By: Marco Antonio Guimares Dias Internal Consultant by Petrobras, Brazil Doctoral Candidate by PUCRi

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By Marco Antonio Guimarães Dias- Internal
Consultant by Petrobras, Brazil- Doctoral
Candidate by PUC-Rio Visit the first real
options website www.puc-rio.br/marco.ind/

• . Real Options in Petroleum An Overview
• Real Options Valuation in the New Economy
• July 4-6, 2002 - Coral Beach, Cyprus

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Presentation Outline

• Introduction and overview of real options in
  upstream petroleum (exploration production)
• Intuition and classical model
• Stochastic processes for oil prices
• Applications of real options in petroleum
• Petrobras research program called PRAVAP-14
  Valuation of Development Projects under
  Uncertainties
• Combination of technical and market
  uncertainties in most cases
• Selection of mutually exclusive alternatives for
  oilfield development under oil price uncertainty
• Exploratory investment and information revelation
• Investment in information dynamic value of
  information
• Option to expand the production with optional
  wells

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Managerial View of Real Options (RO)

• RO can be viewed as an optimization problem
• Maximize the NPV (typical objective function)
  subject to
• (a) Market uncertainties (eg., oil price)
• (b) Technical uncertainties (eg., reserve
  volume)
• (c) Relevant Options (managerial flexibilities)
  and
• (d) Others firms interactions (real options
  game theory)
• The first paper combining real options and game
  theory for petroleum applications was Dias (1997)
• See the drilling game in my website
  (option-games)

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Main Petroleum Real Options and Examples
5
EP as a Sequential Real Options Process
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Economic Quality of the Developed Reserve

• Imagine that you want to buy 100 million barrels
  of developed oil reserves.
• Suppose that the long run oil price is 20
  US/bbl.
• How much you shall pay for each barrel of
  developed reserve?
• It depends of many technical and economic factors
  like
• The reservoir permo-porosity quality
  (productivity)
• Fluids quality (heavy x light oil, etc.)
• Country (fiscal regime, politic risk)
• Specific reserve location (deepwaters location
  has higher operational cost than shallow-waters
  and onshore reserve)
• The capital in place (extraction speed and so the
  present value of revenue depends of number of
  producing wells) etc.

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Economic Quality of the Developed Reserve

• The relation between the value for one barrel of
  (sub-surface) developed reserve v and the
  (surface) oil price barrel P is named the
  economic quality of that reserve q (higher q,
  higher v)
• Value of one barrel of reserve v q . P
• Where q economic quality of the developed
  reserve
• The value of the developed reserve is v times the
  reserve size (B)
• So, let us use the equation for NPV V - D q P
  B - D
• D development cost (investment cost or
  exercise price of the option)

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Intuition (1) Timing Option and Oilfield Value

• Assume that simple equation for the oilfield
  development NPV
• NPV q B P - D 0.2 x 500 x 18 1850 - 50
  million
• Do you sell the oilfield for US 3 million?
• Suppose the following two-periods problem and
  uncertainty with only two scenarios at the second
  period for oil prices P.

EP 19 ? NPV 50 million
EP 18 /bbl NPV(t0) - 50 million
EP- 17 ? NPV - 150 million
Rational manager will not exercise this option ?
Max (NPV-, 0) zero
Hence, at t 1, the project NPV is positive
(50 x 50) (50 x 0) 25 million
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Intuition (2) Timing Option and Waiting Value

• Suppose the same case but with a small positive
  NPV. What is better develop now or wait and see?
• NPV q B P - D 0.2 x 500 x 18 1750 50
  million
• Discount rate 10

EP 19 ? NPV 150 million
EP 18 /bbl NPV(t0) 50 million
Hence, at t 1, the project NPV is (50 x 150)
(50 x 0) 75 million The present value
is NPVwait(t0) 75/1.1 68.2 gt 50
Hence is better to wait and see, exercising the
option only in favorable scenario
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Intuition (3) Deep-in-the-Money Real Option

• Suppose the same case but with a higher NPV.
• What is better develop now or wait and see?
• NPV q B P - D 0.25 x 500 x 18 1750 500
  million
• Discount rate 10

EP 19 ? NPV 625 million
EP 18 /bbl NPV(t0) 500 million
Hence, at t 1, the project NPV is (50 x 625)
(50 x 375) 500 million The present value
is NPVwait(t0) 500/1.1 454.5 lt 500
Immediate exercise is optimal because this
project is deep-in-the-money (high NPV) There is
a value between 50 and 500 that value of wait
exercise now (threshold)
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Classical Model of Real Options in Petroleum

