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/ : 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/ . Real Options in Petroleum: An Overview
Real Options Valuation in the New Economy
July 4-6, 2002 - Coral Beach, Cyprus
Presentation Outline : Presentation Outline Introduction and overview of real options in upstream petroleum (exploration & production)
Intuition and classical model
Stochastic processes for oil prices
Applications of real options in petroleum
Petrobras research program called “PRAVAP-14 ” Valuation of Development Projects under Uncertainties
Combination of technical and market uncertainties in most cases
Selection of mutually exclusive alternatives for oilfield development under oil price uncertainty
Exploratory investment and information revelation
Investment in information: dynamic value of information
Option to expand the production with optional wells
Managerial View of Real Options (RO) : Managerial View of Real Options (RO) RO can be viewed as an optimization problem:
Maximize the NPV (typical objective function) subject to:
(a) Market uncertainties (eg., oil price);
(b) Technical uncertainties (eg., reserve volume);
(c) Relevant Options (managerial flexibilities); and
(d) Others firms interactions (real options + game theory)
The first paper combining real options and game theory for petroleum applications was Dias (1997)
See the “drilling game” in my website (option-games)
Main Petroleum Real Options and Examples : Main Petroleum Real Options and Examples
E&P as a Sequential Real Options Process : E&P as a Sequential Real Options Process
Economic Quality of the Developed Reserve : Economic Quality of the Developed Reserve Imagine that you want to buy 100 million barrels of developed oil reserves.
Suppose that the long run oil price is 20 US$/bbl.
How much you shall pay for each barrel of developed reserve?
It depends of many technical and economic factors like:
The reservoir permo-porosity quality (productivity);
Fluids quality (heavy x light oil, etc.);
Country (fiscal regime, politic risk);
Specific reserve location (deepwaters location has higher operational cost than shallow-waters and onshore reserve);
The capital in place (extraction speed and so the present value of revenue depends of number of producing wells); etc.
Economic Quality of the Developed Reserve : Economic Quality of the Developed Reserve The relation between the value for one barrel of (sub-surface) developed reserve v and the (surface) oil price barrel P is named the economic quality of that reserve q (higher q, higher v)
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)
So, let us use the equation for NPV = V - D = q P B - D
D = development cost (investment cost or exercise price of the option)
Intuition (1): Timing Option and Oilfield Value : Intuition (1): Timing Option and Oilfield Value Assume that simple equation for the oilfield development NPV:
NPV = q B P - D = 0.2 x 500 x 18 – 1850 = - 50 million $
Do you sell the oilfield for US$ 3 million?
Suppose the following two-periods problem and uncertainty with only two scenarios at the second period for oil prices P. E[P] = 18 $/bbl
NPV(t=0) = - 50 million $ E[P+] = 19 NPV = + 50 million $ E[P-] = 17 NPV = - 150 million $ Rational manager will not exercise
this option Max (NPV-, 0) = zero Hence, at t = 1, the project NPV is positive: (50% x 50) + (50% x 0) = + 25 million $
Intuition (2): Timing Option and Waiting Value : Intuition (2): Timing Option and Waiting Value Suppose the same case but with a small positive NPV. What is better: develop now or wait and see?
NPV = q B P - D = 0.2 x 500 x 18 – 1750 = + 50 million $
Discount rate = 10% E[P] = 18 /bbl
NPV(t=0) = + 50 million $ E[P+] = 19 NPV+ = + 150 million $ Hence, at t = 1, the project NPV is: (50% x 150) + (50% x 0) = + 75 million $
The present value is: NPVwait(t=0) = 75/1.1 = 68.2 > 50 Hence is better to wait and see, exercising the option only in favorable scenario
Intuition (3): Deep-in-the-Money Real Option : Intuition (3): Deep-in-the-Money Real Option Suppose the same case but with a higher NPV.
What is better: develop now or wait and see?
