Visual FAQ’s on Real Options   Celebrating the Fifth Anniversary of the Website:   Real Options Approach to Petroleum Inve...
Visual FAQ’s on Real Options <ul><li>Selection of  frequently asked questions  (FAQ’s) by practitioners and academics  </l...
Visual FAQ’s on Real Options: 1 <ul><li>Are the real options premium important? </li></ul><ul><ul><li>Real Option Premium ...
Real Options Premium <ul><li>The options premium can be important or not, depending of the of the project  moneyness </li>...
Visual FAQ’s on Real Options: 2 <ul><li>What are the effects of interest rate, volatility, and other parameters in both op...
Timing Suite : Real Options Spreadsheets  <ul><li>A set of interactive Excel  spreadsheets  Timing Suite   are  used to ca...
“Timing”: Standard Version
“Timing” Standard Version: Charts
“Timing” Standard Version: Charts
Timing Suite: Others  Spreadsheets <ul><li>Timing with Two Uncertainties : </li></ul><ul><ul><li>Project value V and inves...
Visual FAQ’s on Real Options: 3 <ul><li>Where the real options value comes from?  </li></ul><ul><li>Why real options value...
Uncertainty Over the Expansion Value <ul><li>Considering combined uncertainties: in product prices and demand, exercise pr...
Option to Expand the Production <ul><li>Rational managers will not exercise the option to expand @ t = 2 years in case of ...
Real Options Asymmetry and Valuation + = Prospect Valuation Traditional Value =   5 Options Value(T)  =  + 5 <ul><li>The...
E&P Process and Options <ul><li>Drill the wildcat? Wait? Extend? </li></ul><ul><li>Revelation, option-game: waiting incent...
Option to Expand the Production <ul><li>Analyzing a large ultra-deepwater project in Campos Basin, Brazil, we faced two pr...
Modeling the Option to Expand <ul><li>Define the quantity of wells “deep-in-the-money” to start the basic investment in de...
Visual FAQ’s on Real Options: 4 <ul><li>Does risk-neutral valuation mean that investors are risk-neutral? </li></ul><ul><l...
Geometric Brownian Motion Simulation  <ul><li>The real simulation of a GBM uses the real drift   . The price at future ti...
Risk-Neutral Simulation x Real Simulation  <ul><li>For the  underlying asset , you get the same value:  </li></ul><ul><ul>...
Visual FAQ’s on Real Options: 5 <ul><li>Is possible to use real options for incomplete markets?  </li></ul><ul><li>What ch...
Incomplete Markets and Real Options <ul><li>In case of incomplete market, the  alternatives  to real options valuation are...
Visual FAQ’s on Real Options: 6 <ul><li>Is true that mean-reversion  always  reduces the options premium?  </li></ul><ul><...
Geometric Brownian Motion (GBM) <ul><li>This is the most popular stochastic process, underlying the famous Black-Scholes-M...
<ul><li>In this process, the price tends to revert toward a long-run average price  (or an  equilibrium level ) P.  </li><...
Nominal Prices for Brent and Similar Oils (1970-1999) <ul><li>We see oil prices  jumps  in both directions, depending of t...
Mean-Reversion + Jumps for Oil Prices <ul><li>Adopted in the Marlim Project Finance (equity modeling) a mean-reverting pro...
Equation for Mean-Reversion + Jumps <ul><li>The interpretation of the jump-reversion equation is: </li></ul>mean-reversion...
Mean-Reversion x GBM: Option Premium <ul><li>The chart compares mean-reversion with GBM for an at-the-money project at cur...
Mean-Reversion with Jumps x GBM <ul><li>Chart comparing mean-reversion  with jumps  versus GBM for an at-the-money project...
Mean-Reversion x GBM <ul><li>Chart comparing mean-reversion with GBM for an at-the-money project at current 15 $/bbl (supp...
Mean-Reversion with Jumps  x GBM <ul><li>Chart comparing mean-reversion with jumps versus GBM for an at-the-money project ...
