Real Options: Evaluating Corporate Investment Opportunities in a Dynamic World - Hardcover

David Newton; Dean Paxson; Sydney Howell; Mustafa Cavus; Andrew Stark

Hardcover

ISBN 10: 0273653024 ISBN 13: 9780273653028

Publisher: FT Press, 2001

Synopsis

Offers specific guidance on directing or applying real options analysis in financial decision-making. Contains outlines of spreadsheet solutions. All four authors are senior academics at Manchester Business School, a leading business school in Great Britain.

About this title

About the Author

Sydney Howell

is a Senior Lecturer in Management Accounting and Control at Manchester Business School. He has over 20 years experience as a teacher, manager and consultant in all areas of real options, and has taught for many companies including IBM, Tesco and C&A.

Andrew Stark is Professor of Accounting at Manchester Business School, and is presently Director of the Manchester MBA programme. He is a well-known contributor to conferences on real options and has taught at Maryland, Yale and Manchester universities.

David Newton is Lecturer in Accounting and Finance at Manchester Business School, and has a wide-ranging expertise in teaching real options theory and practice to students and practitioners alike. He wrote a seminal paper on the application of options theory to R&D.

Dean Paxson is Professor of Finance and Accounting at Manchester Business School where he has taught real options to MBAs for several years. He was educated at Amherst College, Oxford and Harvard Business School, and has a number of well-received books on real options.

Mustafa Cavus is a senior consultant with Capstone Energy Consulting, and specialises, among other fields, in options and futures in electricity generation. Mustafa holds Master¿s degrees from German and British universities, as well as a PhD from Manchester Business School.

José Antonio de Azevedo-Pereira is a graduate of ISEG (Technical University of Lisbon) and Manchester Business School. He is presently Professor Auxiliar at ISEG and has previously held a number of Board and Executive positions in Portuguese companies.

Kanak Patel is Lecturer in Property Finance at the Department of Land Economy, University of Cambridge. Initially a risk analyst at Lloyd¿s of London, she has also taught finance at Manchester Business School and at the Management School, Imperial College, University of London.

 

From the Back Cover

What is the correct price to pay for a brand?

When should you cease operating an asset?

What should the maximum investment in a research project be?

How much should you buy or sell technology or a licence for?

Real option analysis allows us to make the right decision at the right time. Providing for the first time an integrated framework that can address decisions under an extreme form of uncertainty, real options analysis is one of the most important developments in business decision analysis of the last century.

Real option analysis enables us to integrate our decisions on investment, operations and disinvestment, and is altering economics, strategy, psychology and other disciplines. It follows the understanding that at least one of the value-determining variables is evolving unforecastably, following a random walk, but there will be flexibility in how we respond as that uncertainty unfolds.

Real Options

is an enlightening guide to the world of real options, explaining the concepts and offering practical information supported by case studies on how to maximize the value of real option analysis to your business.

Excerpt. © Reprinted by permission. All rights reserved.

This book is an enlarged sequel to Real Options: An introduction for executives, and it shares much of the introductory material. However, the present book is aimed at practitioners, consultants and MBA (or other) finance students, as well as at general managers. That is to say, it aims to help both numerate and non-numerate readers. The book aims to take a non-numerate reader through from ignorance of any kind of option to a clear understanding of how and why real options methods work, what real options can contribute to business, and what questions to ask of a real options analyst. Such readers should be able to make sense of most of the main text, except for the more formal parts of Chapter 4.

If a numerate reader starts with little or no knowledge of finance or of options, they should be able to gain a strong intuition for the mathematics and the economics by reading the main text. In addition, by studying all the Appendices and the formal parts of Chapter 4, such readers should pick up all the formal knowledge required to build and solve real option models using both continuous time and binomial models, and to appreciate fully what is going on in the case examples of Chapters 5 to 10, and in the more advanced texts and journals. We hope that numerate readers - even if they have no experience of finance - after working carefully through the book should be able to tackle with confidence the fundamental mathematical texts by Dixit and Pindyck and Wilmott, Howison and Dewynne. We have included many references to these excellent texts, and have largely followed the notation of the latter.

This book gives several new intuitive and visual guides to what real options mathematics is doing. In Chapter 2 we introduce a plot of the valuation surface, in both asset price and time V(S,t). This not only gives an intuitively powerful demonstration of diffusion but also correctly reflects how the Black-Scholes equation actually operates mathematically, to define a surface within well-posed boundaries. It also displays the entire set of boundary conditions simultaneousIy, and it shows how, at a fixed price S, option value declines approximately with the square root of the remaining time to expiry, as does volatility.

In Chapter 10 Jose Pereira and David Newton generalize this type of plot to show the value surface at a given time t for a two-factor model, which we could call V_t(S₁,S₂). An awareness of the time dimension, which is usually omitted from plots of option value, has also helped us in Chapter 2 to give what we hope is a better explanation than usual of the sometimes troublesome concepts of value matching and smooth pasting.