• Paddock Siegel Smith wrote a series of papers
  on valuation of offshore reserves in 80s
  (published in 87/88)
• It is the best known model for oilfields
  development decisions
• It explores the analogy financial options with
  real options

Time to Expiration of the Option Time to
Expiration of the Investment Rights (t)
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Equation of the Undeveloped Reserve (F)

• Partial (t, V) Differential Equation (PDE) for
  the option F

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The Undeveloped Oilfield Value Real Options and
NPV

• Assume that V q B P, so that we can use chart F
  x V or F x P
• Suppose the development break-even (NPV 0)
  occurs at US15/bbl

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Threshold Curve The Optimal Decision Rule

• At or above the threshold line, is optimal the
  immediate development. Below the line wait,
  learn and see

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Stochastic Processes for Oil Prices GBM

• Like Black-Scholes-Merton equation, the classical
  model of Paddock et al uses the popular Geometric
  Brownian Motion
• Prices have a log-normal distribution in every
  future time
• Expected curve is a exponential growth (or
  decline)
• The variance grows with the time horizon
  (unbounded)

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Mean-Reverting Process

• In this process, the price tends to revert
  towards a long-run average price (or an
  equilibrium level) P.
• Model analogy spring (reversion force is
  proportional to the distance between current
  position and the equilibrium level).
• In this case, variance initially grows and
  stabilize afterwards

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Stochastic Processes Alternatives for Oil Prices

• There are many models of stochastic processes for
  oil prices in real options literature. I classify
  them into three classes.

• The nice properties of Geometric Brownian Motion
  (few parameters, homogeneity) is a great
  incentive to use it in real options applications.
  
• Pindyck (1999) wrote the GBM assumption is
  unlikely to lead to large errors in the optimal
  investment rule

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Nominal Prices for Brent and Similar Oils
(1970-2001)

• With an adequate long-term scale, we can see that
  oil prices jumps in both directions, depending
  of the kind of abnormal news jumps-up in
  1973/4, 1978/9, 1990, 1999 and jumps-down in
  1986, 1991, 1997, 2001

Jumps-up
Jumps-down
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Mean-Reversion Jumps Dias Rocha (98)

• We (Dias Rocha, 1998/9) adapted the
  jump-diffusion idea of Merton (1976) to the oil
  prices case, considering
• Normal news cause only marginal adjustment in oil
  prices, modeled with the continuous-time process
  of mean-reversion
• Abnormal rare news (war, OPEC surprises, ...)
  cause abnormal adjustment (jumps) in petroleum
  prices, modeled with a discrete-time Poisson
  process (we allow both jumps-up jumps-down)
• Model has more economic logic (supply x demand)
• Normal information causes smoothing changes in
  oil prices (marginal variations) and means both
• Marginal interaction between production and
  demand
• Depletion versus new reserves discoveries in
  non-OPEC countries
• Abnormal information means very important news
• In few months, this kind of news causes jumps in
  the prices, due the expected large variation in
  either supply or demand

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Real Case with Mean-Reversion Jumps

• A similar process of mean-reversion with jumps
  was used by Dias for the equity design (US 200
  million) of the Project Finance of Marlim Field
  (oil prices-linked spread)
• Equity investors reward
• Basic interest-rate spread (linked to oil
  business risk)
• Oil prices-linked transparent deal (no agency
  cost) and win-win
• Higher oil prices ? higher spread, and vice
  versa (good for both)
• Deal was in December 1998 when oil price was 10
  /bbl
• We convince investors that the expected oil
  prices curve was a fast reversion towards US
  20/bbl (equilibrium level)
• Looking the jumps-up down, we limit the spread
  by putting both cap (maximum spread) and floor
  (to prevent negative spread)
• This jumps insight proved be very important
• Few months later the oil prices jumped-up (price
  doubled by Aug/99)
• The cap protected Petrobras from paying a very
  high spread

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PRAVAP-14 and Real Options Projects

• PRAVAP-14 is a systemic research program named
  Valuation of Development Projects under
  Uncertainties
• I coordinate this systemic project by
  Petrobras/EP-Corporative
• We analyzed different stochastic processes and
  solution methods
• Stochastic processes geometric Brownian motion
  mean-reversion jumps three different
  mean-reversion models
• Solution methods Finite differences Monte Carlo
  simulation for American options and even genetic
  algorithms
• Genetic algorithms are used for optimization
  thresholds curves evolution, with the fitness
  evaluated by Monte Carlo simulation
• I call this method of evolutionary real options
  (see in my website two papers on this subject)
• Let us see some real options projects from
  Pravap-14

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EP Process and Options
Oil/Gas Success Probability p

• Drill the wildcat (pioneer)? Wait and See?
• Revelation and technical uncertainty modeling

Expected Volume of Reserves B
Revised Volume B

• Appraisal phase delineation of reserves
• Invest in additional information?

