By: Marco Antonio Guimar

1
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/

• . Investment in Information in Petroleum Real
  Options and Revelation
• 6th Annual International Conference on Real
  Options - Theory Meets Practice
• July 4-6, 2002 - Coral Beach, Cyprus

2
EP Process As Real Options
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Motivation and Investment in Information

• Motivation Answer questions related to a
  discovered and delineated oilfield, but with
  remaining technical uncertainties about the
  reserve size and quality
• Is better to invest in information, to develop,
  or to wait?
• What is the best alternative to invest in
  information?

• What are the properties of the distribution of
  scenarios revealed after the new information
  (revelation distribution)?

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Technical Uncertainty Modeling Revelation

• How to model the technical uncertainty and its
  evolution after one or more investment in
  information?
• Investments in information permit both a
  reduction of the technical uncertainty and a
  revision of our expectations.
• 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 EX I
• The process of accumulating data about a
  technical parameter is a learning process towards
  the truth about this parameter
• This suggest the names information revelation and
  revelation distribution
• Dont confound with the revelation principle in
  Bayesian games that addresses the truth on a type
  of player. Here is truth on a parameter value
• The distribution of conditional expectations EX
  I is named here revelation distribution, that
  is, the distribution of RX EX I

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Conditional Expectations and Revelation

• 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) EX - g( I )2 . The choice of g that
  minimizes the error measure MSE(g) is exactly the
  conditional expectation EX I .
• This is a very known property used in
  econometrics (optimal predictor)
• 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
• In general we need consider alternatives of
  investment in information
• With different costs to gather and process the
  information
• With different time to learn (time to gather and
  process the information) and
• With different revelation powers (related with
  the of reduction of variance)
• In order to both estimate the value of
  information and to compare alternatives with
  different revelation powers, we need the nice
  properties of the revelation distribution
  (propositions)

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The Revelation Distribution Properties

• 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
• EEX I ERX EX (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
• VarEX I VarRX VarX - EVarX I
  Expected Variance Reduction
• Proposition 4 In a sequential investment in
  information process, the the sequence RX,1,
  RX,2, RX,3, is an event-driven martingale
• In short, ex-ante these random variables have the
  same mean

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Investment in Information 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)

• 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)

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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 with 12.5 chances ( 0.5 3 )
• 200 MM bbl with 37,5 chances ( 3 x 0.5 3 )
• 300 MM bbl with 37,5 chances
• 400 MM bbl with 12,5 chances
• The variance of this prior distribution is 7500
  (million bbl)2

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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
• E1BA1 100 100 (0.5 x 100) (0.5 x
  100) 300 MM bbl
• In case of negative revelation (50 chances) the
  expected value is
• E2BA1 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
• EA1RB 50 x E1(BA1) 50 x E2(BA1)
  250 million bbl EB
• As expected by Proposition 2
• And the variance of the revealed scenarios is
• VarA1RB 50 x (300 - 250)2 50 x (200 -
  250)2 2500 (MM bbl)2
• Let us check if the Proposition 3 was satisfied

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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

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Visualization of Revealed Scenarios Revelation
Distribution
All the revelation distributions have the same
mean (maringale) Prop. 4 OK!
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Posterior Distribution x Revelation Distribution

• Higher volatility, higher option value. Why
  invest to reduce uncertainty?

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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 of each relevant
  technical parameter? That is, the prior
  probability distribution parameters
• 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

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Oilfield Development Option and the NPV Equation

• Let us see an example. When development option is
  exercised, the payoff is the net present value
  (NPV) given by NPV V - D q P B -
  D
• q economic quality of the reserve, which has
  technical uncertainty (modeled with the
  revelation distribution)
• P(t) is the oil price (/bbl) source of the
  market uncertainty, modeled with the risk neutral
  Geometric Brownian motion
• B reserve size (million barrels), which has
  technical uncertainty
• D oilfield development cost, function of the
  reserve size B and possibly following also a
  correlated geometric Brownian motion, through a
  stochastic factor u (t) with u (t 0) 1, given
  by
• D(B, t) u (t). Fixed Cost Variable Cost x
  B ? D u . FC VC . B
• So, the development exercise price D changes
  after the information revelation on the reserve
  size B, and also evolves along the time

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NPV x P Chart and the Quality of Reserve
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Real x Risk-Neutral Simulation

• The GBM simulation paths real drift a, and the
  risk-neutral drift r - d a - p . We use
  the risk-neutral measure, which suppresses a
  risk-premium p from the real drift in the
  simulation.

