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. Real Options in Petroleum: An Overview Real Options Valuation in the New Economy July 4-6, 2002 - Coral Beach, CyprusPowerPoint Presentation

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

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By: Marco Antonio Guimarães Dias - Internal Consultant by Petrobras, Brazil - Doctoral Candidate by PUC-Rio Visit the first real options website: www.puc-rio.br/marco.ind/. . Real Options in Petroleum: An Overview Real Options Valuation in the New Economy

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

. Real Options in Petroleum: An Overview

Real Options Valuation in the New Economy

July 4-6, 2002 - Coral Beach, Cyprus

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

- Petrobras research program called “PRAVAP-14 ” Valuation of Development Projects under Uncertainties

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)

- Maximize the NPV (typical objective function) subject to:
- 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

- Concession: Option to Drill the Wildcat

Development Investment

Exploratory (wildcat)

Investment

Expected Volume

of Reserves = B

Revised

Volume = B’

- Undelineated Field: Option to Appraise

Appraisal Investment

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

- 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 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 reserveq (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

t = 1

50%

t = 0

50%

- 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+] = 19 NPV = + 50 million $

E[P] = 18 $/bbl

NPV(t=0) = - 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 $

Intuition (2): Timing Option and Waiting Value

t = 1

50%

t = 0

E[P-] = 17 NPV - = - 50 million $

50%

Rational manager will not exercise

this option Max (NPV-, 0) = zero

- 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+] = 19 NPV+ = + 150 million $

E[P] = 18 /bbl

NPV(t=0) = + 50 million $

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

t = 1

50%

t = 0

E[P-] = 17 NPV = 375 million $

50%

- 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+] = 19 NPV = 625 million $

E[P] = 18 /bbl

NPV(t=0) = 500 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’s

Real Options

Black-Scholes-Merton’s

Financial 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)

- 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

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

Equation of the Undeveloped Reserve (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

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

- For V = V*, F (V*, t) = V* - D
- “Smooth Pasting”, FV (V*, t) = 1

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

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 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

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

- Normal information causes smoothing changes in oil prices (marginal variations) and means both:

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)

- Equity investors reward:
- 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

- Few months later the oil prices jumped-up (price doubled by Aug/99)

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

Oil/Gas Success

Probability = p

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

Expected Volume

of Reserves = B

Revised

Volume = B’

- Appraisal phase: delineation of reserves
- Invest in additional information?

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

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

Selection of Alternatives under Uncertainty

- In the equation for the developed reserve valueV = 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 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 (threshold) along the time?

- Depending of P, exercise A2 or A3

Threshold Curves for Three Alternatives

Investments

D3 > D2 > D1

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

E&P Process and Options

Oil/Gas Success

Probability = p

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

Expected Volume

of Reserves = B

Revised

Volume = B’

- Appraisal phase: delineation of reserves
- Invest in additional information?

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

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

Technical Uncertainty and Risk Reduction

HigherRisk

Lower Risk

ExpectedValue

ExpectedValue

confidence interval

Lack of Knowledge Trunk of Cone

Project evaluation with additionalinformation(t = T)

Risk reduction by the investment in information

of all firms in the basin

(driver is the investment, not the passage of time directly)

Current project

evaluation

(t=0)

- 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:

Technical Uncertainty and Revelation

t = T

Value withgood revelation

Value withneutral revelation

E[V]

Value withbad revelation

Investment in

Information

Project valueafter investment

Current project

evaluation (t=0)

- 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

- The expected value after the investment in information (conditional expectation) can be very different of the initial estimative

Valuation of Exploratory 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 $

“Compact Tree”

Success

15% (CF = chance factor)

Dry Hole

20 million $

(IW = wildcat investment)

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

NPV = q P B - D = (20% . 20 . 150) - 500 = + 100 MM$

However, there is only 15% chances to find petroleum

EMV = Expected Monetary Value = - IW + (CF . NPV)

EMV =- 20 + (15% . 100) = - 5 million $

Do you sell the prospect rights for US$ 3 million?

Monte Carlo Combination of Uncertainties

Distribution of Expectations

(Revelation Distributions)

- 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:

Real x Risk-Neutral Simulation

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

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

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

Expected Volume

of Reserves = B

Revised

Volume = B’

- Appraisal phase: delineation of reserves
- Invest in additional information?

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

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

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

- Because the model takes into account the factor time:
- 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

- I use the concept of revelation distribution for technical uncertainty

Combination of Uncertainties in Real Options

A

B

Present Value (t = 0)

F(t = 2) = 0

Option F(t = 1) = V - D

F(t = 0) =

= F(t=1) * exp (- r*t)

ExpiredWorthless

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

Vt/D = (q Pt B)/D

E&P Process and Options

Oil/Gas Success

Probability = p

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

Expected Volume

of Reserves = B

Revised

Volume = B’

- Appraisal phase: delineation of reserves
- Technical uncertainty: sequential options

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

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

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.

- Remaining technical uncertainty of reservoirs is still important.
- 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

- The oil migrates from the original area so that the exercise of the option gradually become less probable (decreasing NPV)

Secondary Depletion Effect: A Complication

optional wells

oil migration

(secondary depletion)

petroleum reservoir (top view) and the grid of wells

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

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

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

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?

Likelihood of receiving new information

Low

High

U n c e r t a i n t y

High

High Flexibility Value

Moderate Flexibility Value

Room for Managerial Flexibility

Ability to respond

Moderate Flexibility Value

Low Flexibility Value

Low

- Based on the textbook “Real Options” by Copeland & Antikarov
- Real options are as valuable as greater are the uncertainties and the flexibility to respond

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.

- Transactions in the developed reserves market (USA)

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 of long-term oil prices (~ 20% p.a.)
- For development decisions the value of the benefit is linked to the long-term oil prices, not the (more volatile) spot prices
- A good market proxy is the longest maturity contract in futures markets with liquidity (Nymex 18th month; Brent 12th month)

- Dividend yield (or long-term convenience yield) ~ 6% p.a.
- Paddock & Siegel & Smith: equation using cash-flows
- If V = k P, we can estimate d from oil prices futures market

- Pickles & 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

Mean-Reversion + Jump: the Sample Paths

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

Technical Uncertainty in New Basins

Investment

in information

(wildcat drilling, etc.)

RevelationDistribution

Investment in information

(costly and free-rider)

Possible

scenarios

after the

information

arrived

during the

option lease

term

.

t = 0

t = T

t = 1

Todaytechnical

and economic

valuation

Possible scenarios

after the information

arrived during the

first year of option term

- 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

Simulation Issues

P

Inv

E[B]

Inv

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

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

Company Y tract

Company X tract

- 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

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