• Delineated but Undeveloped Reserves.
• Develop? Wait and See for better conditions?
  What is the best alternative?

• Developed Reserves.
• Expand the production? Stop Temporally? Abandon?

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Selection of Alternatives under Uncertainty

• In the equation for the developed reserve value V
  q P B, the economic quality of reserve (q)
  gives also an idea of how fast the reserve volume
  will be produced.
• For a given reserve, if we drill more wells the
  reserve will be depleted faster, increasing the
  present value of revenues
• Higher number of wells ? higher q ?
  higher V
• However, higher number of wells ? higher
  development cost D
• For the equation NPV q P B - D, there is a
  trade off between q and D, when selecting the
  system capacity (number of wells, platform
  process capacity, pipeline diameter, etc.)
• For the alternative j with n wells, we get
  NPVj qj P B - Dj

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The Best Alternative at Expiration (Now or Never)

• The chart below presents the now-or-never case
  for three alternatives. In this case, the NPV
  rule holds (choose the higher one).
• Alternatives A1(D1, q1) A2(D1, q1) A3(D3, q3),
  with D1 lt D2 lt D3 and q1 lt q2 lt q3

• Hence, the best alternative depends on the oil
  price P. However, P is uncertain!

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The Best Alternative Before the Expiration

• Imagine that we have t years before the
  expiration and in addition the long-run oil
  prices follow the geometric Brownian
• We can calculate the option curves for the three
  alternatives, drawing only the upper real option
  curve(s) (in this case only A2), see below.

• The decision rule is
• If P lt P2 , wait and see
• Alone, A1 can be even deep-in-the-money, but wait
  for A2 is more valuable
• If P P2 , invest now with A2
• Wait is not more valuable
• If P gt P2 , invest now with the higher NPV
  alternative (A2 or A3 )
• Depending of P, exercise A2 or A3
• How about the decision rule (threshold)
  along the time?

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Threshold Curves for Three Alternatives

• There are regions of wait and see and others that
  the immediate investment is optimal for each
  alternative

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EP Process and Options
Oil/Gas Success Probability p

• Drill the wildcat (pioneer)? Wait and See?
• Revelation and technical uncertainty modeling

Expected Volume of Reserves B
Revised Volume B

• Appraisal phase delineation of reserves
• Invest in additional information?

• Delineated but Undeveloped Reserves.
• Develop? Wait and See for better conditions?
  What is the best alternative?

• Developed Reserves.
• Expand the production? Stop Temporally? Abandon?

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Technical Uncertainty and Risk Reduction

• Technical uncertainty decreases when efficient
  investments in information are performed
  (learning process).
• Suppose a new basin with large geological
  uncertainty. It is reduced by the exploratory
  investment of the whole industry
• The cone of uncertainty idea (Amram
  Kulatilaka) is adapted

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Technical Uncertainty and Revelation

• But in addition to the risk reduction process,
  there is another important issue revision of
  expectations (revelation process)
• The expected value after the investment in
  information (conditional expectation) can be very
  different of the initial estimative
• Investments in information can reveal good or
  bad news

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Valuation of Exploratory Prospect

• Suppose that the firm has 5 years option to drill
  the wildcat
• Other firm wants to buy the rights of the tract
  for 3 million .
• Do you sell? How valuable is this prospect?

? NPV q P B - D (20 . 20 . 150) - 500
100 MM However, there is only 15 chances
to find petroleum
EMV Expected Monetary Value - IW (CF . NPV)
? ? EMV - 20 (15 . 100) - 5 million
Do you sell the prospect rights for US 3 million?
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Monte Carlo Combination of Uncertainties

• Considering that (a) there are a lot of
  uncertainties in that low known basin and (b)
  many oil companies will drill wildcats in that
  area in the next 5 years
• The expectations in 5 years almost surely will
  change and so the prospect value
• The revelation distributions and the risk-neutral
  distribution for oil prices are

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Real x Risk-Neutral Simulation

• The GBM simulation paths one real (a) and the
  other risk-neutral (r - d). In reality r - d a
  - p, where p is a risk-premium

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A Visual Equation for Real Options

• Today the prospects EMV is negative, but there
  is 5 years for wildcat decision and new
  scenarios will be revealed by the exploratory
  investment in that basin.

