Visual FAQ

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Visual FAQs on Real Options Celebrating the
Fifth Anniversary of the Website Real Options
Approach to Petroleum Investmentshttp//www.puc-r
io.br/marco.ind/
Real Options 2000 ConferenceCapitalizing on
Uncertainty and Volatility in the New
MillenniumSeptember 25, 2000 - Chicago

• By Marco Antônio Guimarães Dias
• Petrobras and PUC-Rio, Brazil

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Visual FAQs on Real Options

• Selection of frequently asked questions (FAQs)
  by practitioners and academics
• Something comprehensive but I confess some bias
  in petroleum questions
• Use of some facilities to visual answer
• Real options models present two results
• The value of the investment oportunity (option
  value)
• How much to pay (or sell) for an asset with
  options?
• The decision rule (thresholds)
• Invest now? Wait and See? Abandon? Expand the
  production? Switch use of an asset?
• Option value and thresholds are the focus of
  most visual FAQs

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Visual FAQs on Real Options 1

• Are the real options premium important?
• Real Option Premium Real Option Value - NPV
• Answer with an analogy
• Investments can be viewed as call options
• You get an operating project V (like a stock) by
  paying the investment cost I (exercise price)
• Sometimes this option has a time of expiration
  (petroleum, patents, etc.), sometimes is
  perpetual (real estate, etc.)
• Suppose a 3 years to expiration petroleum
  undeveloped reserve. The immediate exercise of
  the option gets the NPV
• NPV V - I

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Real Options Premium

• The options premium can be important or not,
  depending of the of the project moneyness

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Visual FAQs on Real Options 2

• What are the effects of interest rate,
  volatility, and other parameters in both option
  value and the decision rule?
• Answer with Timing Suite
• Three spreadsheets that uses a simple model
  analogy of real options problem with American
  call option
• Lets go to the Excel spreadsheets to see the
  effects

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Timing Suite Real Options Spreadsheets

• A set of interactive Excel spreadsheets Timing
  Suite are used to calculate both the option
  value and the threshold
• Solve American options with the analytic
  approximation of Barone-Adesi Whaley
  (instantaneous response)

• The underlying asset is the project value V which
  can be developed by investing I
• Uncertainty Geometric Brownian Motion, the same
  of Black-Scholes
• Three spreadsheets
• Timing (Standard)
• Timing With Two Uncertainties
• Timing Switch (two uncertainties)

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Timing Standard Version
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Timing Standard Version Charts
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Timing Standard Version Charts
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Timing Suite Others Spreadsheets

• Timing with Two Uncertainties
• Project value V and investment I are both
  stochastic
• Used again Barone-Adesi Whaley but for v V/I.
  
• This is possible thanks to the PDE first degree
  homogeneity in V and I F(V, I, t) I. F/I(V/I,
  1, t) D. f(v, 1, t)
• Timing Switch abandon and switch use decisions
• Myers Majd (1990) model, case of two risk
  assets both project and alternative asset values
  are uncertain
• Exs. (a) abandon a project for the salvage
  value (b) redevelopment of a real estate (c)
  conversion of a tanker to a floating production
  system (oilfield).
• Exploits analogy with American put and use the
  call-put symmetry C (V, I, r, d , T, s ) P (
  I, V, d , r, T, s )
• Knowing the call value you have also the put
  value vice versa

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Visual FAQs on Real Options 3

• Where the real options value comes from?
• Why real options value is different of the static
  net present value (NPV)?
• Answer with example option to expand
• Suppose a manager embed an option to expand into
  her project, by a cost of US 1 million
• The static NPV - 5 million if the option is
  exercise today, and in future is expected the
  same negative NPV
• Spending a million for an expected negative
  NPV Is the manager becoming crazy?

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Uncertainty Over the Expansion Value

• Considering combined uncertainties in product
  prices and demand, exercise price of the real
  option, operational costs, etc., the future value
  (2 years ahead) of the expansion has an expected
  value of - 5 million
• The traditional discount cash will not recommend
  to embed an option to expansion which is expected
  to be negative
• But the expansion is an option, not an
  obligation!

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Option to Expand the Production

• Rational managers will not exercise the option to
  expand _at_ t 2 years in case of bad news
  (negative value)
• Option will be exercised only if the NPV gt 0.
  So, the unfavorable scenarios will be pruned (for
  NPV lt 0, value 0)
• Options asymmetry leverage prospect valuation.
  Option 5

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Real Options Asymmetry and Valuation

• The visual equation for Where the options value
  comes from?

Prospect Valuation Traditional Value - 5
Options Value(T) 5
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EP Process and Options
Oil/Gas Success Probability p

• Drill the wildcat? Wait? Extend?
• Revelation, option-game waiting incentives

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 for better conditions?
  Extend the option?