Visual FAQ’s on Real Options: 7 <ul><li>How to model the effect of the competitor entry in my investment decisions? </li><...
Duopoly Entry under Uncertainty <ul><li>The leader entry threshold: both players are indifferent about to be the leader or...
Other Example: Oil Drilling Game <ul><li>Oil exploration: the waiting game of drilling </li></ul><ul><li>Two companies X a...
Visual FAQ’s on Real Options: 8 <ul><li>Does Real Options Theory (ROT) speed up the firms investments or slow down investm...
Visual FAQ’s on Real Options: 9 <ul><li>Is possible real options theory to recommend investment in a negative NPV project?...
Sequential Options (Dias, 1997) <ul><li>Traditional method, looking only expected values, undervaluate the prospect ( EMV ...
Sequential Options and Uncertainty <ul><li>Suppose that each appraisal well reveal 2 scenarios (good and bad news)   </li>...
Option to Abandon the Project <ul><li>Assume it is a “now or never” option </li></ul><ul><li>If we get continuous bad news...
Visual FAQ’s on Real Options: 10 <ul><li>Is the options decision rule (invest at or above the threshold curve) the policy ...
Thresholds: Optimum and Sub-Optima <ul><li>The theoretical optimum (red) of an American call option (real option to develo...
Optima Region <ul><li>Using a risk-neutral simulation, I find out here that the optimum is over a “plateau” (optima region...
Real Options Premium <ul><li>Now a relation optimum with option premium is clear: near of the point A (theoretical thresho...
Visual FAQ’s on Real Options: 11 <ul><li>How Real Options Sees the Choice of Mutually Exclusive Alternatives to Develop a ...
Conclusions <ul><li>The Visual FAQ’s on Real Options illustrated: </li></ul><ul><ul><li>Option premium; visual equation fo...
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香港六合彩

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香港六合彩

  1. 1. Visual FAQ’s on Real Options Celebrating the Fifth Anniversary of the Website: Real Options Approach to Petroleum Investments http://www.puc-rio.br/marco.ind/ By: Marco Antônio Guimarães Dias Petrobras and PUC-Rio, Brazil Real Options 2000 Conference Capitalizing on Uncertainty and Volatility in the New Millennium September 25, 2000  Chicago
  2. 2. Visual FAQ’s on Real Options <ul><li>Selection of frequently asked questions (FAQ’s) by practitioners and academics </li></ul><ul><ul><li>Something comprehensive but I confess some bias in petroleum questions </li></ul></ul><ul><ul><li>Use of some facilities to visual answer </li></ul></ul><ul><li>Real options models present two results: </li></ul><ul><ul><li>The value of the investment oportunity (option value) </li></ul></ul><ul><ul><ul><li>How much to pay (or sell) for an asset with options? </li></ul></ul></ul><ul><ul><li>The decision rule (thresholds) </li></ul></ul><ul><ul><ul><li>Invest now? Wait and See? Abandon? Expand the production? Switch use of an asset? </li></ul></ul></ul><ul><li>Option value and thresholds are the focus of most visual FAQ’s </li></ul>
  3. 3. Visual FAQ’s on Real Options: 1 <ul><li>Are the real options premium important? </li></ul><ul><ul><li>Real Option Premium = Real Option Value  NPV </li></ul></ul><ul><li>Answer with an analogy: </li></ul><ul><ul><li>Investments can be viewed as call options </li></ul></ul><ul><ul><ul><li>You get an operating project V (like a stock) by paying the investment cost I (exercise price) </li></ul></ul></ul><ul><ul><ul><li>Sometimes this option has a time of expiration (petroleum, patents, etc.), sometimes is perpetual (real estate, etc.) </li></ul></ul></ul><ul><ul><ul><li>Suppose a 3 years to expiration petroleum undeveloped reserve. The immediate exercise of the option gets the NPV </li></ul></ul></ul><ul><ul><ul><li>NPV = V  I </li></ul></ul></ul>
  4. 4. Real Options Premium <ul><li>The options premium can be important or not, depending of the of the project moneyness </li></ul>