Prospect Evaluation (in million ) Traditional
Value - 5 Options Value (at T) 12.5
Options Value (at t0) 7.6
So, refuse the 3 million offer!
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EP Process and Options
Oil/Gas Success Probability p

• Drill the wildcat (pioneer)? Wait and See?
• Revelation and technical uncertainty modeling

Expected Volume of Reserves B
Revised Volume B

• Appraisal phase delineation of reserves
• Invest in additional information?

• Delineated but Undeveloped Reserves.
• Develop? Wait and See for better conditions?
  What is the best alternative?

• Developed Reserves.
• Expand the production? Stop Temporally? Abandon?

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Dynamic Value of Information

• Value of Information has been studied by decision
  analysis theory. I extend this view with real
  options tools
• I call dynamic value of information. Why dynamic?
• Because the model takes into account the factor
  time
• Time to expiration for the rights to commit the
  development plan
• Time to learn the learning process takes time to
  gather and process data, revealing new
  expectations on technical parameters and
• Continuous-time process for the market
  uncertainties (oil prices) interacting with the
  current expectations on technical parameters
• How to model the technical uncertainty and its
  evolution after one or more investment in
  information?
• I use the concept of revelation distribution for
  technical uncertainty
• Revelation distribution is the distribution of
  conditional expectations
• See details in my presentation at the Academic
  Conference (Saturday)
• Let us see the combination of technical and
  market uncertanties

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Combination of Uncertainties in Real Options

• The Vt/D sample paths are checked with the
  threshold (V/D)

Vt/D (q Pt B)/D
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EP Process and Options
Oil/Gas Success Probability p

• Drill the wildcat? Wait? Extend?
• Revelation and technical uncertainty modeling

Expected Volume of Reserves B
Revised Volume B

• Appraisal phase delineation of reserves
• Technical uncertainty sequential options

• Delineated but Undeveloped Reserves.
• Develop? Wait and See? Extend the option? Invest
  in additional information?

• Developed Reserves.
• Expand the production?
• Stop Temporally? Abandon?

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Option to Expand the Production

• Analyzing a deepwater project we faced two
  problems
• Remaining technical uncertainty of reservoirs is
  still important.
• In this case, the best way to solve the
  uncertainty is not by drilling more appraisal
  wells. Its better learn from the initial
  production profile.
• In the preliminary development plan, some wells
  presented both reservoir risk and small NPV.
• Some wells with small positive NPV (are not
  deep-in-the-money)
• Depending of the information from the initial
  production, some wells could be not necessary or
  could be placed at the wrong location.
• Solution leave these wells as optional wells
• Buy flexibility with an additional investment in
  the production system platform with capacity to
  expand (free area and load)
• It permits a fast and low cost future integration
  of these wells
• The exercise of the option to drill the
  additional wells will depend of both market (oil
  prices, rig costs) and the initial reservoir
  production response

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Oilfield Development with Option to Expand

• The timeline below represents a case analyzed in
  PUC-Rio project, with time to build of 3 years
  and information revelation with 1 year of
  accumulated production

• The practical now-or-never is mainly because in
  many cases the effect of secondary depletion is
  relevant
• The oil migrates from the original area so that
  the exercise of the option gradually become less
  probable (decreasing NPV)
• In addition, distant exercise of the option has
  small present value
• Recall the expenses to embed flexibility occur
  between t 0 and t 3

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Secondary Depletion Effect A Complication

• With the main area production, occurs a slow oil
  migration from the optional wells areas toward
  the depleted main area

• It is like an additional opportunity cost to
  delay the exercise of the option to expand. So,
  the effect of secondary depletion is like the
  effect of dividend yield

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Conclusions

• The real options models provide rich framework to
  consider optimal investment under uncertainty in
  petroleum, recognizing the managerial
  flexibilities
• Traditional discounted cash flow is very limited
  and can induce to serious errors in negotiations
  and decisions
• We saw the classical model working with the
  intuition
• We saw different stochastic processes and
  different models
• We got an idea about the real options research at
  Petrobras and PUC-Rio (PRAVAP-14)
• We saw options along all petroleum EP process
• We worked mainly with models combining technical
  and market uncertainties (Monte Carlo for
  American options)
• Thank you very much for your time

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Anexos

• APPENDIX
• SUPPORT SLIDES

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Managerial View of Real Options (RO)