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

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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
  better way to solve the uncertainty is by looking
  the production profile instead drilling
  additional appraisal wells
• In the preliminary development plan, some wells
  presented both reservoir risk and small NPV.
• Some wells with small positive NPV (not
  deep-in-the-money) and others even with
  negative NPV
• Depending of the initial production information,
  some wells can be not necessary
• Solution leave these wells as optional wells
• Small investment to permit a fast and low cost
  future integration of these wells, depending of
  both market (oil prices, costs) and the
  production profile response

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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 (or the accumulated production)
  that the reservoir information will be revealed
• Define the scenarios (or distributions) of
  marginal production of each optional well as
  function of time.
• Consider the depletion if we wait after learn
  about reservoir
• Add market uncertainty (reversion jumps for oil
  prices)
• Combine uncertainties using Monte Carlo
  simulation (risk-neutral simulation if possible,
  next FAQ)
• Use 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 frontier
  research area
• Petrobras-PUC project Monte Carlo for American
  options

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Visual FAQs on Real Options 4

• Does risk-neutral valuation mean that investors
  are risk-neutral?
• What is the difference between real simulation
  and risk-neutral simulation?
• Answers
• Risk-neutral valuation (RNV) does not assume
  investors or firms with risk-neutral preferences
• RNV does not use real probabilities. It uses risk
  neutral probabilities (martingale measure)
• Real simulation real probabilities, uses real
  drift a
• Risk-neutral simulation the sample paths are
  risk-adjusted. It uses a risk-neutral drift a
  r - d

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Geometric Brownian Motion Simulation

• The real simulation of a GBM uses the real drift
  a. The price at future time t is given by

• By sampling the standard Normal distribution N(0,
  1) you get the values forPt
• With real drift use a risk-adjusted (to P)
  discount rate
• The risk-neutral simulation of a GBM uses the
  risk-neutral drift a r - d . The price at t
  is

• With risk-neutral drift, the correct discount
  rate is the risk-free interest rate.

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Risk-Neutral Simulation x Real Simulation

• For the underlying asset, you get the same value
  
• Simulating with real drift and discounting with
  risk-adjusted discount rate r ( where r a
  d )
• Or simulating with risk-neutral drift (r - d) but
  discounting with the risk-free interest rate (r)
• For an option/derivative, the same is not true
• Risk-neutral simulation gives the correct option
  result (discounting with r) but the real
  simulation does not gives the correct value
  (discounting with r)
• Why? Because the risk-adjusted discount rate is
  adjusted to the underlying asset, not to the
  option
• Risk-neutral valuation is based on the absence of
  arbitrage, portfolio replication (complete
  market)
• Incomplete markets see next FAQ

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Visual FAQs on Real Options 5

• Is possible to use real options for incomplete
  markets?
• What change? What are the possible ways?
• Answer Yes, is possible to use.
• For incomplete markets the risk-neutral
  probability (martingale measure) is not unique
• So, risk-neutral valuation is not rigorously
  correct because there is a lack of market values
• Academics and practitioners use some ways to
  estimate the real option value, see next slide

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Incomplete Markets and Real Options

• In case of incomplete market, the alternatives to
  real options valuation are
• Assume that the market is approximately complete
  (your estimative of market value is reliable)
  and use risk-neutral valuation (with risk-neutral
  probability)
• Assume firms are risk-neutral and discount with
  risk-free interest rate (with real probability)
• Specify preferences (the utility function) of
  single-agent or the equilibrium at detailed level
  (Duffie)
• Used by finance academics. In practice is
  difficult to specify the utility of a corporation
  (managers, stockholders)
• Use the dynamic programming framework with an
  exogenous discount rate
• Used by academics economists Dixit Pindyck,
  Lucas, etc.
• Corporate discount rate express the corporate
  preferences?

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Visual FAQs on Real Options 6

• Is true that mean-reversion always reduces the
  options premium?
• What is the effect of jumps in the options
  premium?
• Answers
• First, well see some different processes to
  model the uncertainty over the oil prices (for
  example)
• Second, well compare the option premium for an
  oilfield using different stochastic processes
• All cases are at-the-money real options (current
  NPV 0)
• The equilibrium price is 20 /bbl for all
  reversion cases

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Geometric Brownian Motion (GBM)

• This is the most popular stochastic process,
  underlying the famous Black-Scholes-Merton
  options equation
• GBM expected curve is a exponential growth (or
  decrease) prices have a log-normal distribution
  in every future time and the variance grows
  linearly with the time

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Mean-Reverting Process

• In this process, the price tends to revert toward
  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
• Charts the variance of distributions stabilizes
  after ti

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Nominal Prices for Brent and Similar Oils
(1970-1999)