  5. 5. Visual FAQ’s on Real Options: 2 <ul><li>What are the effects of interest rate, volatility, and other parameters in both option value and the decision rule? </li></ul><ul><li>Answer with “Timing Suite” </li></ul><ul><ul><li>Three spreadsheets that uses a simple model analogy of real options problem with American call option </li></ul></ul><ul><ul><li>Lets go to the Excel spreadsheets to see the effects </li></ul></ul>
  6. 6. Timing Suite : Real Options Spreadsheets <ul><li>A set of interactive Excel spreadsheets Timing Suite are used to calculate both the option value and the threshold </li></ul><ul><li>Solve American options with the analytic approximation of Barone-Adesi & Whaley (instantaneous response) </li></ul><ul><li>The underlying asset is the project value V which can be developed by investing I </li></ul><ul><li>Uncertainty: Geometric Brownian Motion, the same of Black-Scholes </li></ul><ul><li>Three spreadsheets: </li></ul><ul><ul><li>Timing (Standard) </li></ul></ul><ul><ul><li>Timing With Two Uncertainties </li></ul></ul><ul><ul><li>Timing Switch (two uncertainties) </li></ul></ul>
  7. 7. “Timing”: Standard Version
  8. 8. “Timing” Standard Version: Charts
  9. 9. “Timing” Standard Version: Charts
  10. 10. Timing Suite: Others Spreadsheets <ul><li>Timing with Two Uncertainties : </li></ul><ul><ul><li>Project value V and investment I are both stochastic </li></ul></ul><ul><ul><ul><li>Used again Barone-Adesi & Whaley but for v = V/I. </li></ul></ul></ul><ul><ul><ul><li>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) </li></ul></ul></ul><ul><li>Timing Switch: abandon and switch use decisions </li></ul><ul><ul><li>Myers & Majd (1990) model, case of two risk assets: both project and alternative asset values are uncertain </li></ul></ul><ul><ul><li>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). </li></ul></ul><ul><ul><li>Exploits analogy with American put and u se the call-put symmetry: C (V, I, r,  , T,  ) = P ( I, V,  r, T,  ) </li></ul></ul><ul><ul><ul><li>Knowing the call value you have also the put value & vice versa </li></ul></ul></ul>
  11. 11. Visual FAQ’s on Real Options: 3 <ul><li>Where the real options value comes from? </li></ul><ul><li>Why real options value is different of the static net present value (NPV)? </li></ul><ul><li>Answer with example: option to expand </li></ul><ul><ul><li>Suppose a manager embed an option to expand into her project, by a cost of US$ 1 million </li></ul></ul><ul><ul><li>The static NPV =  5 million if the option is exercise today, and in future is expected the same negative NPV </li></ul></ul><ul><ul><li>Spending a million $ for an expected negative NPV: Is the manager becoming crazy? </li></ul></ul>
  12. 12. Uncertainty Over the Expansion Value <ul><li>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 </li></ul><ul><ul><li>The traditional discount cash will not recommend to embed an option to expansion which is expected to be negative </li></ul></ul><ul><ul><li>But the expansion is an option, not an obligation! </li></ul></ul>
  13. 13. Option to Expand the Production <ul><li>Rational managers will not exercise the option to expand @ t = 2 years in case of bad news (negative value) </li></ul><ul><ul><li>Option will be exercised only if the NPV > 0. So, the unfavorable scenarios will be pruned (for NPV < 0, value = 0) </li></ul></ul><ul><ul><li>Options asymmetry leverage prospect valuation. Option = + 5 </li></ul></ul>
  14. 14. Real Options Asymmetry and Valuation + = Prospect Valuation Traditional Value =  5 Options Value(T) = + 5 <ul><li>The visual equation for “Where the options value comes from?” </li></ul>