NPV = q B P - D = 0.25 x 500 x 18 – 1750 = + 500 million $
Discount rate = 10% E[P] = 18 /bbl
NPV(t=0) = 500 million $ E[P+] = 19 NPV = 625 million $ Hence, at t = 1, the project NPV is: (50% x 625) + (50% x 375) = 500 million $
The present value is: NPVwait(t=0) = 500/1.1 = 454.5 < 500 Immediate exercise is optimal because this project is deep-in-the-money (high NPV)
There is a value between 50 and 500 that value of wait = exercise now (threshold)
Classical Model of Real Options in Petroleum : Classical Model of Real Options in Petroleum Paddock & Siegel & Smith wrote a series of papers on valuation of offshore reserves in 80’s (published in 87/88)
It is the best known model for oilfields development decisions
It explores the analogy financial options with real options Time to Expiration of the Option Time to Expiration of the Investment Rights (t)
Equation of the Undeveloped Reserve (F) : Equation of the Undeveloped Reserve (F) Partial (t, V) Differential Equation (PDE) for the option F
The Undeveloped Oilfield Value: Real Options and NPV : The Undeveloped Oilfield Value: Real Options and NPV Assume that V = q B P, so that we can use chart F x V or F x P
Suppose the development break-even (NPV = 0) occurs at US$15/bbl
Threshold Curve: The Optimal Decision Rule : Threshold Curve: The Optimal Decision Rule At or above the threshold line, is optimal the immediate development. Below the line: “wait, learn and see”
Stochastic Processes for Oil Prices: GBM : Stochastic Processes for Oil Prices: GBM Like Black-Scholes-Merton equation, the classical model of Paddock et al uses the popular Geometric Brownian Motion
Prices have a log-normal distribution in every future time;
Expected curve is a exponential growth (or decline);
The variance grows with the time horizon (unbounded)
Mean-Reverting Process : In this process, the price tends to revert towards 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 Mean-Reverting Process
Stochastic Processes Alternatives for Oil Prices : Stochastic Processes Alternatives for Oil Prices There are many models of stochastic processes for oil prices in real options literature. I classify them into three classes. The nice properties of Geometric Brownian Motion (few parameters, homogeneity) is a great incentive to use it in real options applications.
Pindyck (1999) wrote: “the GBM assumption is unlikely to lead to large errors in the optimal investment rule”
Nominal Prices for Brent and Similar Oils (1970-2001) : Nominal Prices for Brent and Similar Oils (1970-2001) With an adequate long-term scale, we can see that 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, 2001 Jumps-up Jumps-down
Mean-Reversion + Jumps: Dias & Rocha (98) : Mean-Reversion + Jumps: Dias & Rocha (98) We (Dias & Rocha, 1998/9) adapted the jump-diffusion idea of Merton (1976) to the oil prices case, considering:
Normal news cause only marginal adjustment in oil prices, modeled with the continuous-time process of mean-reversion
Abnormal rare news (war, OPEC surprises, ...) cause abnormal adjustment (jumps) in petroleum prices, modeled with a discrete-time Poisson process (we allow both jumps-up & jumps-down)
Model has more economic logic (supply x demand)
Normal information causes smoothing changes in oil prices (marginal variations) and means both:
Marginal interaction between production and demand;
Depletion versus new reserves discoveries in non-OPEC countries
Abnormal information means very important news:
In few months, this kind of news causes jumps in the prices, due the expected large variation in either supply or demand
Real Case with Mean-Reversion + Jumps : Real Case with Mean-Reversion + Jumps A similar process of mean-reversion with jumps was used by Dias for the equity design (US$ 200 million) of the Project Finance of Marlim Field (oil prices-linked spread)
Equity investors reward:
Basic interest-rate + spread (linked to oil business risk)
Oil prices-linked: transparent deal (no agency cost) and win-win:
Higher oil prices higher spread, and vice versa (good for both)
Deal was in December 1998 when oil price was 10 $/bbl
We convince investors that the expected oil prices curve was a fast reversion towards US$ 20/bbl (equilibrium level)
Looking the jumps-up & down, we limit the spread by putting both cap (maximum spread) and floor (to prevent negative spread)
This jumps insight proved be very important:
Few months later the oil prices jumped-up (price doubled by Aug/99)
The cap protected Petrobras from paying a very high spread
PRAVAP-14 and Real Options Projects : PRAVAP-14 and Real Options Projects PRAVAP-14 is a systemic research program named Valuation of Development Projects under Uncertainties
I coordinate this systemic project by Petrobras/E&P-Corporative
We analyzed different stochastic processes and solution methods
Stochastic processes: geometric Brownian motion; mean-reversion + jumps; three different mean-reversion models
Solution methods: Finite differences; Monte Carlo simulation for American options; and even genetic algorithms
Genetic algorithms are used for optimization: thresholds curves evolution, with the fitness evaluated by Monte Carlo simulation
I call this method of evolutionary real options (see in my website two papers on this subject)
Let us see some real options projects from Pravap-14
E&P Process and Options : E&P Process and Options Drill the wildcat (pioneer)? Wait and See?