• We see 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

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Mean-Reversion Jumps for Oil Prices

• Adopted in the Marlim Project Finance (equity
  modeling) a mean-reverting process with jumps

(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)
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Equation for Mean-Reversion Jumps

• The interpretation of the jump-reversion equation
  is

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Mean-Reversion x GBM Option Premium

• The chart compares mean-reversion with GBM for an
  at-the-money project at current 25 /bbl
• NPV is expected to revert from zero to a negative
  value

Reversion in all cases to 20 /bbl
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Mean-Reversion with Jumps x GBM

• Chart comparing mean-reversion with jumps versus
  GBM for an at-the-money project at current 25
  /bbl
• NPV still is expected to revert from zero to a
  negative value

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Mean-Reversion x GBM

• Chart comparing mean-reversion with GBM for an
  at-the-money project at current 15 /bbl
  (suppose)
• NPV is expected to revert from zero to a positive
  value

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Mean-Reversion with Jumps x GBM

• Chart comparing mean-reversion with jumps versus
  GBM for an at-the-money project at current 15
  /bbl (suppose)
• Again NPV is expected to revert from zero to a
  positive value

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Visual FAQs on Real Options 7

• How to model the effect of the competitor entry
  in my investment decisions?
• Answer option-games, the combination of the
• real options with game-theory
• First example Duopoly under Uncertainty (Dixit
  Pindyck, 1994 Smets, 1993)
• Demand for a product follows a GBM
• Only two players in the market for that product
  (duopoly)

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Duopoly Entry under Uncertainty

• The leader entry threshold both players are
  indifferent about to be the leader or the
  follower.
• Entry NPV gt 0 but earlier than monopolistic case

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Other Example Oil Drilling Game

• Oil exploration 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 Xs prospect increases
  dramatically. If Y drilling gets a dry hole,
  this information is also valuable for X.
• Here the effect of the competitor presence is the
  opposite to increase the value of waiting to
  invest

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Visual FAQs on Real Options 8

• Does Real Options Theory (ROT) speed up the firms
  investments or slow down investments?
• Answer depends of the kind of investment
• ROT speeds up today strategic investments that
  create options to invest in the future. Examples
  investment in capabilities, training, RD,
  exploration, new markets...
• ROT slows down large irreversible investment of
  projects with positive NPV but not deep in the
  money
• Large projects but with high profitability (deep
  in the money) must be done by both ROT and
  static NPV.

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Visual FAQs 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

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Sequential Options (Dias, 1997)
Compact Decision-Tree
Note in million US
( Developed Reserves Value )
( Appraisal Investment 3 wells )
( Development Investment )
EMV - 15 20 x (400 - 50 - 300) ? EMV - 5
MM
( Wildcat Investment )

• 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.

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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

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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)
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Visual FAQs on Real Options 10

• Is the options decision rule (invest at or above
  the threshold curve) the policy to get the
  maximum option value?
• How much value I lose if I invest a little above
  or little below the optimum threshold?
• Answer yes, investing at or above the threshold
  line you maximize the option value.
• But sometimes you dont lose much investing near
  of the optimum (instead at the optimum)
• Example oilfield development as American call
  option. Suppose oil prices follow a GBM to
  simplify.

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Thresholds Optimum and Sub-Optima

• The theoretical optimum (red) of an American call
  option (real option to develop an oilfield) and
  the sub-optima thresholds (10 above and below)

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Optima Region

• Using a risk-neutral simulation, I find out here
  that the optimum is over a plateau (optima
  region) not a hill
• So, investing 10 above or below the
  theoretical optimum gets rough the same value

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Real Options Premium

• Now a relation optimum with option premium is
  clear near of the point A (theoretical
  threshold) the option premium can be very small.

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Visual FAQs on Real Options 11

• How Real Options Sees the Choice of Mutually
  Exclusive Alternatives to Develop a Project?
• Answer very interesting and important
  application
• Petrobras-PUC is starting a project to compare
  alternatives of development, alternatives of
  investment in information, alternatives with
  option to expand, etc.
• One simple model is presented by Dixit (1993).
• Let see directly in the website this model

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Conclusions

• The Visual FAQs on Real Options illustrated
• Option premium visual equation for option value
  uncertainty modeling decision rule (thresholds)
  risk-neutral x real simulation/valuation Timing
  Suite effect of competition optimum problem,
  etc.
• The idea was to develop the intuition to
  understand several results in the real options
  literature
• The use of real options changes real assets
  valuation and decision making when compared with
  static NPV
• There are several other important questions
• The Visual FAQs on Real Options is a webpage
  with a growth option!
• Dont miss the new updates with the new FAQs at
• http//www.puc-rio.br/marco.ind/faqs.html