  15. 15. E&P Process and Options <ul><li>Drill the wildcat? Wait? Extend? </li></ul><ul><li>Revelation, option-game: waiting incentives </li></ul>Oil/Gas Success Probability = p Expected Volume of Reserves = B Revised Volume = B’ <ul><li>Appraisal phase: delineation of reserves </li></ul><ul><li>Technical uncertainty: sequential options </li></ul><ul><li>Developed Reserves. </li></ul><ul><li>Expand the production? </li></ul><ul><li>Stop Temporally? Abandon? </li></ul><ul><li>Delineated but Undeveloped Reserves. </li></ul><ul><li>Develop? “Wait and See” for better conditions? Extend the option? </li></ul>
  16. 16. Option to Expand the Production <ul><li>Analyzing a large ultra-deepwater project in Campos Basin, Brazil, we faced two problems: </li></ul><ul><ul><li>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 </li></ul></ul><ul><ul><li>In the preliminary development plan, some wells presented both reservoir risk and small NPV. </li></ul></ul><ul><ul><ul><li>Some wells with small positive NPV (not “deep-in-the-money”) and others even with negative NPV </li></ul></ul></ul><ul><ul><ul><li>Depending of the initial production information, some wells can be not necessary </li></ul></ul></ul><ul><li>Solution: leave these wells as optional wells </li></ul><ul><ul><li>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 </li></ul></ul>
  17. 17. Modeling the Option to Expand <ul><li>Define the quantity of wells “deep-in-the-money” to start the basic investment in development </li></ul><ul><li>Define the maximum number of optional wells </li></ul><ul><li>Define the timing (or the accumulated production) that the reservoir information will be revealed </li></ul><ul><li>Define the scenarios (or distributions) of marginal production of each optional well as function of time. </li></ul><ul><ul><li>Consider the depletion if we wait after learn about reservoir </li></ul></ul><ul><li>Add market uncertainty (reversion + jumps for oil prices) </li></ul><ul><li>Combine uncertainties using Monte Carlo simulation ( risk-neutral simulation if possible, next FAQ) </li></ul><ul><li>Use optimization method to consider the earlier exercise of the option to drill the wells, and calculate option value </li></ul><ul><ul><li>Monte Carlo for American options is a frontier research area </li></ul></ul><ul><ul><li>Petrobras-PUC project: Monte Carlo for American options </li></ul></ul>
  18. 18. Visual FAQ’s on Real Options: 4 <ul><li>Does risk-neutral valuation mean that investors are risk-neutral? </li></ul><ul><li>What is the difference between real simulation and risk-neutral simulation? </li></ul><ul><li>Answers </li></ul><ul><ul><li>Risk-neutral valuation (RNV) does not assume investors or firms with risk-neutral preferences </li></ul></ul><ul><ul><li>RNV does not use real probabilities. It uses risk neutral probabilities (“martingale measure”) </li></ul></ul><ul><ul><li>Real simulation: real probabilities, uses real drift   </li></ul></ul><ul><ul><li>Risk-neutral simulation: the sample paths are risk-adjusted. It uses a risk-neutral drift :  ’ = r  </li></ul></ul>
  19. 19. Geometric Brownian Motion Simulation <ul><li>The real simulation of a GBM uses the real drift  . The price at future time t is given by: </li></ul><ul><ul><li>By sampling the standard Normal distribution N(0, 1) you get the values forP t </li></ul></ul><ul><ul><li>With real drift use a risk-adjusted (to P) discount rate </li></ul></ul><ul><li>The risk-neutral simulation of a GBM uses the risk-neutral drift  ’ = r  . The price at t is: </li></ul><ul><ul><li>With risk-neutral drift, the correct discount rate is the risk-free interest rate. </li></ul></ul>P t = P 0 exp{ (    )  t +  P t = P 0 exp{ ( r    )  t + 
  20. 20. Risk-Neutral Simulation x Real Simulation <ul><li>For the underlying asset , you get the same value: </li></ul><ul><ul><li>Simulating with real drift and discounting with risk-adjusted discount rate  ( where  ) </li></ul></ul><ul><ul><li>Or simulating with risk-neutral drift (r  ) but discounting with the risk-free interest rate (r) </li></ul></ul><ul><li>For an option/derivative, the same is not true: </li></ul><ul><ul><li>Risk-neutral simulation gives the correct option result (discounting with r) but the real simulation does not gives the correct value (discounting with  ) </li></ul></ul><ul><ul><li>Why? Because the risk-adjusted discount rate is “adjusted” to the underlying asset, not to the option </li></ul></ul><ul><li>Risk-neutral valuation is based on the absence of arbitrage, portfolio replication (complete market) </li></ul><ul><ul><li>Incomplete markets: see next FAQ </li></ul></ul>
