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

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

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

effects

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

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

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

obligation!

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

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 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

is

- 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

option - Risk-neutral valuation is based on the absence of

arbitrage, portfolio replication (complete

market) - Incomplete markets see next FAQ

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

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?

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

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

(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

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)

Equation for Mean-Reversion Jumps

- The interpretation of the jump-reversion equation

is

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

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

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

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)

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

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

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.

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

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.

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

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)

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.

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

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

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