
Real Options in Theory and Practice
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Content
- Cover
- Real Options in Theory and Practice
- Copyright
- Dedication
- Preface
- Acknowledgments
- Contents
- 1. Introduction
- 1.1 THE AIM OF REAL OPTIONS ANALYSIS
- 1.2 PLACING REAL OPTIONS ANALYSIS IN CONTEXT
- 1.2.1 Static DCF Analysis
- 1.2.2 Decision Tree Analysis
- 1.2.3 Real Options Analysis
- 1.3 OUTLINE OF THE BOOK
- 1.4 SPREADSHEETS
- Part I. FOUNDATIONS
- 2. The Modeling Framework
- 2.1 CHOOSING AN OBJECTIVE FUNCTION
- 2.1.1 Shareholder Unanimity
- 2.1.2 A Special Case: The Net Present Value Rule
- 2.1.3 Calculating the Objective Function
- 2.2 MODELING RISK AND TIME
- 2.3 STATIC VERSUS DYNAMIC DECISION MAKING
- 2.4 PROBLEMS
- 3. Valuing Single-period Cash Flows
- 3.1 ARBITRAGE-FREE ASSET PRICES
- 3.2 VALUATIONWHENTHE STATE VARIABLE IS THE PRICE OF A TRADED ASSET
- 3.3 VALUATION USING FORWARD AND FUTURES CONTRACTS
- 3.4 VALUATIONWHENTHE STATE VARIABLE IS NOT NECESSARILY THE PRICE OF A TRADED ASSET
- 3.4.1 Capital Asset Pricing Model
- 3.4.2 Risk-neutral Probabilities Implied by the CAPM
- 3.5 SUMMARIZING THE VALUATION APPROACH
- 3.6 PROBLEMS
- 3.A APPENDIX
- 3.A.1 The Fundamental Asset Pricing Formula
- 3.A.2 Properties of the Risk-neutral Probabilities
- 3.A.3 The Certainty-equivalent Form of the CAPM
- 3.A.4 The RADR Form of the CAPM
- 4. Valuing Multi-period Cash Flows
- 4.1 VALUING DISTANT CASH FLOWS USING BACKWARD INDUCTION
- 4.2 TWO SITUATIONS WHERE VALUATION CAN BE STREAMLINED
- 4.2.1 A "One-shot" Valuation Approach
- 4.2.2 Valuing Cash Flows that are Proportional to the State Variable
- 4.3 VALUING MULTI-PERIOD CASH FLOWS AS PORTFOLIOS
- 4.3.1 The Portfolio Approach
- 4.3.2 Relationship with Static DCF Analysis
- 4.3.3 Valuing Annuities
- 4.4 VALUING MULTI-PERIOD CASH FLOWS USINGBACKWARDINDUCTION
- 4.5 SUMMARIZING THE VALUATION APPROACH
- 4.6 PROBLEMS
- 4.A APPENDIX: THE RADR FORM OF THE CAPM
- 4.B APPENDIX: VALUATION WITH PERSONAL TAXES
- 4.B.1 Risk-neutral Pricing Formula
- 4.B.2 Valuation when the State Variable is the Price of a Traded Asset
- 4.B.3 Valuation Using the CAPM
- 5. Combining Valuation and Decision Making
- 5.1 A SIMPLE EXAMPLE OF A REAL OPTION
- 5.1.1 Invest Now or Not at All
- 5.1.2 Invest Now or Wait and See
- 5.2 DECISION TREES
- 5.3 FUNDAMENTAL VALUATION EQUATION
- 5.4 FILLING IN THE TREES USING DYNAMIC PROGRAMMING
- 5.5 SUMMARIZING OUR APPROACH TO ANALYZING REAL OPTIONS
- 5.6 PROBLEMS
- Part II.COMPONENT REAL OPTIONS
- 6. Options that do not Affect the State of a Project
- 6.1 EXAMPLES OF OPTIONS THAT DO NOT AFFECT THE STATE OF A PROJECT
- 6.2 SOLVING THE PRODUCTION-SUSPENSION PROBLEM
- 6.2.1 Setting Up the Production-suspension Problem
- 6.2.2 Valuation without the Suspension Option
- 6.2.3 Valuation with the Suspension Option
- 6.2.4 A Numerical Example
- 6.2.5 Can we Use Static DCF Analysis to Examine this Problem?