• RO is a modern methodology for economic
  evaluation of projects and investment decisions
  under uncertainty
• RO approach complements (not substitutes) the
  corporate tools (yet)
• Corporate diffusion of RO takes time, training,
  and marketing
• RO considers the uncertainties and the options
  (managerial flexibilities), giving two linked
  answers
• The value of the investment opportunity (value of
  the option) and
• The optimal decision rule (threshold curve)

44
When Real Options Are Valuable?

• Based on the textbook Real Options by Copeland
  Antikarov
• Real options are as valuable as greater are the
  uncertainties and the flexibility to respond

45
Estimating the Underlying Asset Value

• How to estimate the value of underlying asset V?
• Transactions in the developed reserves market
  (USA)
• v value of one barrel of developed reserve
  (stochastic)
• V v B where B is the reserve volume (number
  of barrels)
• v is proportional to petroleum prices P, that
  is, v q P
• For q 1/3 we have the one-third rule of thumb
  (average value in USA)
• So, Paddock et al. used the concept of economic
  quality (q)
• This is a business view on reserve value
  (reserves market oriented view)
• Discounted cash flow (DCF) estimate of V, that
  is
• NPV V - D ? V NPV D
• For fiscal regime of concessions the chart NPV x
  P is a straight line. Let us assume that V is
  proportional to P
• Again is used the concept of quality of reserve,
  but calculated from a DCF spreadsheet, largely
  used in oil companies.

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Estimating the Model Parameters

• If V k P, we have sV sP and dV dP (DP
  p.178. Why?)
• Risk-neutral Geometric Brownian dV (r - dV) V
  dt sV V dz
• Volatility of long-term oil prices ( 20 p.a.)
• For development decisions the value of the
  benefit is linked to the long-term oil prices,
  not the (more volatile) spot prices
• A good market proxy is the longest maturity
  contract in futures markets with liquidity (Nymex
  18th month Brent 12th month)
• Dividend yield (or long-term convenience yield)
  6 p.a.
• Paddock Siegel Smith equation using
  cash-flows
• If V k P, we can estimate d from oil prices
  futures market
• Pickles Smiths Rule (1993) r d (in the
  long-run)
• We suggest that option valuations use,
  initially, the normal value of net convenience
  yield, which seems to equal approximately the
  risk-free nominal interest rate

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NYMEX-WTI Oil Prices Spot x Futures

• Note that the spot prices reach more extreme
  values and have more nervous movements (more
  volatile) than the long-term futures prices

48
Mean-Reversion Jump the Sample Paths

• 100 sample paths for mean-reversion jumps (l
  1 jump each 5 years)

49
Technical Uncertainty in New Basins

• The number of possible scenarios to be revealed
  (new expectations) is proportional to the
  cumulative investment in information
• Information can be costly (our investment) or
  free, from the other firms investment
  (free-rider) in this under-explored basin

• The arrival of information process leverage the
  option value of a tract

50
Simulation Issues

• The differences between the oil prices and
  revelation processes are
• Oil price (like other market uncertainties)
  evolves continually along the time and it is
  non-controllable by oil companies (non-OPEC)
• Revelation distributions occur as result of
  events (investment in information) in discrete
  points along the time
• In many cases (appraisal phase) only our
  investment in information is relevant and it is
  totally controllable by us (activated by
  management)

• Let us consider that the exercise price of the
  option (development cost D) is function of B. So,
  D changes just at the information revelation on
  B.
• In order to calculate only one development
  threshold we work with the normalized threshold
  (V/D) that doesnt change in the simulation

51
Modeling the Option to Expand

• Define the quantity of wells deep-in-the-money
  to start the basic investment in development
• Define the maximum number of optional wells
• Define the timing (accumulated production) that
  reservoir information will be revealed and the
  revelation distributions
• Define for each revealed scenario the marginal
  production of each optional well as function of
  time.
• Consider the secondary depletion if we wait after
  learn about reservoir
• Add market uncertainty (stochastic process for
  oil prices)
• Combine uncertainties using Monte Carlo
  simulation
• Use an optimization method to consider the
  earlier exercise of the option to drill the
  wells, and calculate option value
• Monte Carlo for American options is a growing
  research area

52
Bayesian Drilling Game (Dias, 1997)

• Oil exploration with two or few oil companies
  exploring a basin, can be important to consider
  the waiting game of drilling
• Two companies X and Y with neighbor tracts and
  correlated oil prospects drilling reveal
  information
• If Y drills and the oilfield is discovered, the
  success probability for Xs prospect increases
  dramatically. If Y drilling gets a dry hole,
  this information is also valuable for X.
• In this case the effect of the competitor
  presence is to increase the value of waiting to
  invest