  21. 21. Visual FAQ’s on Real Options: 5 <ul><li>Is possible to use real options for incomplete markets? </li></ul><ul><li>What change? What are the possible ways? </li></ul><ul><li>Answer: Yes, is possible to use. </li></ul><ul><ul><li>For incomplete markets the risk-neutral probability ( martingale measure ) is not unique </li></ul></ul><ul><ul><li>So, risk-neutral valuation is not rigorously correct because there is a lack of market values </li></ul></ul><ul><ul><li>Academics and practitioners use some ways to estimate the real option value, see next slide </li></ul></ul>
  22. 22. Incomplete Markets and Real Options <ul><li>In case of incomplete market, the alternatives to real options valuation are: </li></ul><ul><li>Assume that the market is approximately complete (your estimative of market value is reliable) and use risk-neutral valuation (with risk-neutral probability) </li></ul><ul><li>Assume firms are risk-neutral and discount with risk-free interest rate (with real probability) </li></ul><ul><li>Specify preferences (the utility function ) of single-agent or the equilibrium at detailed level (Duffie) </li></ul><ul><ul><ul><li>Used by finance academics. In practice is difficult to specify the utility of a corporation (managers, stockholders) </li></ul></ul></ul><ul><li>Use the dynamic programming framework with an exogenous discount rate </li></ul><ul><ul><ul><li>Used by academics economists: Dixit & Pindyck, Lucas, etc. </li></ul></ul></ul><ul><ul><ul><li>Corporate discount rate express the corporate preferences? </li></ul></ul></ul>
  23. 23. Visual FAQ’s on Real Options: 6 <ul><li>Is true that mean-reversion always reduces the options premium? </li></ul><ul><li>What is the effect of jumps in the options premium? </li></ul><ul><li>Answers: </li></ul><ul><ul><li>First, we’ll see some different processes to model the uncertainty over the oil prices (for example) </li></ul></ul><ul><ul><li>Second, we’ll compare the option premium for an oilfield using different stochastic processes </li></ul></ul><ul><ul><ul><li>All cases are at-the-money real options (current NPV = 0) </li></ul></ul></ul><ul><ul><ul><li>The equilibrium price is 20 $/bbl for all reversion cases </li></ul></ul></ul>
  24. 24. Geometric Brownian Motion (GBM) <ul><li>This is the most popular stochastic process, underlying the famous Black-Scholes-Merton options equation </li></ul><ul><ul><li>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 </li></ul></ul>
  25. 25. <ul><li>In this process, the price tends to revert toward a long-run average price (or an equilibrium level ) P. </li></ul><ul><ul><li>Model analogy: spring (reversion force is proportional to the distance between current position and the equilibrium level). </li></ul></ul><ul><ul><li>In this case, variance initially grows and stabilize afterwards </li></ul></ul><ul><ul><li>Charts: the variance of distributions stabilizes after t i </li></ul></ul>Mean-Reverting Process
  26. 26. Nominal Prices for Brent and Similar Oils (1970-1999) <ul><li>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 </li></ul>Jumps-up Jumps-down
  27. 27. Mean-Reversion + Jumps for Oil Prices <ul><li>Adopted in the Marlim Project Finance (equity modeling) a mean-reverting process with jumps: </li></ul><ul><li>The jump size/direction are random :  ~ 2N </li></ul><ul><li>In case of jump-up, prices are expected to double </li></ul><ul><ul><li>OBS: E(  ) up = ln2 = 0.6931 </li></ul></ul><ul><li>In case of jump-down, prices are expected to halve </li></ul><ul><ul><li>OBS: ln(½) =  ln2 =  0.6931 </li></ul></ul>(the probability of jumps) (jump size) where:
