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

E&P Process As Real Options

Delineated but undeveloped reserves Develop? “Wait and See” for better conditions?

RevisedVolume = B’ Appraisal phase: delineation of reserves

Invest in additional information?

Developed reserves Not included: Options to expand the production, stop

temporally, and abandon

Oil/Gas SuccessProbability = p

Expected Volumeof Reserves = B

Drill the wildcat (pioneer)? Wait and See? Technical uncertainty model is required

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)?

E[V]Expected Value of Project (before the information)

Investment inInformation

E[V | bad news]

E[V | neutral news]

E[V | good news]

Revealed Scenarios

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 E[X | 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 Don’t 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 E[X | I] is named here revelation distribution, that is, the distribution of RX = E[X | I]

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) = E[X g( I )]2 . The choice of g* that minimizes the error measure MSE(g) is exactly the conditional expectation E[X | 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)

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 E[E[X | I ]] = E[RX] = E[X] (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 Var[E[X | I ]] = Var[RX] = Var[X] E[Var[X | 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

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)

A B

DC

Area A: provedBA = 100 MM bbl

Area B: possible50% chances of

BB = 100 MM bbl& 50% of nothing

Area D: possible50% chances of

BD = 100 MM bbl& 50% of nothing

Area C: possible50% chances of

BC = 100 MM bbl& 50% of nothing

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)

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

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:

E1[B|A1] = 100 + 100 + (0.5 x 100) + (0.5 x 100) = 300 MM bbl In case of negative revelation (50% chances) the expected value is:

E2[B|A1] = 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: EA1[RB] = 50% x E1(B|A1) + 50% x E2(B|A1) = 250 million bbl = E[B]

As expected by Proposition 2

And the variance of the revealed scenarios is: VarA1[RB] = 50% x (300 250)2 + 50% x (200 250)2 = 2500 (MM bbl)2

Let us check if the Proposition 3 was satisfied

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

Visualization of Revealed Scenarios: Revelation Distribution

This is exactly the prior distribution of B (Prop. 1 OK!)

All th

e revelation d

istribu

tions h

ave the sam

e mean

(marin

gale): Prop

. 4 OK

!

Posterior Distribution x Revelation Distribution Higher volatility, higher option value. Why invest to reduce uncertainty?

Reduction of technical uncertainty

Increase thevariance ofrevelationdistribution(and so the option value)

Why learn?

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 parametersBy 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

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 (t) with (t = 0) = 1, given by: D(B, t) = (t). [Fixed Cost + Variable Cost x B]

D = . [ 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

NPV x P Chart and the Quality of Reserve

tangent = q . B

D

P ($/bbl)

NP

V (

mil

lion

$) Linear Equation for the NPV:

NPV = q P B D

NPV in function of P

The quality of reserve (q) is relatedwith the inclination of the NPV line

Real x Risk-Neutral Simulation The GBM simulation paths: real drift = , and the risk-neutral drift = r . We use the risk-

neutral measure, which suppresses a risk-premium from the real drift in the simulation.

0

5

10

15

20

25

30

35

40

45

0.0

0.3

0.5

0.8

1.0

1.3

1.5

1.8

2.0

2.3

2.5

2.8

3.0

3.3

3.5

3.8

4.0

4.3

4.5

4.8

5.0

5.3

5.5

5.8

6.0

Time (Years)

Oil

Pri

ce ($

/bb

l)

Real Simulation

Risk-Neutral Simulation

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; andContinuous-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)

Best Alternative of Investment in Information

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:

Where EQ is the expectation under risk-neutral measure, which is evaluated with Monte Carlo simulation, and t* is the stopping time (optimal exercise timing). For the path i:

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

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, ,

change. But these factors don’t 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.

Combination of Uncertainties in Real Options The simulated sample paths are checked with the threshold (V/D)*

A

Option F(t = 1) = V DF(t = 0) == F(t=1) * exp (r*t)

Present Value (t = 0)

B

F(t = 2) = 0ExpiredWorthless

Vt/Dt = (q Pt B)/Dt

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)

Anexos

APPENDIXSUPPORT SLIDES

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

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:

Risk reduction by the investment in information of all firms in the basin(driver is the investment, not the passage of time directly)

Project evaluation with additionalinformation(t = T)

Lower Risk

ExpectedValue

Current project evaluation(t=0)

HigherRisk

ExpectedValue

con

fid

ence

in

terv

al

Lack of Knowledge Trunk of Cone

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

Value withgood revelation

Value withbad revelation

Current project evaluation (t=0)

