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

By Lenos Trigeorgis | Go to book overview

(15.A1)

Since v ≥ 0 and A2 ≠ 0, it must be the case that A2 > 0.

Finally, recall that the call must be a convex function of the underlying asset price when the distribution of returns on the asset is independent of the level of the asset price (see Theorem 10 in Merton, 1973). Therefore, A2v(v - 1)qv-2 = D″(q) ≥ 0. Since A2 > 0, then v ≥ 1. When v = 1, by Equation (15.32) A1 + A2 = 1, but this relationship holds in (15.31) only when w is infinite, and infinite w is not consistent with premature exercise. Therefore, v > 1, or γ > σ2/2.

ACKNOWLEDGMENTS

This paper was prepared as part of my doctoral dissertation at the University of California at Berkeley. I gratefully acknowledge valuable discussions with Nancy Wallace, Hayne Leland, Robert Edelstein, Jim Wilcox, Peter Berck, and Phelim Boyle.

NOTES
1.
Williams ( 1990b) assumes that the state variable is the building's rent, rather than the building value, and that this rent follows a geometric Brownian motion. It is necessary to assume this process in order to solve the option-pricing problem using standard methods, but Williams's approach implies that if rent becomes zero at any point in time, the rent, and thus the value of the building, will be zero from then on. We avoid this limitation by valuing land as a contingent claim on the building value itself.
2.
Like William, Capozza and Sic assumed that the state variable is the future rent. However, unlike Williams, they assumed that rent follows an additive Brownian motion, which allows rents to become zero, or even negative, with no permanent effect on the building value. Their assumption is essentially equivalent to ours of a building price-process that follows a geometric Brownian motion.

Capozza and Sick posed an individual household maximization problem that takes advantage of arbitrage-based option-pricing methods. However, the household facing this problem is unlikely to be able to hedge and diversify its portfolio. In order for arbitrage-based option valuation to be used in this way, one must assume that the asset is priced as if the markets were dynamically complete. This assumption is more readily applied in cases where investors have access to the

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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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