Revelation and technical uncertainty modeling Oil/Gas Success
Probability = p Expected Volume
of Reserves = B Revised
Volume = B’ Appraisal phase: delineation of reserves
Invest in additional information? Delineated but Undeveloped Reserves.
Develop? “Wait and See” for better conditions? What is the best alternative? Developed Reserves.
Expand the production? Stop Temporally? Abandon?
Selection of Alternatives under Uncertainty : Selection of Alternatives under Uncertainty In the equation for the developed reserve value V = q P B, the economic quality of reserve (q) gives also an idea of how fast the reserve volume will be produced.
For a given reserve, if we drill more wells the reserve will be depleted faster, increasing the present value of revenues
Higher number of wells higher q higher V
However, higher number of wells higher development cost D
For the equation NPV = q P B - D, there is a trade off between q and D, when selecting the system capacity (number of wells, platform process capacity, pipeline diameter, etc.)
For the alternative “j” with n wells, we get NPVj = qj P B - Dj
The Best Alternative at Expiration (Now or Never) : The Best Alternative at Expiration (Now or Never) The chart below presents the “now-or-never” case for three alternatives. In this case, the NPV rule holds (choose the higher one).
Alternatives: A1(D1, q1); A2(D1, q1); A3(D3, q3), with D1 < D2 < D3 and q1 < q2 < q3 Hence, the best alternative depends on the oil price P. However, P is uncertain!
The Best Alternative Before the Expiration : The Best Alternative Before the Expiration Imagine that we have t years before the expiration and in addition the long-run oil prices follow the geometric Brownian
We can calculate the option curves for the three alternatives, drawing only the upper real option curve(s) (in this case only A2), see below. The decision rule is:
If P < P*2 , “wait and see”
Alone, A1 can be even deep-in-the-money, but wait for A2 is more valuable
If P = P*2 , invest now with A2
Wait is not more valuable
If P > P*2 , invest now with the higher NPV alternative (A2 or A3 )
Depending of P, exercise A2 or A3
How about the decision rule (threshold) along the time?
Threshold Curves for Three Alternatives : Threshold Curves for Three Alternatives There are regions of wait and see and others that the immediate investment is optimal for each alternative
E&P Process and Options : E&P Process and Options Drill the wildcat (pioneer)? Wait and See?
Revelation and technical uncertainty modeling Oil/Gas Success
Probability = p Expected Volume
of Reserves = B Revised
Volume = B’ Appraisal phase: delineation of reserves
Invest in additional information? Delineated but Undeveloped Reserves.
Develop? “Wait and See” for better conditions? What is the best alternative? Developed Reserves.
Expand the production? Stop Temporally? Abandon?
Technical Uncertainty and Risk Reduction : 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” idea (Amram & Kulatilaka) is adapted:
Technical Uncertainty and Revelation : 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
Valuation of Exploratory Prospect : Valuation of Exploratory Prospect Suppose that the firm has 5 years option to drill the wildcat
Other firm wants to buy the rights of the tract for 3 million $.
Do you sell? How valuable is this prospect? NPV = q P B - D = (20% . 20 . 150) - 500 = + 100 MM$
However, there is only 15% chances to find petroleum EMV = Expected Monetary Value = - IW + (CF . NPV)
EMV = - 20 + (15% . 100) = - 5 million $ Do you sell the prospect rights for US$ 3 million?
