real options in petroleum: an overview real options valuation in the new economy

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

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

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 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

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

Undelineated Field: Option to Appraise

Appraisal InvestmentAppraisal Investment

RevisedVolume = B’

Developed Reserves: Options to Expand, to Stop Temporally, and to Abandon.

E&P as a Sequential Real Options Process Concession: Option to Drill the Wildcat

Exploratory (wildcat) Exploratory (wildcat) InvestmentInvestment

Oil/Gas SuccessProbability = p

Expected Volumeof Reserves = B

Delineated Undeveloped Reserves: Option to Develop (What is the best alternative?)

Development InvestmentDevelopment Investment

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.

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.

E[P] = 18 $/bblNPV(t=0) = 50 million $

E[P+] = 19 NPV = + 50 million $

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 $

50%

50%

t = 1

t = 0

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%

E[P] = 18 /bblNPV(t=0) = 50 million $

E[P+] = 19 NPV+ = + 150 million $

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

50%

50%

t = 1

t = 0

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 $ Discount rate = 10%

E[P] = 18 /bbl NPV(t=0) = 500 million $

E[P+] = 19 NPV = 625 million $

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

50%

50%

t = 1

t = 0

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

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)

Time to Expiration of the Option Time to Expiration of the Investment Rights ()

Paddock, Siegel & Smith’s Real Options

Black-Scholes-Merton’s Financial Options

Stock Dividend Yield Cash Flow Net of Depletion as Proportion of V ()

Risk-Free Interest Rate Risk-Free Interest Rate (r)

Stock Volatility Volatility of Developed Reserve Value ()

Equation of the Undeveloped Reserve (F) Partial (t, V) Differential Equation (PDE) for the option F

Managerial Action Is Inserted into the Model

Boundary Conditions:

For V = 0, F (0, t) = 0 For t = T, F (V, T) = max [V D, 0] = max [NPV, 0]

}} Conditions at the Point of Optimal Early Investment

Conditions at the Point of Optimal Early Investment

For V = V*, F (V*, t) = V* D “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; = dividend yield for V ; = volatility of V

0.5 2 V2 FVV + (r ) V FV r F = Ft

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)

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

Mean-Reverting Process

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 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

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

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; 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

E&P Process and Options Drill the wildcat (pioneer)? Wait and See? Revelation and technical uncertainty modeling



RevisedVolume = 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?

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

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 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 (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

InvestmentsD3 > D2 > D1






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

alternative?



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:

Risk reduction by the investment in information of all firms in the basin(driver is the investment, not the passage of time directly)

Project evaluation with additionalinformation(t = T)

Lower Risk

ExpectedValue

Current project evaluation(t=0)

HigherRisk

ExpectedValue

con

fid

ence

in

terv

al

Lack of Knowledge Trunk of Cone

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

Value withgood revelation

Value withbad revelation

Current project evaluation (t=0)

Investment inInformation

Project valueafter investment

t = T

Value withneutral revelation

E[V]

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?

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

EMV = Expected Monetary Value = IW + (CF . NPV) EMV = 20 + (15% . 100) = 5 million $

20 million $(IW = wildcat investment)

15% (CF = chance factor)

Dry Hole

“Compact Tree”

Su

cces

s

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:

Dis

trib

utio

n o

f E

xpec

tati

ons

(Rev

elat

ion

Dis

trib

uti

ons)

Real x Risk-Neutral Simulation The GBM simulation paths: one real () and the other risk-neutral (r ). In reality r = , where is a

risk-premium

0

5

10

15

20

25

30

35

40

45

0.0

0.3

0.5

0.8

1.0

1.3

1.5

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2.5

2.8

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3.3

3.5

3.8

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4.3

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5.5

5.8

6.0

Time (Years)

Oil

Pri

ce ($

/bb

l)

Real Simulation

Risk-Neutral Simulation

A Visual Equation for Real Options

Prospect Evaluation(in million $)

Traditional Value = 5

Options Value (at T) = + 12.5

Options Value (at t=0) = + 7.6

+

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.

=So, refuse the $ 3 million offer!






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

alternative?



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; andContinuous-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)*

A

Option F(t = 1) = V DF(t = 0) == F(t=1) * exp (r*t)

Present Value (t = 0)

B

F(t = 2) = 0ExpiredWorthless

Vt/D = (q Pt B)/D

E&P Process and Options Drill the wildcat? Wait? Extend? Revelation and technical uncertainty modeling




Technical uncertainty: sequential options

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

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

information?

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

petroleum reservoir (top view) and the grid of wells

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)

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

APPENDIXSUPPORT 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 respondA

bili

ty t

o re

spon

d

Low

High

Likelihood of receiving new informationLow High

U n c e r t a i n t y

Roo

m f

or

Man

ager

ial F

lexi

bil

ity

Moderate Flexibility Value

Moderate Flexibility Value

Low Flexibility Value

High

Flexibility Value

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 V = P and V = P (D&P p.178. Why?)

Risk-neutral Geometric Brownian: dV = (r V) V dt + V 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 from oil prices futures market

Pickles & Smith’s Rule (1993): r = (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 pricesWTI Nymex Prices: Spot (First Month) vs. 18 Months

Jul/1996 - Jan/2002

5

10

15

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35

407/

22/1

996

10/2

2/19

96

1/22

/199

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2/20

00

1/22

/200

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2/20

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1/22

/200

2

WT

I (U

S$/

bb

l)

WTI Nymex Spot (1st Mth) Close (US$/bbl)

WTI Nymex Mth18 Close (US$/bbl)

Mean-Reversion + Jump: the Sample Paths 100 sample paths for mean-reversion + jumps ( = jump each 5years)

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

.

Investmentin information(wildcat drilling, etc.)

Investment in information(costly and free-rider)

Todaytechnicaland economicvaluation

t = 0 t = 1

Possible scenariosafter the informationarrived during the first year of option term

t = T

Possible scenariosafter the informationarrived during the option leaseterm

RevelationDistribution

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

E[B]Inv

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 tractCompany X tract Company Y tractCompany Y tract

real options in petroleum: an overview real options valuation in the new economy

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