Transcript Real Options and Investment under Uncertainty in E&P

. Overview of
Real Options in Petroleum
Workshop on Real Options
Turku, Finland - May 6-8, 2002
By: Marco Antonio Guimarães Dias
- 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 (with real case study)
 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
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 interconnected answers:


The value of the investment opportunity (value of the option); and
The optimal decision rule (threshold)
 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)
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 a long run oil price is 20 US$/bbl.
 How much you shall pay for each barrel of developed reserve?

It depends of many factors like the reservoir permo-porosity quality
(productivity), fluids quality (heavy x light oil, etc.), country (fiscal regime,
politic risk), specific reserve location (deepwaters has higher operational
cost than onshore reserve), the capital in place (extraction speed and so the
present value of revenue depends of number of producing wells), etc.
 As
higher is the percentual value for the reserve barrel in
relation to the barrel oil price (on the surface), higher is the
economic quality: 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
P+ = 19  NPV = + 50 million $
50%
t=0
E[P] = 18 $/bbl
NPV(t=0) = - 50 million $
50%
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%
P+ = 19  NPV+ = + 150 million $
50%
t=0
E[P] = 18 /bbl
NPV(t=0) = + 50 million $
50%
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%
P+ = 19  NPV = 625 million $
50%
t=0
E[P] = 18 /bbl
NPV(t=0) = 500 million $
50%
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)
Later, will be discussed the problem of probability, discount rate, etc.
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
Classical Real Options in Petroleum Model
 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
Uncertainty is modeled using the Geometric Brownian Motion
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)
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 (USA mean);
– 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, so that we can assume that V is proportional to P
 Again is used the concept of quality of reserve, but calculated
from a DCF spreadsheet, which everybody use in oil
companies. Let us see how.

NPV x P Chart and the Quality of Reserve
Using a simple DCF spreadsheet we can get the reserve quality value
NPV (million $)

Linear Equation for the NPV:
NPV = q P B - D
NPV in function of P
tangent q = q . B
P ($/bbl)
-D
The quality of reserve (q) is related
with the inclination of the NPV line
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)
Volatily = standard-deviation of ( Ln Pt - Ln Pt-1 )
 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)

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
 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
}
 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
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 classic 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);
In this model the variance grows with the time horizon
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”
Mean-Reversion + Jump: the Sample Paths

100 sample paths for mean-reversion + jumps (l = 1 jump each 5 years)
Nominal Prices for Brent and Similar Oils (1970-2001)

With an adequate long-term scale, we can see that oil prices jump 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
 We
(Dias & Rocha, 1998/9) adapt the Merton (1976)
jump-diffusion idea for 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 (inventory levels as
indicator); and
 Depletion versus new reserves discoveries for non-OPEC (the ratio of
reserves/production is an indicator)

Abnormal information means very important news:
 In
few months, this kind of news causes jumps in the prices, due to large
variation (or 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 + (oil business risk linked) spread
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 jump-up (price doubled by Aug/99)
– The cap protected Petrobras from paying a very high spread
PRAVAP-14: Some 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
 I’ll





present some real options projects developed:
Selection of mutually exclusive alternatives of development
investment under oil prices uncertainty (with PUC-Rio)
Exploratory revelation with focus in bids (pre-PRAVAP-14)
Dynamic value of information for development projects
Analysis of alternatives of development with option to expand,
considering both oil price and technical uncertainties (with PUC)
We analyze different stochastic processes and solution methods



Geometric Brownian, reversion + jumps, different mean-reversion models
Finite differences, Monte Carlo for American options, genetic algorithms
Genetic algorithms are used for optimization (thresholds curves evolution)
I
call this method of evolutionary real options (I have two papers on this)
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: additional waiting incentives
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
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, the
platform process capacity, pipeline diameter, etc.)

For the alternative “j” with n wells, we get NPVj = qj P B - Dj
 Hence, an important investment decision is:
 How select the best one from a set of mutually exclusive alternatives?
Or, What is the best intensity of investment for a specific oilfield?
 I follow the paper of Dixit (1993), but considering finite-lived options.
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-the-money,
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 along
the time? (thresholds curve)

Let us see from a PRAVAP-14 software
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: additional waiting incentives

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” (Amram & Kulatilaka) can be adapted to
understand the technical uncertainty:
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
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
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 $.
 Do
you sell? How valuable is the prospect?
“Compact Tree”
Success
E[B] = 150 million barrels (expected reserve size)
E[q] = 20% (expected quality of developed reserve)
P(t = 0) = US$ 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: additional waiting incentives
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?
A Dynamic View on Value of Information

Value of Information has been studied by decision analysis
theory. I extend this view using real options tools, adopting
the name dynamic value of information. Why dynamic?