Monte Carlo Combination of Uncertainties : Monte Carlo Combination of Uncertainties Considering that: (a) there are a lot of uncertainties in that low known basin; and (b) many oil companies will drill wildcats in that area in the next 5 years:
The expectations in 5 years almost surely will change and so the prospect value
The revelation distributions and the risk-neutral distribution for oil prices are:
Real x Risk-Neutral Simulation : Real x Risk-Neutral Simulation The GBM simulation paths: one real (a) and the other risk-neutral (r - d). In reality r - d = a - p, where p is a risk-premium
A Visual Equation for Real Options : A Visual Equation for Real Options Prospect Evaluation
(in million $)
Traditional Value = - 5
Options Value (at T) = + 12.5
Options Value (at t=0) = + 7.6 Today the prospect´s EMV is negative, but there is 5 years for wildcat decision and new scenarios will be revealed by the exploratory investment in that basin. So, refuse the $ 3 million offer!
E&P Process and Options : E&P Process and Options Drill the wildcat (pioneer)? Wait and See?
Revelation and technical uncertainty modeling Oil/Gas Success
Probability = p Expected Volume
of Reserves = B Revised
Volume = B’ Appraisal phase: delineation of reserves
Invest in additional information? Delineated but Undeveloped Reserves.
Develop? “Wait and See” for better conditions? What is the best alternative? Developed Reserves.
Expand the production? Stop Temporally? Abandon?
Dynamic Value of Information : 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
How to model the technical uncertainty and its evolution after one or more investment in information?
I use the concept of revelation distribution for technical uncertainty
Revelation distribution is the distribution of conditional expectations
See details in my presentation at the Academic Conference (Saturday)
Let us see the combination of technical and market uncertanties
Combination of Uncertainties in Real Options : Combination of Uncertainties in Real Options The Vt/D sample paths are checked with the threshold (V/D)* Vt/D = (q Pt B)/D
E&P Process and Options : E&P Process and Options Drill the wildcat? Wait? Extend?
Revelation and technical uncertainty modeling Oil/Gas Success
Probability = p Expected Volume
of Reserves = B Revised
Volume = 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? Extend the option? Invest in additional information?
Option to Expand the Production : Option to Expand the Production Analyzing a deepwater project we faced two problems:
Remaining technical uncertainty of reservoirs is still important.
In this case, the best way to solve the uncertainty is not by drilling more appraisal wells. It’s better learn from the initial production profile.
In the preliminary development plan, some wells presented both reservoir risk and small NPV.
Some wells with small positive NPV (are not “deep-in-the-money”)
Depending of the information from the initial production, some wells could be not necessary or could be placed at the wrong location.
Solution: leave these wells as optional wells
Buy flexibility with an additional investment in the production system: platform with capacity to expand (free area and load)
It permits a fast and low cost future integration of these wells
The exercise of the option to drill the additional wells will depend of both market (oil prices, rig costs) and the initial reservoir production response
Oilfield Development with Option to Expand : Oilfield Development with Option to Expand The timeline below represents a case analyzed in PUC-Rio project, with time to build of 3 years and information revelation with 1 year of accumulated production The practical “now-or-never” is mainly because in many cases the effect of secondary depletion is relevant
The oil migrates from the original area so that the exercise of the option gradually become less probable (decreasing NPV)
In addition, distant exercise of the option has small present value
Recall the expenses to embed flexibility occur between t = 0 and t = 3
Secondary Depletion Effect: A Complication : Secondary Depletion Effect: A Complication With the main area production, occurs a slow oil migration from the optional wells areas toward the depleted main area It is like an additional opportunity cost to delay the exercise of the option to expand. So, the effect of secondary depletion is like the effect of dividend yield
Conclusions : Conclusions The real options models provide rich framework to consider optimal investment under uncertainty in petroleum, recognizing the managerial flexibilities
Traditional discounted cash flow is very limited and can induce to serious errors in negotiations and decisions
We saw the classical model working with the intuition
We saw different stochastic processes and different models
We got an idea about the real options research at Petrobras and PUC-Rio (PRAVAP-14)
We saw options along all petroleum E&P process
We worked mainly with models combining technical and market uncertainties (Monte Carlo for American options)
Thank you very much for your time
Anexos : Anexos APPENDIX
SUPPORT SLIDES
Managerial View of Real Options (RO) : Managerial View of Real Options (RO) RO is a modern methodology for economic evaluation of projects and investment decisions under uncertainty
RO approach complements (not substitutes) the corporate tools (yet)
Corporate diffusion of RO takes time, training, and marketing
RO considers the uncertainties and the options (managerial flexibilities), giving two linked answers:
The value of the investment opportunity (value of the option); and
The optimal decision rule (threshold curve)
When Real Options Are Valuable? : When Real Options Are Valuable? Based on the textbook “Real Options” by Copeland & Antikarov
Real options are as valuable as greater are the uncertainties and the flexibility to respond
Estimating the Underlying Asset Value : Estimating the Underlying Asset Value How to estimate the value of underlying asset V?
