# Real Options in Capital Investment: Models, Strategies, and Applications

By Lenos Trigeorgis | Go to book overview

APPENDIX

This Appendix describes the price model and the valuation method used in the analysis, and also presents the comparative statics for different reference times.

A.1 The Price Process

The price model is formulated in terms of the evolution of the price expectations. The information needed to determine the revision of future expectations is assumed to be provided by the most recent unanticipated revision in the expectation of the current price. For any given period, s to s + ds, the revision of expectations for all times at or after s + ds is determined by a normal random variable, dzs, having zero expectation and variance ds. This variable represents information coming from the output market during the period just after time s, in the form of the final movement in the expectation for the price at the end of that period. It is independent of the other dzs, because each dz represents new information at a different time.

The revision of each price expectation is modeled to be proportional to the expectation of that price at the beginning of the period and to the normalized information for that period. Thus, given the expectation at the beginning of period's for the price that will occur at time t, Es(Pt), the change over that period in the expectation of that price is:

dEs(Pt) = Es(Pt)σs,tdzs, (11.A1)

where the proportionality constant σs,t is the volatility of the expectation of the price at, time t in the period beginning at time s.

Two restrictions are placed on the form of the volatility of σs,t (see Jacoby and Laughton, 1991). First, σs,t at any future time's must be modeled as known with certainty at the time of the analysis, namely, it may not vary according to the state of the economy at the time s. This assumption allows the use of a simple nonstochastic discounting model in the valuation. Second, the decay in the volatility term structure is expressed by an exponential form,

σs,t = σs exp[-γ(t - s)], (11.A2)

where 7 is the rate of decay. As noted, the amount of reversion may also be measured by the half-life H of the decay process, where H ≡ 1n(2)/γ. In Laughton and Jacoby ( 1993) it was shown that a one-dimensional state space, indexed by the contemporaneous price, occurs only for price models from a slightly more general class of processes among those with multivariate lognormal probability measures.

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Real Options in Capital Investment: Models, Strategies, and Applications

• Title Page iii
• Contents v
• Tables and Figures ix
• Preface xiii
• Chapter 1 Real Options: An Overview 1
• Introduction 1
• Acknowledgments 28
• Notes 28
• Part I Real Options and Alternative Valuation Paradigms 29
• Chapter 2 Methods for Evaluating Capital Investment Decisions Under Uncertainty 31
• Introduction 31
• Conclusion 44
• Notes 45
• Chapter 3 Merging Finance Theory and Decision Analysis 47
• Introduction 47
• Summary and Conclusion 65
• Acknowledgments 66
• Notes 66
• Chapter 4 The Strategic Capital Budgeting Process: A Review of Theories and Practice 69
• Introduction 69
• Conclusions 84
• Acknowledgments 86
• Notes 86
• Part II General Exchange or Switching Options and Options Interdependencies 87
• Chapter 5 The Value of Flexibility: A General Model of Real Options 89
• Introduction 89
• Concluding Remarks 105
• Acknowledgments 105
• Notes 106
• Chapter 6 The Valuation of American Exchange Options with Application to Real Options 109
• Introduction 109
• Conclusion 119
• Acknowledgments 120
• Notes 120
• Chapter 7 Operating Flexibilities in Capital Budgeting: Substitutability and Complementarity in Real Options 121
• Introduction 121
• Conclusion 130
• Acknowledgments 131
• Notes 131
• Part III Strategy, Infrastructure, and Foreign Investment Options 133
• Chapter 8 The Value of Options in Strategic Acquisitions 135
• Introduction 135
• Implications and Conclusions 147
• Acknowledgments 148
• Notes 148
• Chapter 9 Corporate Governance, Long-term Investment Orientation, and Real Options in Japan 151
• Introduction 151
• Implications and Conclusions 158
• Notes 160
• Chapter 10 Volatile Exchange Rates and the Multinational Firm: Entry, Exit, and Capacity Options 163
• Introduction 163
• Conclusions 178
• Acknowledgments 180
• Notes 180
• Part IV Mean Reversion/ Alternative Formulations in Natural Resources, Shipping, and Start - Up Ventures 183
• Chapter 11 The Effects of Reversion on Commodity Projects of Different Length 185
• Introduction 185
• Conclusions and Extensions 199
• Appendix 201
• Acknowledgments 204
• Notes 204
• Chapter 12 Contingent Claims Evaluation of Mean-Reverting Cash Flows in Shipping 207
• Introduction 207
• Conclusions 216
• Appendix 217
• Acknowledgments 218
• Notes 218
• Chapter 13 Valuing Start-Up Venture Growth Options 221
• Introduction 221
• Conclusion 236
• Appendix 237
• Acknowledgments 238
• Notes 238
• Part V Other Applications: Pollution Compliance, Land Development, Flexible Manufacturing, and Financial Default 241
• Chapter 14 Investment in Pollution Compliance Options: The Case of Georgia Power 243
• Introduction 243
• Notes 262
• Chapter 15 Optimal Land Development 265
• Introduction 265
• Conclusions and Extensions 277
• Appendix 278
• Acknowledgments 279
• Notes 279
• Chapter 16 Multiproduct Manufacturing with Stochastic Input Prices and Output Yield Uncertainty 281
• Introduction 281
• Conclusion 298
• Appendix 300
• Notes 301
• Chapter 17 Default Risk in the Contingent Claims Model of Debt 303
• Introduction 303
• Conclusions and Extensions 317
• Acknowledgments 318
• Notes 319
• Bibliography 323
• Author Index 347
• Subject Index 351
• About the Editor and Contributors 357
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