Visual FAQ’s on Real OptionsVisual FAQ’s on Real Options Celebrating the Fifth Anniversary of the Website:Celebrating the Fifth Anniversary of the Website:

Real Options Approach to Petroleum InvestmentsReal Options Approach to Petroleum Investments

http://www.puc-rio.br/marco.ind/http://www.puc-rio.br/marco.ind/

By: Marco Antônio Guimarães DiasPetrobras and PUC-Rio, Brazil

Real Options 2000 ConferenceReal Options 2000 ConferenceCapitalizing on Uncertainty and Volatility in the New MillenniumCapitalizing on Uncertainty and Volatility in the New Millennium

September 25, 2000 September 25, 2000 Chicago Chicago

Visual FAQ’s on Real OptionsVisual FAQ’s on Real Options Selection of frequently asked questions (FAQ’s) 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 FAQ’s

Visual FAQ’s on Real Options: 1Visual FAQ’s 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 PremiumReal Options Premium The options premium can be important or not, depending of the of the project moneyness

Visual FAQ’s on Real Options: 2Visual FAQ’s 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

Visual FAQ’s on Real Options: 3Visual FAQ’s 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 ValueUncertainty 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!

Option to Expand the ProductionOption to Expand the Production Rational managers will not exercise the option to expand @ t = 2 years in case of bad news (negative value)

Option will be exercised only if the NPV > 0. So, the unfavorable scenarios will be pruned (for NPV < 0, value = 0) Options asymmetry leverage prospect valuation. Option = + 5

Real Options Asymmetry and ValuationReal Options Asymmetry and Valuation

+

=Prospect Valuation

Traditional Value = 5

Options Value(T) = + 5

The visual equation for “Where the options value comes from?”

E&P Process and OptionsE&P Process and Options Drill the wildcat? Wait? Extend? Revelation, option-game: waiting incentives

Oil/Gas SuccessProbability = p

Expected Volumeof Reserves = B

RevisedVolume = B’ Appraisal phase: delineation of reserves

Technical uncertainty: sequential options

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

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

option?

Option to Expand the ProductionOption 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 NPVDepending 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 ExpandModeling 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

Visual FAQ’s on Real Options: 4Visual FAQ’s 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 Risk-neutral simulation: the sample paths are risk-adjusted.

It uses a risk-neutral drift: ’ = r

Geometric Brownian Motion Simulation Geometric Brownian Motion Simulation The real simulation of a GBM uses the real drift . The price at future time t is

given by:

Pt = P0 exp{ () t + t 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 ’ = r . The price at t is:

Pt = P0 exp{ (r ) t + t With risk-neutral drift, the correct discount rate is the risk-free interest rate.

Risk-Neutral Simulation x Real Simulation 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 ( where ) Or simulating with risk-neutral drift (r ) 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 ) 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

Visual FAQ’s on Real Options: 5Visual FAQ’s 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

Incomplete Markets and Real OptionsIncomplete 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?

Visual FAQ’s on Real Options: 6Visual FAQ’s 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, we’ll see some different processes to model the

uncertainty over the oil prices (for example) Second, we’ll compare the option premium for an

oilfield using different stochastic processesAll cases are at-the-money real options (current NPV = 0)The equilibrium price is 20 $/bbl for all reversion cases

Geometric Brownian Motion (GBM)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

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

Mean-Reverting ProcessMean-Reverting Process

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

Jumps-up Jumps-down

Mean-Reversion + Jumps for Oil PricesMean-Reversion + Jumps for Oil Prices Adopted in the Marlim Project Finance (equity

modeling) a mean-reverting process with jumps:

The jump size/direction are random: ~ 2N

In case of jump-up, prices are expected to double OBS: E()up = ln2 = 0.6931

In case of jump-down, prices are expected to halve OBS: ln(½) = ln2 = 0.6931

where:(the probability of jumps)

(jump size)

Equation for Mean-Reversion + JumpsEquation for Mean-Reversion + Jumps The interpretation of the jump-reversion equation is:

mean-reversion drift:positive drift if P < Pnegative drift if P > P

{uncertainty overthe continuous

process (reversion){variation of thestochastic variablefor time interval dt

uncertainty overthe discreteprocess (jumps)

continuous (diffusion) process

discreteprocess(jumps)

Mean-Reversion x GBM: Option PremiumMean-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

Mean-Reversion with Jumps x GBMMean-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

Mean-Reversion x GBMMean-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

Mean-Reversion with Jumps x GBMMean-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 FAQ’s on Real Options: 7Visual FAQ’s 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 GBMOnly two players in the market for that product (duopoly)

Duopoly Entry under UncertaintyDuopoly Entry under Uncertainty The leader entry threshold: both players are indifferent about to be the leader or the follower.

Entry: NPV > 0 but earlier than monopolistic case

Other Example: Oil Drilling GameOther 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 X’s 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

Company X tractCompany X tract Company Y tractCompany Y tract

Visual FAQ’s on Real Options: 8Visual FAQ’s 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, R&D, 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.

Visual FAQ’s on Real Options: 9Visual FAQ’s 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 wildcatStatic NPV is negative and traditional theory recommends to give

up the rights on the tractReal 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)Sequential Options (Dias, 1997)

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.

( Wildcat Investment )

( Developed Reserves Value )

( Appraisal Investment: 3 wells )

( Development Investment )

Note: in million US$“Compact Decision-Tree”

EMV = 15 + [20% x (400 50 300)] EMV = 5 MM$

Sequential Options and UncertaintySequential 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 ProjectOption 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:

(Values in millions)

$ 2.25 stopping development

$ 6 stopping appraisal

$ 8.25 total EMV gain

Visual FAQ’s on Real Options: 10Visual FAQ’s 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 don’t 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.

Thresholds: Optimum and Sub-OptimaThresholds: 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 RegionOptima 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 PremiumReal 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 FAQ’s on Real Options: 11Visual FAQ’s 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

ConclusionsConclusions The Visual FAQ’s 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 FAQ’s on Real Options is a webpage with a growth

option! Don’t miss the new updates with the new FAQ’s at:

http://www.puc-rio.br/marco.ind/faqs.html