  28. 28. Equation for Mean-Reversion + Jumps <ul><li>The interpretation of the jump-reversion equation is: </li></ul>mean-reversion drift: positive drift if P < P negative drift if P > P { uncertainty over the continuous process (reversion) { variation of the stochastic variable for time interval dt uncertainty over the discrete process (jumps) continuous ( diffusion ) process discrete process ( jumps )
  29. 29. Mean-Reversion x GBM: Option Premium <ul><li>The chart compares mean-reversion with GBM for an at-the-money project at current 25 $/bbl </li></ul><ul><ul><li>NPV is expected to revert from zero to a negative value </li></ul></ul>Reversion in all cases: to 20 $/bbl
  30. 30. Mean-Reversion with Jumps x GBM <ul><li>Chart comparing mean-reversion with jumps versus GBM for an at-the-money project at current 25 $/bbl </li></ul><ul><ul><li>NPV still is expected to revert from zero to a negative value </li></ul></ul>
  31. 31. Mean-Reversion x GBM <ul><li>Chart comparing mean-reversion with GBM for an at-the-money project at current 15 $/bbl (suppose) </li></ul><ul><ul><li>NPV is expected to revert from zero to a positive value </li></ul></ul>
  32. 32. Mean-Reversion with Jumps x GBM <ul><li>Chart comparing mean-reversion with jumps versus GBM for an at-the-money project at current 15 $/bbl (suppose) </li></ul><ul><ul><li>Again NPV is expected to revert from zero to a positive value </li></ul></ul>
  33. 33. Visual FAQ’s on Real Options: 7 <ul><li>How to model the effect of the competitor entry in my investment decisions? </li></ul><ul><li>Answer : option-games, the combination of the </li></ul><ul><li>real options with game-theory </li></ul><ul><ul><li>First example: Duopoly under Uncertainty (Dixit & Pindyck, 1994; Smets, 1993) </li></ul></ul><ul><ul><ul><li>Demand for a product follows a GBM </li></ul></ul></ul><ul><ul><ul><li>Only two players in the market for that product (duopoly) </li></ul></ul></ul>
  34. 34. Duopoly Entry under Uncertainty <ul><li>The leader entry threshold: both players are indifferent about to be the leader or the follower. </li></ul><ul><ul><li>Entry: NPV > 0 but earlier than monopolistic case </li></ul></ul>
  35. 35. Other Example: Oil Drilling Game <ul><li>Oil exploration: the waiting game of drilling </li></ul><ul><li>Two companies X and Y with neighbor tracts and correlated oil prospects: drilling reveal information </li></ul><ul><ul><li>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. </li></ul></ul><ul><ul><li>Here the effect of the competitor presence is the opposite: to increase the value of waiting to invest </li></ul></ul>Company X tract Company Y tract
  36. 36. Visual FAQ’s on Real Options: 8 <ul><li>Does Real Options Theory (ROT) speed up the firms investments or slow down investments? </li></ul><ul><li>Answer: depends of the kind of investment </li></ul><ul><ul><li>ROT speeds up today strategic investments that create options to invest in the future. Examples: investment in capabilities, training, R&D, exploration, new markets... </li></ul></ul><ul><ul><li>ROT slows down large irreversible investment of projects with positive NPV but not “deep in the money” </li></ul></ul><ul><ul><li>Large projects but with high profitability (“deep in the money”) must be done by both ROT and static NPV. </li></ul></ul>
  37. 37. Visual FAQ’s on Real Options: 9 <ul><li>Is possible real options theory to recommend investment in a negative NPV project? </li></ul><ul><li>Answer: yes, mainly sequential options with investment revealing new informations </li></ul><ul><ul><li>Example: exploratory oil prospect (Dias 1997) </li></ul></ul><ul><ul><ul><li>Suppose a “now or never” option to drill a wildcat </li></ul></ul></ul><ul><ul><ul><li>Static NPV is negative and traditional theory recommends to give up the rights on the tract </li></ul></ul></ul><ul><ul><ul><li>Real options will recommend to start the sequential investment, and depending of the information revealed, go ahead (exercise more options) or stop </li></ul></ul></ul>
