Hubbert oil peak and Hotelling rent revisited by a simulation model

Transcription

1 Hubbert oil peak and Hotelling rent revisited by a simulation model 32 nd IAEE International Conference San Francisco June 24 th 2009 Pierre-Noël GIRAUD Aline SUTTER Timothée DENIS (CERNA, Mines ParisTech) (EDF R&D)

2 At stakes: the oil depletion path Gb demand for fuel oil price = substitute fuel price late asymmetrical peak with dropping sharply CO 2 Hubbert symmetrical peak 2010? 2050? year 2 32 nd IAEE San Francisco June 24 th 2009

3 Purpose Joint academic work with Prof. P.-N. Giraud (Ecole des Mines) Simulation model representing: rationally driven agents subjected to incomplete information 3 32 nd IAEE San Francisco June 24 th 2009

4 Outline 1. Model principles 2. Results a. Single agent exploring 1 global area b. Single agent exploring 2 areas c. Stackelberg duopoly 4 32 nd IAEE San Francisco June 24 th 2009

5 Model Hotelling, Hubbert, Ricardo 5 32 nd IAEE San Francisco June 24 th 2009

6 Hotelling rent Assumptions exhaustible resource given total amount and extraction cost abundant and immediately available backstop technology e.g. CTL given and inelastic demand exhaustion date market with a rate of return r random P = P e + ( Ps Pe )exp( r( T T0 )) Hotelling scarcity rent What happens if T 0 is a random variable with a decreasing variance along time? 6 32 nd IAEE San Francisco June 24 th 2009

7 Hubbert oil peak (1/2) Starting point Hubbert forecasted the 48-US oil production peak 15 years in advance (with a 1 year error!) 7 32 nd IAEE San Francisco June 24 th

8 Hubbert oil peak (2/2) Total production of a multi-deposit region is supposed to show a peak when half of total reserves is depleted What happens with more realistic exploration dynamics exploration responding to price signals? production path of several oil wells through time At a global scale, the symmetry of the total production profile is subjected to strong hypothesis related to the exploration strategy 8 32 nd IAEE San Francisco June 24 th 2009

9 Model features We consider the need to explore to produce oil the explorer being a cost minimizing agent with imperfect information the (random) discovery of new reserves through exploration reserves exhaustion oil production technical constraints different production costs: Ricardian rents 9 32 nd IAEE San Francisco June 24 th 2009

10 Model Structure Exploration-Production heuristics Hotelling scarcity rent calculation The explorer-producer The oilfield owner explores and produces to meet the (exogenous) demand at minimal cost improves the common knowledge on the remaining reserves assess the risk of holding oil as an asset marginal production cost Hotelling scarcity rent Oil Price nd IAEE San Francisco June 24 th 2009

11 Exploration heuristics (1/2) Explore-producer agent is short-sighted Heuristics holds only for the following time steps no inter-temporal optimisation For each time period the agent owns an inherited oilfield portfolio it sets an exploration level such that: E[Cost exploration ] + E[marginal Cost production (new port.)] be less or equal than E[marginal Cost production (old port.)] exploration then returns size and production cost of discovered oilfields nd IAEE San Francisco June 24 th 2009

12 Exploration heuristics (2/2) Expected total cost curve shows a global minimum (for each time step) nd IAEE San Francisco June 24 th 2009

13 Production constraint Demand is satisfied by building a production merit order for oilfields, under a technical constraint an oilfield yields a constant rate of production during τ years Production more realistic shape Time nd IAEE San Francisco June 24 th 2009 Profile of a producing oilfield

14 Agent knowledge At the beginning, the agent knows the total number of oilfields but ignores the sizes, costs and distribution of the oilfields to be discovered is given the standard deviation of the expected depletion date (considered as common knowledge ) Progressive update of his knowledge Total oil left estimated by agent (Gb) Coefficient of variation (mean over 100 scenarios) (Gb) % 140% 120% 100% 80% 60% 40% 20% nd IAEE San Francisco Explorations June 24 th %

15 Inferring (uncertain future) Hotelling rent We consider oil deposits as financial assets characterized through risk and return Equilibrium rent level is set through hedging with financial assets P = P e + ( Ps Pe ) exp( r ( T T0 )) buying an oilfield and keeping the oil in the ground till depletion date buying a financial asset with the same risk nd IAEE San Francisco June 24 th 2009 E(r) 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% CAPM 0% 20% 40% 60% 80% 100% 120% V(r)

16 Results Single agent exploring one global area nd IAEE San Francisco June 24 th 2009

17 Data and hypothesis constant and inelastic demand: D = k t 5 cost-differentiated types of oil available spread into 330 unknown oilfields of 3 different sizes constant discovery cost per oilfield nd IAEE San Francisco June 24 th 2009

18 Single agent exploring one global area 100 scenarios nd IAEE San Francisco June 24 th 2009

19 Results Single agent exploring 2 areas nd IAEE San Francisco June 24 th 2009

20 Data Area 1 larger and more competitive reserves Area 2 smaller and more expensive reserves nd IAEE San Francisco June 24 th 2009

21 Single agent exploring 2 areas 1 scenario nd IAEE San Francisco June 24 th 2009

22 Conclusions No global Hubbert peak in model base case Setting a constraint on exploration yields a Hubbert peak technical bottlenecks OPEC quotas Uncertainty in future discoveries offsets Hotelling rent for most of the time period Evidence of Hubbert local peaks OPEC reserves asymmetrical peak US 70 s peak non OPEC reserves future symmetrical peak Hotelling rent comes into play when all reserves have been explored nd IAEE San Francisco June 24 th 2009

23 Summary Case Exploration constraints Production curve characteristics Hotelling rent in uncertain future Single agent exploring one global area Budget constraint No global Hubbert peak Becomes equal to classical Hotelling rent Exogenous constraint Global symmetrical Hubbert peak Much lower than classical Hotelling rent until close to depletion Single agent exploring two different areas Budget constraint in Area 1 and 2 No global Hubbert peak Area 1: One asymmetrical peak Area 2: Two symmetrical peaks Becomes equal to classical Hotelling rent Exogenous constraint in Area 1 Budget constraint in Area 2 No global Hubbert peak Area 1: One asymmetrical peak Area 2: One very flat peak Lower than classical Hotelling rent until close to depletion nd IAEE San Francisco June 24 th 2009

24 Thank you for your attention Pierre-Noël GIRAUD Aline SUTTER Timothée DENIS (CERNA, Mines ParisTech) (EDF R&D)

25 Backup slides nd IAEE San Francisco June 24 th 2009

26 Current Model calibration Distribution of oilfield numbers by category Oil volume (Gb) Cumulated volume Number of reserves 0 small medium large Oilfields categories nd IAEE San Francisco June 24 th 2009

27 Current Model calibration Distribution of oilfield numbers by category Oil volume (Gb) Zone 1 Zone 2 Reserves zone 1 Reserves zone small medium large Oilfields categories nd IAEE San Francisco June 24 th 2009

28 Stackelberg duopoly OPEC as duopoly heart nd IAEE San Francisco June 24 th 2009

29 Introducing 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 nd IAEE San Francisco June 24 th 2009

30 OPEC competitive fringe Modelling of interaction nd IAEE San Francisco June 24 th 2009

31 OPEC as duopoly heart 1 scenario nd IAEE San Francisco June 24 th 2009