Because the model takes into account the factor time:
 Time
to expiration for the real option to commit the development plan;
 Time to learn: the learning process takes time. Time of gathering data,
processing, and analysis to get new knowledge on technical parameters
 Continuous-time process for the market uncertainties (oil prices) interacting
with the current expectations of technical parameters
 How
to model the technical uncertainty and its evolution
after one or more investment in information?

The process of accumulating data about a technical parameter is a
learning process towards the “truth” about this parameter
 This

suggest the names of information revelation and revelation distribution
In finance (even in derivatives) we work with expectations
 Revelation
distribution is the distribution of conditional expectations
– The conditioning is the new information (see details in www.realoptions.org/)

Simulation Issues
The differences between the oil prices and revelation processes are:
 Oil price (and 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
Combination of Uncertainties in Real Options

The Vt/D sample paths are checked with the threshold (V/D)*
Vt/D = (q Pt B)/D(B)
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, option-game: waiting incentives

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 large ultra-deepwater project in Campos
Basin, Brazil, we faced two problems:

Remaining technical uncertainty of reservoirs is still important.
 In
this specific case, the best way to solve the uncertainty is not by drilling
additional 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
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
Many Petrobras-PUC projects use Monte Carlo for American options
Conclusions
 The
real options models in petroleum bring a rich
framework to consider optimal investment under
uncertainty, 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 other models
I
gave 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 uncertainties
with market uncertainty (Monte Carlo for American options)
 The
model using the revelation distribution gives the correct incentives for
investment in information (more formal paper in Cyprus, July 2002)
 Thank
you very much for your time
Anexos
APPENDIX
SUPPORT SLIDES

See more on real options in the first website on real options at:
http://www.puc-rio.br/marco.ind/
Example in E&P with the Options Lens
 In
a negotiation, important mistakes can be done if we
don´t consider the relevant options
 Consider two
marginal oilfields, with 100 million bbl, both
non-developed and both with NPV = - 3 millions in the
current market conditions

The oilfield A has a time to expiration for the rights of only 6
months, while for the oilfield B this time is of 3 years
 Cia
X offers US 1 million for the rights of each oilfield.
Do you accept the offer?
 With the static NPV, these fields have no value and even
worse, we cannot see differences between these two fields


It is intuitive that these rights have value due the uncertainty and the
option to wait for better conditions. Today the NPV is negative, but
there are probabilities for the NPV become positive in the future
In addition, the field B is more valuable (higher option) than the field A
Other Parameters for the Simulation
 Other important
parameters are the risk-free interest
rate r and the dividend yield d (or convenience yield for
commodities)

Even more important is the difference r - d (the risk-neutral
drift) or the relative value between r and d
 Pickles
& Smith (Energy Journal, 1993) suggest for
long-run analysis (real options) to set r = d

“We suggest that option valuations use, initially, the ‘normal’ value of d,
which seems to equal approximately the risk-free nominal interest rate.
Variations in this value could then be used to investigate sensitivity to
parameter changes induced by short-term market fluctuations”
Reasonable values for r and d range from 4 to 8% p.a.
 By using r = d the risk-neutral drift is zero, which looks
reasonable for a risk-neutral process

Relevance of the Revelation Distribution
 Investments
in information permit both a reduction of the
uncertainty and a revision of our expectations on the basic
technical parameters.




Firms use the new expectation to calculate the NPV or the real options
exercise payoff. This new expectation is conditional to information.
When we are evaluating the investment in information, the conditional
expectation of the parameter X is itself a random variable E[X | I]
The distribution of conditional expectations E[X | I] is named here
revelation distribution, that is, the distribution of RX = E[X | I]
The concept of conditional expectation is also theoretically sound:
 We
want to estimate X by observing I, using a function g( I ).
 The most frequent measure of quality of a predictor g is its mean square
error defined by MSE(g) = E[X - g( I )]2 . The choice of g* that minimizes
the error measure MSE(g) is exactly the conditional expectation E[X | I ].
 This is a very known property used in econometrics

The revelation distribution has nice practical properties (propositions)
The Revelation Distribution Properties

Full revelation definition: when new information reveal all the
truth about the technical parameter, we have full revelation


Much more common is the partial revelation case, but full revelation is
important as the limit goal for any investment in information process
The revelation distributions RX (or distributions of conditional
expectations with the new information) have at least 4 nice
properties for the real options practitioner:


Proposition 1: for the full revelation case, the distribution of revelation RX is
equal to the unconditional (prior) distribution of X
Proposition 2: The expected value for the revelation distribution is equal the
expected value of the original (a priori) technical parameter X distribution
 That

is: E[E[X | I ]] = E[RX] = E[X] (known as law of iterated expectations)
Proposition 3: the variance of the revelation distribution is equal to the
expected reduction of variance induced by the new information
 Var[E[X

| I ]] = Var[RX] = Var[X] - E[Var[X | I ]] = Expected Variance Reduction
Proposition 4: In a sequential investment process, the ex-ante sequential
revelation distributions {RX,1, RX,2, RX,3, …} are (event-driven) martingales
 In
short, ex-ante these random variables have the same mean
Investment in Information x Revelation Propositions
 Suppose
the following stylized case of investment in
information in order to get intuition on the propositions

Only one well was drilled, proving 100 MM bbl (MM = million)
Area A: proved
BA = 100 MM bbl
A
B
Area B: possible
50% chances of
BB = 100 MM bbl
& 50% of nothing
Area C: possible
50% chances of
BC = 100 MM bbl
& 50% of nothing
C
D
Area D: possible
50% chances of
BD = 100 MM bbl
& 50% of nothing

Suppose there are three alternatives of investment in information
(with different revelation powers): (1) drill one well (area B);
(2) drill two wells (areas B + C); (3) drill three wells (B + C + D)
Alternative 0 and the Total Technical Uncertainty
 Alternative


Zero: Not invest in information
This case there is only a single scenario, the current expectation
So, we run economics with the expected value for the reserve B:
E(B) = 100 + (0.5 x 100) + (0.5 x 100) + (0.5 x 100)
E(B) = 250 MM bbl
 But the true value of B can be as low as 100 and as higher
as 400 MM bbl. Hence, the total uncertainty is large.

Without learning, after the development you find one of the values:

100 MM bbl
 200 MM bbl
 300 MM bbl
 400 MM bbl
 The
with
with
with
with
12.5 % chances (= 0.5 3 )
37,5 % chances (= 3 x 0.5 3 )
37,5 % chances
12,5 % chances
variance of this prior distribution is 7500 (million bbl)2
Alternative 1: Invest in Information with Only One Well
 Suppose that we drill only the well in the area B.


This case generated 2 scenarios, because the well B result can be
either dry (50% chances) or success proving more 100 MM bbl
In case of positive revelation (50% chances) the expected value is:
E1[B|A1] = 100 + 100 + (0.5 x 100) + (0.5 x 100) = 300 MM bbl

In case of negative revelation (50% chances) the expected value is:
E2[B|A1] = 100 + 0 + (0.5 x 100) + (0.5 x 100) = 200 MM bbl


Note that with the alternative 1 is impossible to reach extreme scenarios
like 100 MM bbl or 400 MM bbl (its revelation power is not sufficient)
So, the expected value of the revelation distribution is:

EA1[RB] = 50% x E1(B|A1) + 50% x E2(B|A1) = 250 million bbl = E[B]
 As

expected by Proposition 2
And the variance of the revealed scenarios is:

VarA1[RB] = 50% x (300 - 250)2 + 50% x (200 - 250)2 = 2500 (MM bbl)2
 Let
us check if the Proposition 3 was satisfied
Alternative 1: Invest in Information with Only One Well
 In
order to check the Proposition 3, we need to calculated
the expected reduction of variance with the alternative A1
 The prior variance was calculated before (7500).
 The posterior variance has two cases for the well B outcome:





In case of success in B, the residual uncertainty in this scenario is:
 200 MM bbl with 25 % chances (in case of no oil in C and D)
 300 MM bbl with 50 % chances (in case of oil in C or D)
 400 MM bbl with 25 % chances (in case of oil in C and D)
The negative revelation case is analog: can occur 100 MM bbl (25%
chances); 200 MM bbl (50%); and 300 MM bbl (25%)
The residual variance in both scenarios are 5000 (MM bbl)2
So, the expected variance of posterior distribution is also 5000
So, the expected reduction of uncertainty with the alternative
A1 is: 7500 – 5000 = 2500 (MM bbl)2

Equal variance of revelation distribution(!), as expected by Proposition 3
Visualization of Revealed Scenarios: Revelation Distribution
All the revelation distributions have the same mean (maringale): Prop. 4 OK!
This is exactly the prior distribution of B (Prop. 1 OK!)
Posterior Distribution x Revelation Distribution

The picture below help us to answer the question: Why learn?
Why learn?
Reduction
of technical
uncertainty

Increase the
variance of
revelation
distribution
(and so the
option value)
Revelation Distribution and the Experts

The propositions allow a practical way to ask the technical
expert on the revelation power of any specific investment in
information. It is necessary to ask him/her only 2 questions:

What is the total uncertainty on each relevant technical parameter?
That is, the probability distribution (and its mean and variance).
 By
proposition 1, the variance of total initial uncertainty is the variance limit for
the revelation distribution generated from any investment in information
 By proposition 2, the revelation distribution from any investment in information
has the same mean of the total technical uncertainty.

