not so many that they acquire a level of additional complexity that is
not justi

cant additional descriptive capability. Models differ
depending on whether they seek to value a derivative in the short term or a long-
term investment. Two basic elements that appear frequently in energy commodities
are (a) the seasonality caused by alterations in demand (e.g., for heating in winter
and air conditioning in summer), which may depend on geographical location; and
(b) mean reversion. However, in a long-term investment decision seasonality has
little in

ed in terms of signi

uence and does not determine the production strategy (it is relatively
unimportant in valuing a base load power plant, though it may be more signi cant

in valuing a peak power plant) [ 3 ].