. Real Options in Petroleum:
An Overview
Real Options Valuation in the New Economy
July 4-6, 2002 - Coral Beach, Cyprus
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/
Presentation Outline
 Introduction
and overview of real options in upstream
petroleum (exploration & production)

Intuition and classical model
 Stochastic processes for oil prices
 Applications

Petrobras research program called “PRAVAP-14 ” Valuation
of Development Projects under Uncertainties


of real options in petroleum
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
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)
Main Petroleum Real Options and Examples

Option to Delay (Timing Option)
 Wait,
see, learn, optimize before invest
 Oilfield development; wildcat drilling
 Abandonment
Option
 Managers are not obligated to continue a
business plan if it becomes unprofitable
 Sequential appraisal program can be abandoned
earlier if information generated is not favorable

Option to Expand the Production

Depending of market scenario (oil prices, rig rates)
and the petroleum reservoir behavior, new wells
can be added to the production system
E&P as a Sequential Real Options Process
Oil/Gas Success
Probability = p
Expected Volume
of Reserves = B
Revised
Volume = B’
 Concession: Option to Drill the Wildcat
Exploratory (wildcat)
Investment
 Undelineated Field: Option to Appraise
Appraisal Investment
 Delineated Undeveloped Reserves: Option to
Develop (What is the best alternative?)
Development Investment
 Developed Reserves: Options to Expand,
to Stop Temporally, and to Abandon.
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
 It
much you shall pay for each barrel of developed reserve?
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.
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)
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.
t=1
E[P+] = 19  NPV = + 50 million $
50%
t=0
E[P] = 18 $/bbl
NPV(t=0) = - 50 million $
50%
E[P-] = 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 $
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 $
t=1
Discount rate = 10%
E[P+] = 19  NPV+ = + 150 million $
50%
t=0
E[P] = 18 /bbl
NPV(t=0) = + 50 million $
50%
E[P-] = 17  NPV - = - 50 million $
Rational manager will not exercise
this option  Max (NPV-, 0) = zero
Hence, at t = 1, the project NPV is: (50% x 150) + (50% x 0) = + 75 million $
The present value is: NPVwait(t=0) = 75/1.1 = 68.2 > 50
Hence is better to wait and see, exercising the option only in favorable scenario
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 $
t=1
Discount rate = 10%
E[P+] = 19  NPV = 625 million $
50%
t=0
E[P] = 18 /bbl
NPV(t=0) = 500 million $
50%
E[P-] = 17  NPV = 375 million $
Hence, at t = 1, the project NPV is: (50% x 625) + (50% x 375) = 500 million $
The present value is: NPVwait(t=0) = 500/1.1 = 454.5 < 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)
Classical Model of Real Options in Petroleum
 Paddock
& Siegel & Smith wrote a series of papers on
valuation of offshore reserves in 80’s (published in 87/88)


It is the best known model for oilfields development decisions
It explores the analogy financial options with real options
Black-Scholes-Merton’s
Financial Options
Paddock, Siegel & Smith’s
Real Options
Financial Option Value
Real Option Value of an Undeveloped Reserve (F)
Current Stock Price
Current Value of Developed Reserve (V)
Exercise Price of the Option
Investment Cost to Develop the Reserve (D)
Stock Dividend Yield
Cash Flow Net of Depletion as Proportion of V (d)
Risk-Free Interest Rate
Risk-Free Interest Rate (r)
Stock Volatility
Volatility of Developed Reserve Value (s)
Time to Expiration of the Option
Time to Expiration of the Investment Rights (t)
Equation of the Undeveloped Reserve (F)
 Partial
(t, V) Differential Equation (PDE) for the option F
0.5 s2 V2 FVV + (r - d) V FV - r F = - Ft
 Parameters: V =
value of developed reserve (eg., V = q P B);
D = development cost; r = risk-free discount rate;
d = dividend yield for V ; s = volatility of V
 Boundary
Conditions:
Managerial Action Is
Inserted into the Model

For V = 0, F (0, t) = 0
 For t = T, F (V, T) = max [V - D, 0] = max [NPV, 0]
 For V = V*, F (V*, t) = V* - D
Conditions at the Point of
Optimal Early Investment
 “Smooth Pasting”, FV (V*, t) = 1
}
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 US$15/bbl
Threshold Curve: The Optimal Decision Rule
 At
or above the threshold line, is optimal the immediate
development. Below the line: “wait, learn and see”
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)
Mean-Reverting Process
 In
this process, the price tends to revert towards a longrun 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
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”
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
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 discretetime 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
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
 Deal
oil prices  higher spread, and vice versa (good for both)
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
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/E&P-Corporative
 We
analyzed different stochastic processes and
solution methods


Stochastic processes: geometric Brownian motion; meanreversion + 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
E&P Process and Options
Oil/Gas Success
Probability = p

Expected Volume
of Reserves = B

Revised
Volume = B’





Drill the wildcat (pioneer)? Wait and See?
Revelation and technical uncertainty modeling
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?
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
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

For the alternative “j” with n wells, we get NPVj = qj P B - Dj
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 < D2 < D3 and q1 < q2 < q3
Hence, the best alternative depends on the oil price P. However, P is uncertain!
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 < P*2 , “wait and see”
 Alone, A1
can be even deep-in-themoney, but wait for A2 is more valuable