For each alternative of investment in information, what is the expected
reduction of variance on each technical parameter?
 By

proposition 3, this is also the variance of the revelation distribution
In addition, the discounted cash flow analyst together with the
reservoir engineer, need to find the penalty factor gup:

Without full information about the size and productivity of the reserve,
the non-optimized system doesn´t permit to get the full project value
Non-Optimized System and Penalty Factor

If the reserve is larger (and/or more productive) than
expected, with the limited process plant capacity the reserves
will be produced slowly than in case of full information.

This factor can be estimated by running a reservoir simulation with
limited process capacity and calculating the present value of V.
The NPV with technical uncertainty is
calculated using Monte Carlo
simulation and the equations:
NPV = q P B - D(B)
if q B = E[q B]
NPV = q P B gup - D(B) if q B > E[q B]
NPV = q P B gdown- D(B) if q B < E[q B]
In general we have gdown = 1 and gup < 1
The Normalized Threshold and Valuation
 Recall
that the development option is optimally exercised at
the threshold V*, when V is suficiently higher than D
 Exercise
the option only if the project is “deep-in-the-money”

Assume D as a function of B but approximately independent
of q. Assume the linear equation: D = 310 + (2.1 x B) (MM$)
 This means that if B varies, the exercise price D of our option
also varies, and so the threshold V*.


We need perform a Monte Carlo simulation to combine the
uncertainties after an information revelation.


The computational time for V* is much higher than for D
After each B sampling, it is necessary to calculate the new threshold
curve V*(t) to see if the project value V = q P B is deep-in-the money
In order to reduce the computational time, we work with the
normalized threshold (V/D)*. Why?
Normalized Threshold and Valuation

We will perform the valuation considering the optimal
exercise at the normalized threshold level (V/D)*

After each Monte Carlo simulation combining the revelation
distributions of q and B with the risk-neutral simulation of P
 We

Advantage: (V/D)* is homogeneous of degree 0 in V and D.





calculate V = q P B and D(B), so V/D, and compare with (V/D)*
This means that the rule (V/D)* remains valid for any V and D
So, for any revealed scenario of B, changing D, the rule (V/D)* remains
This was proved only for geometric Brownian motions
(V/D)*(t) changes only if the risk-neutral stochastic process parameters
r, d, s change. But these factors don’t change at Monte Carlo simulation
The computational time of using (V/D)* is much lower than V*

The vector (V/D)*(t) is calculated only once, whereas V*(t) needs be recalculated every iteration in the Monte Carlo simulation.
 In
addition V* is a time-consuming calculus

Overall x Phased Development
Let us consider two alternatives



Overall development has higher NPV due to the gain of scale
Phased development has higher capacity to use the information along
the time, but lower NPV
With the information revelation from Phase 1, we can
optimize the project for the Phase 2


In addition, depending of the oil price scenario and other market and
technical conditions, we can not exercise the Phase 2 option
The oil prices can change the decision for Phased development, but not
for the Overall development alternative
The valuation is similar to
the previously presented
Only by running the
simulations is possible to
compare the higher NPV
versus higher flexibility
Real Options Evaluation by Simulation + Threshold Curve

Before the information revelation, V/D changes due the oil prices P (recall
= qPB and NPV = V – D). With revelation on q and B, the value V jumps.
V
A
B
Present Value (t = 0)
F(t = 0) =
= F(t=5.5) * exp (- r*t)
Option F(t = 5.5) = V - D
F(t = 8) = 0
Expires Worthless
Oil Drilling Bayesian 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
Two Sequential Learning: Schematic Tree

Two sequential investment in information (wells “B” and “C”):
Invest
Well “B”
Invest
Well “C”
Posterior
Scenarios
NPV
{
400
300
350 (with 25% chances)
300
{
300
200
250 (with 50% chances)
100
150 (with 25% chances)
- 200
{

Revelation
Scenarios
200
100
The upper branch means good news, whereas the lower one means bad news
Visual FAQ’s on Real Options: 9
 Is
possible real options theory to recommend
investment in a negative NPV project?
Answer:
yes, mainly sequential options with
investment revealing new informations