  38. 38. Sequential Options (Dias, 1997) <ul><li>Traditional method, looking only expected values, undervaluate the prospect ( EMV =  5 MM US$ ): </li></ul><ul><ul><li>There are sequential options, not sequential obligations; </li></ul></ul><ul><ul><li>There are uncertainties, not a single scenario. </li></ul></ul>( 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$
  39. 39. Sequential Options and Uncertainty <ul><li>Suppose that each appraisal well reveal 2 scenarios (good and bad news) </li></ul><ul><li>development option will not be exercised by rational managers </li></ul><ul><li>option to continue the appraisal phase will not be exercised by rational managers </li></ul>
  40. 40. Option to Abandon the Project <ul><li>Assume it is a “now or never” option </li></ul><ul><li>If we get continuous bad news, is better to stop investment </li></ul><ul><li>Sequential options turns the EMV to a positive value </li></ul><ul><li>The EMV gain is </li></ul><ul><li> 3.25  5) = $ 8.25 being: </li></ul>(Values in millions) $ 2.25 stopping development $ 6 stopping appraisal $ 8.25 total EMV gain
  41. 41. Visual FAQ’s on Real Options: 10 <ul><li>Is the options decision rule (invest at or above the threshold curve) the policy to get the maximum option value? </li></ul><ul><li>How much value I lose if I invest a little above or little below the optimum threshold? </li></ul><ul><li>Answer: yes, investing at or above the threshold line you maximize the option value. </li></ul><ul><li>But sometimes you don’t lose much investing near of the optimum (instead at the optimum) </li></ul><ul><ul><li>Example: oilfield development as American call option. Suppose oil prices follow a GBM to simplify. </li></ul></ul>
  42. 42. Thresholds: Optimum and Sub-Optima <ul><li>The theoretical optimum (red) of an American call option (real option to develop an oilfield) and the sub-optima thresholds (~10% above and below) </li></ul>
  43. 43. Optima Region <ul><li>Using a risk-neutral simulation, I find out here that the optimum is over a “plateau” (optima region) not a “hill” </li></ul><ul><li>So, investing ~ 10% above or below the theoretical optimum gets rough the same value </li></ul>
  44. 44. Real Options Premium <ul><li>Now a relation optimum with option premium is clear: near of the point A (theoretical threshold) the option premium can be very small. </li></ul>
  45. 45. Visual FAQ’s on Real Options: 11 <ul><li>How Real Options Sees the Choice of Mutually Exclusive Alternatives to Develop a Project? </li></ul><ul><li>Answer: very interesting and important application </li></ul><ul><ul><li>Petrobras-PUC is starting a project to compare alternatives of development, alternatives of investment in information, alternatives with option to expand, etc. </li></ul></ul><ul><ul><li>One simple model is presented by Dixit (1993). </li></ul></ul><ul><ul><ul><li>Let see directly in the website this model </li></ul></ul></ul>
  46. 46. Conclusions <ul><li>The Visual FAQ’s on Real Options illustrated: </li></ul><ul><ul><li>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. </li></ul></ul><ul><ul><li>The idea was to develop the intuition to understand several results in the real options literature </li></ul></ul><ul><ul><li>The use of real options changes real assets valuation and decision making when compared with static NPV </li></ul></ul><ul><li>There are several other important questions </li></ul><ul><ul><li>The Visual FAQ’s on Real Options is a webpage with a growth option! </li></ul></ul><ul><ul><li>Don’t miss the new updates with the new FAQ’s at: </li></ul></ul><ul><ul><ul><li>http://www.puc-rio.br/marco.ind/faqs.html </li></ul></ul></ul>

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