Transactions in the developed reserves market (USA)
v = value of one barrel of developed reserve (stochastic);
V = v B where B is the reserve volume (number of barrels);
v is ~ proportional to petroleum prices P, that is, v = q P ;
For q = 1/3 we have the one-third rule of thumb (average value in USA);
So, Paddock et al. used the concept of economic quality (q)
This is a business view on reserve value (reserves market oriented view)
Discounted cash flow (DCF) estimate of V, that is:
NPV = V - D V = NPV + D
For fiscal regime of concessions the chart NPV x P is a straight line. Let us assume that V is proportional to P
Again is used the concept of quality of reserve, but calculated from a DCF spreadsheet, largely used in oil companies.
Estimating the Model Parameters : Estimating the Model Parameters If V = k P, we have sV = sP and dV = dP (D&P p.178. Why?)
Risk-neutral Geometric Brownian: dV = (r - dV) V dt + sV V dz
Volatility of long-term oil prices (~ 20% p.a.)
For development decisions the value of the benefit is linked to the long-term oil prices, not the (more volatile) spot prices
A good market proxy is the longest maturity contract in futures markets with liquidity (Nymex 18th month; Brent 12th month)
Dividend yield (or long-term convenience yield) ~ 6% p.a.
Paddock & Siegel & Smith: equation using cash-flows
If V = k P, we can estimate d from oil prices futures market
Pickles & Smith’s Rule (1993): r = d (in the long-run)
“We suggest that option valuations use, initially, the ‘normal’ value of net convenience yield, which seems to equal approximately the risk-free nominal interest rate”
NYMEX-WTI Oil Prices: Spot x Futures : 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
Mean-Reversion + Jump: the Sample Paths : Mean-Reversion + Jump: the Sample Paths 100 sample paths for mean-reversion + jumps (l = 1 jump each 5 years)
Technical Uncertainty in New Basins : Technical Uncertainty in New Basins The number of possible scenarios to be revealed (new expectations) is proportional to the cumulative investment in information
Information can be costly (our investment) or free, from the other firms investment (free-rider) in this under-explored basin The arrival of information process leverage the option value of a tract
Simulation Issues : Simulation Issues The differences between the oil prices and revelation processes are:
Oil price (like 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
In many cases (appraisal phase) only our investment in information is relevant and it is totally controllable by us (activated by management) Let us consider that the exercise price of the option (development cost D) is function of B. So, D changes just at the information revelation on B.
In order to calculate only one development threshold we work with the normalized threshold (V/D)* that doesn´t change in the simulation
Modeling the Option to Expand : 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 (accumulated production) that reservoir information will be revealed and the revelation distributions
Define for each revealed scenario the marginal production of each optional well as function of time.
Consider the secondary depletion if we wait after learn about reservoir
Add market uncertainty (stochastic process for oil prices)
Combine uncertainties using Monte Carlo simulation
Use an 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 growing research area
Bayesian Drilling Game (Dias, 1997) : Bayesian Drilling Game (Dias, 1997) Oil exploration: with two or few oil companies exploring a basin, can be important to consider 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.
In this case the effect of the competitor presence is to increase the value of waiting to invest