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Visual FAQ


Visual FAQ s on Real Options Celebrating the Fifth Anniversary of the Website: Real Options Approach to Petroleum Investments – PowerPoint PPT presentation

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Title: Visual FAQ

Visual FAQs on Real Options Celebrating the
Fifth Anniversary of the Website Real Options
Approach to Petroleum Investmentshttp//www.puc-r
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

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
  • How much to pay (or sell) for an asset with
  • 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

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

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

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

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)

Timing Standard Version
Timing Standard Version Charts
Timing Standard Version Charts
Timing Suite Others Spreadsheets
  • Timing with Two Uncertainties
  • Project value V and investment I are both
  • 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

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?

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

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

Real Options Asymmetry and Valuation
  • The visual equation for Where the options value
    comes from?

Prospect Valuation Traditional Value - 5
Options Value(T) 5
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?

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

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
  • 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

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

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

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
  • Risk-neutral valuation is based on the absence of
    arbitrage, portfolio replication (complete
  • Incomplete markets see next FAQ

Visual FAQs on Real Options 5
  • Is possible to use real options for incomplete
  • 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

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
  • 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
  • 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

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
  • Answers
  • First, well see some different processes to
    model the uncertainty over the oil prices (for
  • 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

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

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

Nominal Prices for Brent and Similar Oils
  • 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

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
  • OBS E(f)up ln2 0.6931
  • In case of jump-down, prices are expected to
  • OBS ln(½) - ln2 - 0.6931

(jump size)
Equation for Mean-Reversion Jumps
  • The interpretation of the jump-reversion equation

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

Reversion in all cases to 20 /bbl
Mean-Reversion with Jumps x GBM
  • Chart comparing mean-reversion with jumps versus
    GBM for an at-the-money project at current 25
  • NPV still is expected to revert from zero to a
    negative value

Mean-Reversion x GBM
  • Chart comparing mean-reversion with GBM for an
    at-the-money project at current 15 /bbl
  • NPV is expected to revert from zero to a positive

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

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

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
  • 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

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
  • Large projects but with high profitability (deep
    in the money) must be done by both ROT and
    static NPV.

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
  • Static NPV is negative and traditional theory
    recommends to give up the rights on the tract
  • Real options will recommend to start the
    sequential investment, and depending of the
    information revealed, go ahead (exercise more
    options) or stop

Sequential Options (Dias, 1997)
Compact Decision-Tree
Note in million US
( Developed Reserves Value )
( Appraisal Investment 3 wells )
( Development Investment )
EMV - 15 20 x (400 - 50 - 300) ? EMV - 5
( Wildcat Investment )
  • Traditional method, looking only expected values,
    undervaluate the prospect (EMV - 5 MM US)
  • There are sequential options, not sequential
  • There are uncertainties, not a single scenario.

Sequential Options and Uncertainty
  • Suppose that each appraisal well reveal 2
    scenarios (good and bad news)
  • development option will not be exercised by
    rational managers
  • option to continue the appraisal phase
    will not be exercised by rational managers

Option to Abandon the Project
  • Assume it is a now or never option
  • If we get continuous bad news, is better to stop
  • Sequential options turns the EMV to a positive
  • 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)
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

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)

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

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.

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
  • 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

  • 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,
  • The idea was to develop the intuition to
    understand several results in the real options
  • 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//
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