Hubbert oil peak and Hotelling rent revisited by a simulation model OTAE 2009 July 7th, 2009, at Mines-ParisTech Pierre-Noël GIRAUD (CERNA, Mines ParisTech) Aline SUTTER – Timothée DENIS (EDF R&D)

Outline Questions addressed Model principles Results Single agent exploring 1 global area Single agent exploring 2 areas Stackelberg oligopoly 2

At stakes: the oil price trajectory on the long term Peak oil: why and when? Scarcity rent: when and how much? Gb $/bl At peak oil: oil price = substitute price demand for fuel late asymmetrical peak with sharp dropping Marginal extraction cost Hubbert symmetrical peak year 2010 ? 2050 ? 3

Hubbert oil peak Starting point Hubbert forecasted the 48-US oil production peak 15 years in advance (with a 1 year error!) 4 1956 4

Hubbert oil peak Total production of a multi-deposit region is supposed to show a peak when 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 production path of several oil wells through time What happens with more realistic exploration dynamics  exploration responding to price signals? 5 5

Hotelling rent Assumptions Hotelling scarcity rent no arbitrage opportunity production of resource is optimal any time constant discounted scarcity rent over time random Hotelling scarcity rent What happens if T0 is a random variable with a decreasing variance along time? 6 6

Model 7

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 8

The explorer-producer The marginal oilfield owner Model Structure Exploration-Production heuristics Learning process about reserves Hotelling scarcity rent calculation 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 improves the common knowledge on the remaining reserves marginal production cost Hotelling scarcity rent Oil Price 9

The learning process on reserves 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 10 10

Exploration 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.)] be less or equal than E[marginal Cost production(old port.)] 11

Exploration heuristics The expected total cost curve shows minimum 12

Production 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 Production more realistic shape Time Profile of a producing oilfield 13

Inferring Hotelling rent Hotelling 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 Le Modèle d'Evaluation des Actifs Financiers ou Capital Assets Pricing Model (CAPM) est utilisé pour évaluer des actions dans un marché en équilibre. Il est basé sur le fait que seul le risque de marché, ou risque non diversifiable, est rémunéré par les investisseurs dans un tel marché. La rentabilité exigée par un investisseur est alors égale au taux de l'argent sans risque majoré d'une prime de risque uniquement liée au risque de marché de l'actif : R = rf + beta x (rm - rf) buying a financial asset with the same risk 14

Current 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 77 76 12 32 30 58 4 15

Results Single agent exploring one global area 16

Results: single actor / mono zone 1 scenario – exploration non caped

Results: single actor / mono zone 1 scenario – exploration caped

Results: single actor / mono zone 100 scenarii exploration caped 19

Comments No symmetric peak oil at the world level, unless exploration is caped

Results Single agent exploring 2 areas 21

Simulation data Area 1: larger and more competitive reserves Area 2: smaller and more expensive reserves oilfields oilfields oilfields oilfields oilfield 22

Allocating exploration between the two regions

Results: single actor / 2 areas 1 scénario exploration non caped 24

Results: 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 ?

Stackelberg oligopoly OPEC as the heart of an oligopoly with a competitive fringe (preliminary) 27

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 28

OPEC – competitive fringe Modelling of interaction 29

Results Stackelberg oligopoly 1 scénario 30

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

Thanks for your attention 33