- 6.3 SOLVING PROBLEMS INVOLVING OPTIONS THAT DO NOT AFFECT THE STATE OF A PROJECT
- 6.4 PROBLEMS
- 7. Simple Timing Options
- 7.1 EXAMPLES OF SIMPLE TIMING OPTIONS
- 7.1.1 The Optimal Time to Invest
- 7.1.2 The Optimal Time to Abandon
- 7.1.3 The Optimal Time to Act when Success is Uncertain
- 7.1.4 The General Simple Timing Option Problem
- 7.2 SOLVING THE INVESTMENT TIMING PROBLEM
- 7.2.1 Setting Up the Investment Timing Problem
- 7.2.2 Analyzing the Investment Timing Problem
- 7.2.3 A Numerical Example
- 7.2.4 Asymmetric Risk and the Value of Waiting
- 7.2.5 Extension: Construction Takes Multiple Periods
- 7.3 SOLVING THE ABANDONMENT TIMING PROBLEM
- 7.3.1 Setting Up the Abandonment Timing Problem
- 7.3.2 Valuing the Project when Production Cannot be Abandoned
- 7.3.3 Valuing the Project when Production Can be Abandoned
- 7.3.4 A Numerical Example
- 7.3.5 Extension: Abandonment Takes Multiple Periods
- 7.4 SOLVING THE R&D TIMING PROBLEM
- 7.4.1 Setting Up the R&D Timing Problem
- 7.4.2 Analyzing the R&D Timing Problem
- 7.4.3 A Numerical Example
- 7.5 SOLVING PROBLEMS INVOLVING SIMPLE TIMING OPTIONS
- 7.6 PROBLEMS
- 8.Compound Timing Options
- 8.1 EXAMPLES OF COMPOUND TIMING OPTIONS
- 8.1.1 Sequential Investment
- 8.1.2 Resource Extraction
- 8.1.3 Sequential Actions when Success is Uncertain
- 8.1.4 The General Compound Timing Option Problem
- 8.2 SOLVING THE SEQUENTIAL INVESTMENT PROBLEM
- 8.2.1 Setting Up the Sequential Investment Problem
- 8.2.2 Analyzing the Sequential Investment Problem
- 8.2.3 A Numerical Example
- 8.2.4 Determinants of Option Value: Capital Expenditure Profile
- 8.3 SOLVING THE RESOURCE EXTRACTION PROBLEM
- 8.3.1 Setting Up the Resource Extraction Problem
- 8.3.2 Analyzing the Resource Extraction Problem
- 8.3.3 A Numerical Example
- 8.3.4 Valuing Copper Reserves
- 8.4 SOLVING THE MULTI-STAGE R&D TIMING PROBLEM
- 8.4.1 Setting Up the R&D Timing Problem
- 8.4.2 Analyzing the R&D Timing Problem
- 8.4.3 A Numerical Example
- 8.5 SOLVING PROBLEMS INVOLVING COMPOUND TIMING OPTIONS
- 8.6 PROBLEMS
- 9. Über-compound Timing Options
- 9.1 EXAMPLES OF ÜBER-COMPOUND TIMING OPTIONS
- 9.1.1 Extending the Simple Timing Options of Chapter 7
- 9.1.2 Extending the Compound Timing Options of Chapter 8
- 9.1.3 The General Über-compound Timing Option Problem
- 9.2 SOLVING THE LAND-DEVELOPMENT PROBLEM
- 9.2.1 Setting Up the Land-development Problem
- 9.2.2 Valuing the Land when the Decision Cannot be Delayed
- 9.2.3 Valuing the Land when the Decision Can be Delayed
- 9.2.4 A Numerical Example
- 9.3 SOLVING THE TIME-TO-BUILD PROBLEM
- 9.3.1 Setting Up the Time-to-build Problem
- 9.3.2 Analyzing the Time-to-build Problem
- 9.3.3 A Numerical Example
- 9.4 SOLVING PROBLEMS INVOLVINGÜBER-COMPOUNDTIMING OPTIONS
- 9.5 PROBLEMS
- 10. Switching Options
- 10.1 EXAMPLES OF SWITCHING OPTIONS
- 10.1.1 The Option to Switch between Two States
- 10.1.2 The Option to Switch between Multiple States
- 10.1.3 The General Switching Option Problem
- 10.2 SOLVING THE PRODUCTION-SUSPENSION PROBLEM
- 10.2.1 Setting Up the Production-suspension Problem
- 10.2.2 Analyzing the Production-suspension Problem
- 10.2.3 A Numerical Example
- Optimal Switching in the Absence of Frictions
- The Impact of Switching Costs
- 10.2.4 The Trade-off between Wages and Severance Pay
- 10.3 SOLVING THE MACHINERY-REPLACEMENT PROBLEM
- 10.3.1 Setting Up the Machinery-replacement Problem
- 10.3.2 Static DCF Analysis
- 10.3.3 Real Options Analysis
- 10.3.4 A Numerical Example
- 10.4 SOLVING PROBLEMS INVOLVING SWITCHING OPTIONS
- 10.5 PROBLEMS
- 11. Learning Options
- 11.1 EXAMPLES OF LEARNING OPTIONS
- 11.2 MODELING INFORMATION GATHERING
- 11.2.1 Generalizing our Concept of the "State of the Project"
- 11.2.2 Using Bayes' Theorem
- 11.3 STAGING THE ROLL-OUT OF A NEW VENTURE
- 11.3.1 Setting Up the Roll-out Problem
- 11.3.2 Analyzing the Roll-out Problem