If P = P*2 , invest now with A2
 Wait

is not more valuable
If P > P*2 , 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?
Threshold Curves for Three Alternatives
 There
are regions of wait and see and others that the
immediate investment is optimal for each alternative
Investments
D3 > D2 > D1
E&P Process and Options
Oil/Gas Success
Probability = p

Expected Volume
of Reserves = B

Revised
Volume = B’
Drill the wildcat (pioneer)? Wait and See?
Revelation and technical uncertainty modeling

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?
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:
Expected
Value
confidence
interval
Higher
Risk
Current
project
evaluation
(t=0)
Lower
Risk
Lack of Knowledge Trunk of Cone
Risk reduction by the
investment in information
of all firms in the basin
(driver is the investment, not
the passage of time directly)
Expected
Value
Project
evaluation
with additional
information
(t = T)
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
t=T
Value with
good revelation
Value with
neutral revelation
E[V]
Value with
bad revelation
Current project
evaluation (t=0)
Investment in
Information
Project value
after investment
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 $.

Do you sell? How valuable is this prospect?
Success
“Compact Tree”
E[B] = 150 million barrels (expected reserve size)
E[q] = 20% (expected quality of developed reserve)
P(t = 0) = US$ 20/bbl (long-run expected price at t = 0)
D(B) = 200 + (2 . B)  D(E[B]) = 500 million $
 NPV = q P B - D = (20% . 20 . 150) - 500 = + 100 MM$
However, there is only 15% chances to find petroleum
Dry Hole
20 million $
(IW = wildcat
investment)
EMV = Expected Monetary Value = - IW + (CF . NPV) 
 EMV = - 20 + (15% . 100) = - 5 million $
Do you sell the prospect rights for US$ 3 million?
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:
Distribution of Expectations
(Revelation Distributions)

Real x Risk-Neutral Simulation
The GBM simulation paths: one real (a) and the other riskneutral (r - d). In reality r - d = a - p, where p is a risk-premium
Real Versus Risk-Neutral Simulations
45
Real Simulation
40
Risk-Neutral Simulation
35
30
25
20
15
10
5
Time (Years)
6.
0
5.
8
5.
5
5.
3
5.
0
4.
8
4.
5
4.
3
4.
0
3.
8
3.
5
3.
3
3.
0
2.
8
2.
5
2.
3
2.
0
1.
8
1.
5
1.
3
1.
0
0.
8
0.
5
0.
3
0
0.
0
Oil Price ($/bbl)

A Visual Equation for Real Options
 Today the prospect´s 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 t=0) = + 7.6
So, refuse the $ 3 million offer!
E&P Process and Options
Oil/Gas Success
Probability = p

Expected Volume
of Reserves = B

Revised
Volume = B’


Drill the wildcat (pioneer)? Wait and See?
Revelation and technical uncertainty modeling
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?
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
Combination of Uncertainties in Real Options

The Vt/D sample paths are checked with the threshold (V/D)*
Vt/D = (q Pt B)/D
A
B
Present Value (t = 0)
F(t = 0) =
= F(t=1) * exp (- r*t)
Option F(t = 1) = V - D
F(t = 2) = 0
Expired
Worthless
E&P Process and Options
Oil/Gas Success
Probability = p
 Drill
Expected Volume
of Reserves = B

Revised
Volume = B’
the wildcat? Wait? Extend?
Revelation and technical uncertainty modeling

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?
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. It’s 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
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
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
optional wells
oil migration
(secondary depletion)
petroleum reservoir (top view) and the grid of wells

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
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 E&P process
 We worked mainly with models combining technical and
market uncertainties (Monte Carlo for American options)
 Thank
you very much for your time
Anexos
APPENDIX
SUPPORT SLIDES
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)
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
Low
Low
Likelihood of receiving new information
Uncertainty
High
Room for
Managerial Flexibility

Ability to respond

Moderate
Flexibility Value
High
Flexibility Value
Low
Flexibility Value
Moderate
Flexibility Value
High
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.

Estimating the Model Parameters
 If V =

k P, we have sV = sP and dV = dP (D&P p.178. Why?)
Risk-neutral Geometric Brownian: dV = (r - dV) V dt + sV V dz
 Volatility


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

of long-term oil prices (~ 20% p.a.)
& Smith’s 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”
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
WTI Nymex Prices: Spot (First Month) vs. 18 Months
Jul/1996 - Jan/2002
40
WTI Nymex Spot (1st Mth) Close (US$/bbl)
WTI Nymex Mth18 Close (US$/bbl)
35
30
25
20
15
10
1/22/2002
10/22/2001
7/22/2001
4/22/2001
1/22/2001
10/22/2000
7/22/2000
4/22/2000
1/22/2000
10/22/1999
7/22/1999
4/22/1999
1/22/1999
10/22/1998
7/22/1998
4/22/1998
1/22/1998
10/22/1997
7/22/1997
4/22/1997
1/22/1997
10/22/1996
5
7/22/1996
WTI (US$/bbl)

Mean-Reversion + Jump: the Sample Paths

100 sample paths for mean-reversion + jumps (l = 1 jump each 5 years)
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
Investment
in information
(wildcat drilling, etc.)
.
t=0
Today
technical
and economic
valuation

Investment in information
(costly and free-rider)
t=T
t=1
Possible scenarios
after the information
arrived during the
first year of option term
Revelation
Distribution
Possible
scenarios
after the
information
arrived
during the
option lease
term
The arrival of information process leverage the option value of a tract

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)
P
Inv
E[B]

Inv
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 doesn´t change in the simulation
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
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 X’s
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
Company X tract
Company Y tract