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Dynamic Value of Information

• Value of Information has been studied by decision
  analysis theory. I extend this view with real
  options tools
• I call dynamic value of information. Why dynamic?
• Because the model takes into account the factor
  time
• Time to expiration for the rights to commit the
  development plan
• Time to learn the learning process takes time to
  gather and process data, revealing new
  expectations on technical parameters and
• Continuous-time process for the market
  uncertainties (oil prices) interacting with the
  current expectations on technical parameters
• When analysing a set of alternatives of
  investment in information, are considered also
  the learning cost and the revelation power for
  each alternative
• The revelation power is the capacity to reduce
  the variance of technical uncertainty ( variance
  of revelation distribution by the Proposition 3)

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Best Alternative of Investment in Information

• Given the set k 0, 1, 2 of alternatives (k 0
  means not invest in information) the best k is
  the one that maximizes Wk

• Where Wk is the value of real option included the
  cost/benefit from the investment in information
  with the alternative k (learning cost Ck, time to
  learn tk), given by

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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 (and D)
• We calculate V q P B and D(B), so V/D, and
  compare it with (V/D)
• Advantage (V/D) is homogeneous of degree 0 in V
  and 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 dont 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 re-calculated every
  iteration in the Monte Carlo simulation.

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Combination of Uncertainties in Real Options

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

Vt/Dt (q Pt B)/Dt
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Conclusions

• The paper main contribution is to help fill the
  gap in the real options literature on technical
  uncertainty modeling
• Revelation distribution (distribution of
  conditional expectations) and its 4 propositions,
  have sound theoretical and practical basis
• The propositions allow a practical way to select
  the best alternative of investment in information
  from a set of alternatives with different
  revelation powers
• We need ask the experts only (1) the total
  technical uncertainty (prior distribution) and
  (2) for each alternative of investment in
  information the expected reduction of variance
• We saw a dynamic model of value of information
  combining technical with market uncertainties
• Used a Monte Carlo simulation combining the
  risk-neutral simulation for market uncertainties
  with the jumps at the revelation time (jump-size
  drawn from the revelation distributions)

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Anexos

• APPENDIX
• SUPPORT SLIDES

• See more on real options in the first website on
  real options at
• http//www.puc-rio.br/marco.ind/

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Technical Uncertainty and Risk Reduction

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

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Technical Uncertainty and Revelation

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

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Geometric Brownian Motion Simulation

• The real simulation of a GBM uses the real drift
  a. The price P at future time (t 1), given the
  current value Pt is given by

• But for a derivative F(P) like the real option to
  develop an oilfiled, we need the risk-neutral
  simulation (assume the market is complete)
• The risk-neutral simulation of a GBM uses the
  risk-neutral drift a r - d . Why? Because by
  supressing a risk-premium from the real drift a
  we get r - d. Proof
• Total return r r p (where p is the
  risk-premium, given by CAPM)
• But total return is also capital gain rate plus
  dividend yield r a d
• Hence, a d r p ? a - p r - d
  
• So, we use the risk-neutral equation below to
  simulate P

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Oil Price Process x Revelation Process

• What are the differences between these two types
  of uncertainties?
• 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
• For exploration of new basins sometimes the
  revelation of information from other firms can be
  relevant (free-rider), but it also occurs in
  discrete-time
• In many cases (appraisal phase) only our
  investment in information is relevant and it is
  totally controllable by us (activated by
  management)
• In short, every day the oil prices changes, but
  our expectation about the reserve size will
  change only when an investment in information is
  performed ? so the expectation can remain the
  same for months!

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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
Eq B NPV q P B gup - D(B) if q B gt Eq
B NPV q P B gdown- D(B) if q B lt Eq B
In general we have gdown 1 and gup lt 1
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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 the barrel of
  developed reserve?
• One reserve in the same country, water depth, oil
  quality, OPEX, etc., is more valuable than other
  if is possible to extract faster (higher
  productivity index, higher quantity of wells)
• A reserve located in a country with lower fiscal
  charge and lower risk, is more valuable (eg., USA
  x Angola)
• 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)

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Overall x Phased Development

• Consider two oilfield development 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
30
Real Options Evaluation by Simulation Threshold
Curve

• Before the information revelation, V/D changes
  due the oil prices P (recall V qPB and NPV
  V D). With revelation on q and B, the value V
  jumps.

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NYMEX-WTI Oil Prices Spot x Futures

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

32
Brent Oil Prices Spot x Futures

• Note that the spot prices reach more extreme
  values than the long-term futures prices

33
Brent Oil Prices Volatility Spot x Futures

• Note that the spot prices volatility is much
  higher than the long-term futures volatility

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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