Example: exploratory oil prospect (Dias 1997)
Suppose
a “now or never” option to drill a wildcat
Static NPV is negative and traditional theory recommends to
give up the rights on the tract
Real options will recommend to start the sequential investment,
and depending of the information revealed, go ahead (exercise
more options) or stop
Sequential Options (Dias, 1997)
“Compact Decision-Tree”
Note: in million US$
( Developed Reserves Value )
( Appraisal Investment: 3 wells )
( Development Investment )
( Wildcat
Investment )

EMV = - 15 + [20% x (400 - 50 - 300)]
 EMV = - 5 MM$
Traditional method, looking only expected values, undervaluate
the prospect (EMV = - 5 MM US$):


There are sequential options, not sequential obligations;
There are uncertainties, not a single scenario.
Sequential Options and Uncertainty

Suppose that each appraisal
well reveal 2 scenarios (good
and bad news)
 development option will not be
exercised by rational managers
 option to continue the
appraisal phase will not be
exercised by rational managers
Option to Abandon the Project

Assume it is a “now or
never” option

If we get continuous bad
news, is better to stop
investment
 Sequential options turns
the EMV to a positive
value

The EMV gain is
3.25 - (- 5) = $ 8.25 being:
$ 2.25 stopping development
$6
stopping appraisal
$ 8.25 total EMV gain
(Values in millions)
Economic Quality of a Developed Reserve
 Concept



by Dias (1998): q = v/P ; v = V/B (in $/bbl)
q = economic quality of the developed reserve
v = value of one barrel of the developed reserve ($/bbl)
P = current petroleum price ($/bbl)
 For the
proportional model, v = q P, the economic quality
of the reserve is constant. We adopt this model.
 The
F
option charts F x V and F x P at the expiration (t = T)
v = q . P; V = v . B
F(t=T) = max (NPV, 0)
F
F(t=T) = max (q P B - D, 0)
NPV = V - D
tg
45o
(tg q)/B = q = economic quality
=1
q
45o
D
V
D/qB
P
Monte Carlo Simulation of Uncertainties
 Simulation
will combine uncertainties (technical and market) for
the equation of option exercise: NPV(t)dyn = q . B . P(t) - D(B)
Parameter
Economic Quality of the
Developed Reserve (q)
(only at t = trevelation)
Reserve Size (B) (only
at t = trevelation)
(in million of barrels)
Oil Price (P) ($/bbl)
(from t = 0 until t = T)
 In
Distribution
Values (example)
Minimum = 10%
Most Likely = 15%
Maximum = 20%
Minimum = 300
Most Likely = 500
Maximum = 700
Mean = 18 US$/bbl
Standard-Deviation:
changes with the time
the case of oil price (P) is performed a risk-neutral simulation of its
stochastic process, because P(t) fluctuates continually along the time
Brent Oil Prices: Spot x Futures
Note that the spot prices reach more extreme values than the longterm futures prices
Brent Prices: Spot (Dated) vs. IPE 12 Month
Jul/1996 - Jan/2002
40
Brent Platt's Dated Mid (US$/bbl)
Brent IPE Mth12 Close (US$/bbl)
35
30
25
20
15
10
1/22/2002
10/22/2001
7/22/2001
4/22/2001
1/22/2001
10/22/2000
7/22/2000
4/22/2000
1/22/2000
10/22/1999
7/22/1999
4/22/1999
1/22/1999
10/22/1998
7/22/1998
4/22/1998
1/22/1998
10/22/1997
7/22/1997
4/22/1997
1/22/1997
10/22/1996
5
7/22/1996
Brent (US$/bbl)

Mean-Reversion + Jumps for Oil Prices
 Adopted
in the Marlim Project Finance (equity
modeling) a mean-reverting process with jumps:
where:
(the probability of jumps)
 The
jump size/direction
are random: f ~ 2N
 In case of jump-up, prices
are expected to double

OBS: E(f)up = ln2 = 0.6931
 In case of jump-down, prices
are expected to halve

OBS: ln(½) = - ln2 = - 0.6931
(jump size)
Equation for Mean-Reversion + Jumps
 The
interpretation of the jump-reversion equation is:
continuous (diffusion) process
variation of the
stochastic variable
for time interval dt
discrete
process
(jumps)
uncertainty from
the continuous-time
process (reversion)
mean-reversion drift:
positive drift if P < P
negative drift if P > P
uncertainty from
the discrete-time
process (jumps)