Investment inInformation

Project valueafter investment

t = T

Value withneutral revelation

E[V]

Geometric Brownian Motion Simulation The real simulation of a GBM uses the real drift . The price P at future time (t + 1), given the current

value Pt is given by:

Pt+1 = Pt exp{ () t + t 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 ’ = r . Why? Because by supressing a risk-premium from the real drift we get r . Proof: Total return = r + (where is the risk-premium, given by CAPM) But total return is also capital gain rate plus dividend yield: = + Hence, + r + = r

So, we use the risk-neutral equation below to simulate P

Pt+1 = Pt exp{ (r ) t + t

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!

P

E[B]Inv

Inv

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 = E[q B]

NPV = q P B up D(B) if q B > E[q B]

NPV = q P B down D(B) if q B < E[q B]

In general we have down = 1 and up < 1

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)

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 alternativeThe valuation is similar to the previously presented

Only by running the simulations is possible to compare the higher NPV versus higher flexibility

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.

A

Option F(t = 5.5) = V DF(t = 0) == F(t=5.5) * exp (r*t)

Present Value (t = 0)

B

F(t = 8) = 0Expires Worthless

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 pricesWTI Nymex Prices: Spot (First Month) vs. 18 Months

Jul/1996 - Jan/2002

5

10

15

20

25

30

35

407/

22/1

996

10/2

2/19

96

1/22

/199

7

4/22

/199

7

7/22

/199

7

10/2

2/19

97

1/22

/199

8

4/22

/199

8

7/22

/199

8

10/2

2/19

98

1/22

/199

9

4/22

/199

9

7/22

/199

9

10/2

2/19

99

1/22

/200

0

4/22

/200

0

7/22

/200

0

10/2

2/20

00

1/22

/200

1

4/22

/200

1

7/22

/200

1

10/2

2/20

01

1/22

/200

2

WT

I (U

S$/

bb

l)

WTI Nymex Spot (1st Mth) Close (US$/bbl)

WTI Nymex Mth18 Close (US$/bbl)

Brent Oil Prices: Spot x Futures Note that the spot prices reach more extreme values than the long-term

futures pricesBrent Prices: Spot (Dated) vs. IPE 12 Month

Jul/1996 - Jan/2002

5

10

15

20

25

30

35

40

7/22

/199

6

10/2

2/19

96

1/22

/199

7

4/22

/199

7

7/22

/199

7

10/2

2/19

97

1/22

/199

8

4/22

/199

8

7/22

/199

8

10/2

2/19

98

1/22

/199

9

4/22

/199

9

7/22

/199

9

10/2

2/19

99

1/22

/200

0

4/22

/200

0

7/22

/200

0

10/2

2/20

00

1/22

/200

1

4/22

/200

1

7/22

/200

1

10/2

2/20

01

1/22

/200

2

Bre

nt

(US

$/b

bl)

Brent Platt's Dated Mid (US$/bbl)

Brent IPE Mth12 Close (US$/bbl)

Brent Oil Prices Volatility: Spot x Futures Note that the spot prices volatility is much higher than the long-term

futures volatilityBrent Volatility: Spot (Dated) vs. 12 Month (500 last data)

Jul/1996 - Jan/2002

10%

15%

20%

25%

30%

35%

40%

45%

50%7/

18/1

996

10/1

8/19

96

1/18

/199

7

4/18

/199

7

7/18

/199

7

10/1

8/19

97

1/18

/199

8

4/18

/199

8

7/18

/199

8

10/1

8/19

98

1/18

/199

9

4/18

/199

9

7/18

/199

9

10/1

8/19

99

1/18

/200

0

4/18

/200

0

7/18

/200

0

10/1

8/20

00

1/18

/200

1

4/18

/200

1

7/18

/200

1

10/1

8/20

01

1/18

/200

2

Vo

lati

lity

(% p

.a.)

Brent Spot (Dated)

Brent IPE 12 Month

Other Parameters for the Simulation Other important parameters are the risk-free interest rate r

and the dividend yield (or convenience yield for commodities) Even more important is the difference r (the risk-neutral drift) or

the relative value between r and Pickles & Smith (Energy Journal, 1993) suggest for long-run

analysis (real options) to set r = “We suggest that option valuations use, initially, the ‘normal’ value of , 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 range from 4 to 8% p.a. By using r = the risk-neutral drift is zero, which looks reasonable

for a risk-neutral process