Download
1 / 33
330 likes | 482 Views
E N D
1. By: Marco Antonio Guimarćes 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
2. E&P Process As Real Options
3. 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?
4. 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
Dont 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]
5. 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)
6. 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
7. 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)
8. 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
9. 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
10. 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
11. Visualization of Revealed Scenarios: Revelation Distribution
12. Posterior Distribution x Revelation Distribution Higher volatility, higher option value. Why invest to reduce uncertainty?
13. 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 parameters
By 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
14. Oilfield Development Option and the NPV Equation
15. NPV x P Chart and the Quality of Reserve
16. Real x Risk-Neutral Simulation The GBM simulation paths: real drift = a, and the risk-neutral drift = r - d = a - p . We use the risk-neutral measure, which suppresses a risk-premium p from the real drift in the simulation.
17. 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; and
Continuous-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)
18. Best Alternative of Investment in Information
19. 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, d, s change. But these factors dont 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.
20. Combination of Uncertainties in Real Options The simulated sample paths are checked with the threshold (V/D)*
21. 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)
22. Anexos APPENDIX
SUPPORT SLIDES
23. 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:
24. 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
25. Geometric Brownian Motion Simulation
26. 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!
27. 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.
28. 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)
29. 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 alternative
30. 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.
31. 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 prices
32. Brent Oil Prices: Spot x Futures Note that the spot prices reach more extreme values than the long-term futures prices
33. Brent Oil Prices Volatility: Spot x Futures Note that the spot prices volatility is much higher than the long-term futures volatility
34. Other Parameters for the Simulation Other important parameters are the risk-free interest rate r and the dividend yield d (or convenience yield for commodities)
Even more important is the difference r - d (the risk-neutral drift) or the relative value between r and d
Pickles & Smith (Energy Journal, 1993) suggest for long-run analysis (real options) to set r = d
We suggest that option valuations use, initially, the normal value of d, 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 d range from 4 to 8% p.a.
By using r = d the risk-neutral drift is zero, which looks reasonable for a risk-neutral process
