pierre-noël giraud (cerna, mines paristech) aline sutter – timothée denis (edf r&d) hubbert...
TRANSCRIPT
Pierre-Noël GIRAUD (CERNA, Mines ParisTech)Aline SUTTER – Timothée DENIS (EDF R&D)
Hubbert oil peak and Hotelling rent revisited by a simulation modelOTAE 2009
July 7th, 2009, at Mines-ParisTech
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Outline
Questions addressed
Model principles
Results
• Single agent exploring 1 global area
• Single agent exploring 2 areas
• Stackelberg oligopoly
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At stakes: the oil price trajectory on the long termPeak oil: why and when?Scarcity rent: when and how much?
Gb
year
demand for fuel
Hubbert symmetrical peak
late asymmetrical peak with sharp dropping
2010 ? 2050 ?
At peak oil:
oil price = substitute price
Marginal extraction cost
$/bl
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Hubbert oil peak
Starting point
Hubbert forecasted the 48-US oil production peak 15 years in advance (with a 1 year error!)
1956
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production path of several oil wells through time
Hubbert oil peak
Total production of a multi-deposit region is supposed to show a peakwhen half of total reserves is depleted
At a global scale, the symmetry of the total production profile is subjected to strong hypothesis related to the exploration strategy
What happens with more realistic exploration dynamics
exploration responding to price signals?
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Hotelling rent
Assumptions
))(exp()( 0TTrPPPP ese
Hotelling scarcity rent
random
no arbitrage opportunity
production of resource is optimal any time
constant discounted scarcity rent over time
What happens if T0 is a random variable with a decreasing variance along time?
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Model
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Model type and objectives
A simulation model with two representative agents:One explorer-producer representing a set of competing companies: it minimizes the cost of meeting the demand of the next time step
The owner of the marginal oilfield in production who hedges between holding oil reserves or financial assets
The model accounts for:The need to explore before producing oil
Oil production technical constraints
A learning process on the volume and cost of the remaining reserves
The explorer- producer being a myopic cost minimizing agent with imperfect but improving information
Oilfield owners with imperfect but improving information
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Model Structure
The explorer-producer
explores and produces to meet the (exogenous)
demand at minimal cost
assess the risk of holding oil as an
asset
The marginal oilfield owner
Oil Price
marginal production cost Hotelling scarcity rent
improves the common
knowledge on the remaining
reserves
Exploration-Production heuristics
Hotelling scarcity rent calculation
Learning process about reserves
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At the beginning
the agent only knows the total number of oilfields: N ( number of sedimentary basins with oilfields)
but it ignores the sizes ( index i) and extraction costs ( index j) of the oilfields to be discovered
It will then use the outcome of its exploration campaigns to progressively update its knowledge
He simply assume the actual distribution by size and extraction costs of the N deposits is homothetic to the sample already discovered.
He then computes an estimated peak oil date, and knows the standard deviation of this estimate
He also compute the probability of discovering an oilfield of size i and extraction cost j during the next campaign
The learning process on reservesThe learning process on reserves
Total oil left estimated by agent (Gb)
0
500
1 000
1 500
2 000
2 500
3 000
1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321
Explorations
(Gb
)
Coefficient of variation (mean over 100 scenarios)
0%
20%
40%
60%
80%
100%
120%
140%
160%
1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321
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Exploration heuristicsExploration heuristics
The explorer producer agent explores as to minimize the cost of meeting the demand only for the following time steps
the agent owns an oilfield portfolio inherited from his exploration/production decisions in the past
it then computes for each period an exploration level which minimizes the cost of meeting the demand for the next steps:
it proceeds with exploration, which randomly returns the size and production cost of the discovered oilfields
E[Cost exploration] + E[marginal Cost production(new port.)]
E[marginal Cost production(old port.)]
be less or equal than
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Exploration heuristicsExploration heuristics
The expected total cost curve shows minimum
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Production constraintProduction constraint
Demand is satisfied by putting new oilfields into production, in the increasing cost order
Under a technical constraint: an oilfield yields a constant rate of production during years
Profile of a producing oilfield
more realistic shape
Production
Time
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0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
0% 20% 40% 60% 80% 100% 120%V(r)
E(r
)
CAPM
Inferring Hotelling rentInferring Hotelling rentHotelling rent is computed by considering the oil deposit as a financial asset
characterized by an expected level of risk and return
The equilibrium rent level is then set through hedging with financial assets
buying an oilfield and keeping the oil in the ground till depletion date
buying a financial asset with the same
risk
))(exp()( 0TTrPPPP ese
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Current Model calibrationCurrent Model calibration
constant and inelastic demand: D = k t
5 cost-differentiated types of oil available spread into 330 unknown oilfields of 3 different sizes (see below)
constant discovery cost per oilfield
randomness on both size and production cost of discovered oilfields
infinitely and immediately available backstop technology at 100 $/bl
Volume (Gb) / Extraction cost ($/b)
15 25 35 45 55
2 0 0 77 77 76
12 0 32 30 30 0
58 4 4 0 0 0
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Results
Single agent exploring one global area
Results: single actor / mono zoneResults: single actor / mono zone
1 scenario – exploration non caped
Results: single actor / mono zoneResults: single actor / mono zone
1 scenario – exploration caped
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Results: single actor / mono zoneResults: single actor / mono zone
100 scenarii exploration caped
Comments
No symmetric peak oil at the world level, unless exploration is caped
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Results
Single agent exploring 2 areas
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Simulation dataSimulation data
Area 1: larger and more competitive reserves
Area 2: smaller and more expensive reserves
oilfields
oilfields
oilfields
oilfields
oilfield
Allocating exploration between the two regions
2max,1max,
1max,2,1,1 22
1
GG
Geee optopt
2max,1max,
2max,2,1,2 22
1
GG
Geee optopt
With:
ie , the exploration level in region i
iopte , , the exploration level which would optimally meet total demand in region i
iGmax, , the maximum earning in region i coming from meeting total demand in region i
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Results: single actor / 2 areasResults: single actor / 2 areas
1 scénario exploration non caped
Results: single actor / 2 areasResults: single actor / 2 areas
1 scénario exploration caped in area 1 ( most favourable zone)
Comments
A peak oil appears in region 2, the region which has progressively proved to be less favourable
The case of the USA exhibited by Hubbert ?
All the more when exploration is caped in the more favourable region: the middle East ?
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Stackelberg oligopoly
OPEC as the heart of an oligopoly with a competitive fringe
(preliminary)
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Introducing OPECIntroducing OPEC
OPEC : Stackelberg oligopoly with a competitive fringe
competitive fringe
has to explore to satisfy demand
minimizes its costs
oligopoly
owns most low cost oil reserves and knows them (no need to explore)
maximises its profit
has to forecast the fringe exploration strategy
perfectly anticipates the fringe exploration outcome
work in progress: faces the random result of exploration as the fringe does
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OPEC – competitive fringeOPEC – competitive fringe
Modelling of interaction
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Results Stackelberg oligopolyResults Stackelberg oligopoly
1 scénario
Comments
An intriguing result:
Optimal oligopoly behaviour leads to price instability….
It’s still a work in progress...Comments warmly welcome on:
That type of model
Modelling the learning process
Oil fields owners behaviour
Modelling the choice between the two zones
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Thanks for your attention