- 11.3.3 A Numerical Example
- 11.4 SOLVING THE OIL EXPLORATION PROBLEM
- 11.4.1 Setting Up the Oil Exploration Problem
- 11.4.2 Analyzing the Oil Exploration Problem
- 11.4.3 A Numerical Example
- 11.5 SOLVING PROBLEMS INVOLVING LEARNING OPTIONS
- 11.6 PROBLEMS
- Part III. CALIBRATING THE MODEL
- 12. Calibration Using Spot and FuturesPrice Data
- 12.1 CALIBRATING A TREE OF PRICES USING HISTORICAL DATA
- 12.1.1 A Price that Follows a Random Walk
- Step 1: Going from the Data to Normalized Estimates of the Parameters
- Step 2: Going from Normalized Estimates to the Tree for the Price
- Step 3: Calculating the Probabilities of Up and Down Moves
- 12.1.2 A Price that is Mean Reverting
- Step 1: Going from the Data to Normalized Estimates of the Parameters
- Step 2: Going from Normalized Estimates to the Tree for the Price
- Step 3: Calculating the Probabilities of Up and Down Moves
- 12.2 CALIBRATING RISK-NEUTRAL PROBABILITIES
- 12.2.1 Using the CAPM
- 12.2.2 Matching the Relationship between Spot and Futures Prices
- 12.2.3 Matching the Current Term Structure of Futures Prices
- 12.3 DECIDING WHICH APPROACH TO USE
- 12.4 PROBLEMS
- 12.A APPENDIX
- 12.A.1 Mean and Variance of Changes in the Log Price
- A Price that Follows a Random Walk
- A Price that is Mean Reverting
- 12.A.2 Truncating the Binomial Tree
- 12.A.3 Estimating Beta when the Spot Price is Mean Reverting
- 12.A.4 Matching the Current Term Structure of Futures Prices
- 13. Calibration Using Option Price Data
- 13.1 IMPLIED VOLATILITY
- 13.2 IMPLIED BINOMIAL TREES: EUROPEAN OPTIONS
- 13.2.1 Estimating the Risk-neutral Probability of Reaching Each Terminal Node
- 13.2.2 Filling in the Remainder of the Futures Price Tree
- 13.3 IMPLIED BINOMIAL TREES: AMERICAN OPTIONS
- 13.4 FROM A FUTURES-PRICE TREE TO A STATE-VARIABLE TREE
- 13.5 PROBLEMS
- 13.A APPENDIX
- 13.A.1 Risk-neutral Probabilities when the State Variable is a Futures Price
- 13.A.2 Rubinstein's Implied Binomial Tree
- 13.A.3 Properties of the State-variable Tree
- 14. Calibrating Trees of Alternative StateVariables
- 14.1 NON-PRICE STATE VARIABLES
- 14.1.1 Calibrating the Tree for the State Variable
- 14.1.2 Calibrating Risk-neutral Probabilities
- 14.2 MARKET VALUES AS STATE VARIABLES
- 14.2.1 Using Comparison Firms
- 14.2.2 Enterprise Value versus Equity Value
- 14.2.3 Estimating Volatility
- 14.2.4 Estimating Risk-neutral Probabilities
- 14.3 THE CHOICE OF STATE VARIABLE
- 14.4 PROBLEMS
- 14.A APPENDIX: CALCULATING ENTERPRISE RETURNS
- Part IV. PUTTING THE PIECES TOGETHER
- 15. Forestry Management and Valuation
- 15.1 SETTING UP THE MODEL
- 15.2 THE SOLUTION PROCEDURE
- 15.3 DATA AND CALIBRATION
- 15.4 RESULTS
- Estimating the Market Value of Bare Land
- Valuing the Trees Currently on the Land
- The Value of Flexibility
- The Effect of Different Sized Binomial Trees
- 15.5 PROBLEMS
- 16. Developing a Gas Field
- 16.1 SETTING UP THE MODEL
- 16.2 THE SOLUTION PROCEDURE
- 16.3 DATA AND CALIBRATION
- 16.4 RESULTS
- Optimal Development of the Gas Field
- The Effect of Volatility in the Market Value of Developed Reserves
- The Effect of Development-cost Risk
- 16.5 PROBLEMS
- 16.A APPENDIX: THE DISTRIBUTION OF THE DEVELOPMENT TIME
- 17.Mothballing an Ethanol Plant
- 17.1 SETTING UP THE MODEL
- 17.2 THE SOLUTION PROCEDURE
- 17.3 DATA AND CALIBRATION
- Constructing Spot and Futures Gross Processing Margins
- Calibrating the Binomial Tree for the State Variable
- Calibrating the Risk-neutral Probabilities
- Calibrating the Remaining Parameters
- 17.4 RESULTS
- Choosing the Step Size
- Should the Plant be Mothballed?
- How Much is the Plant Worth?
- 17.5 PROBLEMS
- 18.Where to from Here?
- 18.1 IMPROVED NUMERICAL ALGORITHMS
- 18.2 GREATER ECONOMETRIC SOPHISTICATION
- 18.3 MULTIPLE STATE VARIABLES
- Bibliography
- Index
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