In Chapter 3 we generalize the plot of the valuation surface V(S,t) from a simple call, which has one mode of exercise, in order to value a one-factor (American call) option, which has multiple modes of exercise. To clarify the early exercise decision, we introduce a direct plot of the surface of the time value of the option (this surface is option value minus intrinsic value; the surface V(S,t) - P(S,T) which generalizes to V(S,t) - P(S,t) in the case of a payoff function which is evolving deterministically over time). This plot, which we call a 'shark's fin', shows how the time value is at a maximum if the asset price S ever puts the option 'at the money' for a choice between alternative actions. It also shows how time value tends to fall with the square root of the remaining time to expiry, when the latter is small, reflecting the fact that volatility is doing the same.

Another concept which can be hard to understand intuitively is delta hedging. In Appendix 3 we have given not only a clear explanation of the algebraic motivation of delta hedging but also a visual illustration of how delta, which is the slope of the option's value function V with respect to S, defines the size of the forward or short sale required to hedge a portfolio's value against small movements of S. By varying S around E we can see how delta varies, and this illustrates why delta hedging an option is only a special case of delta hedging any instrument whose value is a function of S. We see how the other special cases can include both S itself and the risk-free asset.

As a completely independent illustration of the way the Black-Scholes mathematics operates, David Newton has given in Appendix 4 the most complete example yet of how heat diffusion relates to option valuation, a topic which almost every book mentions, but few or none explain satisfyingly. In Appendix 5 David has provided intuition on simple, multiple, correlated and mean reverting random walks. Finally, the editor has waged his personal campaign in Chapter 4 for a more economically complete and intuitively useful interpretation of the confusingly named 'risk neutral probabilities'.

The main part of the book contains various extended applied examples by our contributing authors, all of whom have taught and/or completed their PhD degrees at Manchester Business School. We are delighted to welcome Kanak Patel and Jose Pereira as authors. Their examples range in level of difficulty from MBA teaching material to recent PhD results. The actual cases include various problems from real estate (put, call to invest, call to operate, valuation of lease); there is a case from sport management (stadium rental); also from power generation (call options to produce, in both a discrete and a near-continuous process, including the effects of inertia and exchange options) and from finance (two-factor model for valuing a mortgage). These cases are solved by various methods, including analytic Black-Scholes call option and Margrabe exchange option solutions, explicit finite difference and binomial methods. We also briefly describe some of the important work reported by Dixit and Pindyck on decisions for continuous processes. This work bears on decisions to activate and deactivate resources, for example in shipping and mining, and in the hiring, firing and laying-off of staff.

Collections of work by several authors must inevitably be varied in their styles of presentation, and sometimes a paper may be rather terse for an inexperienced practitioner to follow or to replicate. In order to minimize this diffficulty we have tried to present in Chapter 4 a unified framework, which should allow the reader to appreciate what is constant and what is changing over a wide variety of potential and actual applications of real options analysis.

The essentials of this framework are:

• the problem as intuitively presented to management;
• the decision to be taken;
• any option-like features of the problem;
• any modifications needed to the Black-Scholes equation;
• the boundary conditions needed;
• the solution method;
• the data sources and the key implications of the solution;
• indications of how the model might be generalized further.

To help the reader to apply this framework to the various extended case examples, the editor has tried at the start of each case to summarize how the above essential features have been handled, listing them in a fairly standardized format. Some over-simplifications have inevitably arisen in these introductions (for which the editor apologizes to the contributors) but hopefully readers will find they have been helped to understand the present book. More importantly, readers should then have much greater confidence in exploring the published literature, and in questioning the structure and the outputs of any given real options analysis.

Our style of presentation departs from convention in several ways. We have tried to make the whole text intuitively understandable, including the Appendices, and have made the latter more equal partners with the main text than is usual. In option payoff diagrams we always omit the option premium. This is because in a perfect market, the premium is an output of the calculation of an option's value, not an input to it - the premium simply eliminates the option's value in order to ensure that the act of purchasing an option has an instantaneous net present value (NPV) of zero (no arbitrage profits from buying or selling options).

Conversely, in an imperfect market (which is the case for many real options) the calculation of an option's value is often a completely separate task from estimating what it might cost to create or to acquire that option. Unlike financial markets, real option markets often offer significant opportunities for arbitrage gains and losses. However, in future we can expect to see increasing trading of real options, both between companies and on markets, which should reduce the opportunities for arbitrage but increase those for hedging.

We also devote unusually little space to the classical analytical solutions of the Black-Scholes equation, or to analytic solutions in general, though the classic Black-Scholes formula for the European call appears in Chapter 5 and in Appendix 1 to Chapter 6. Epoch-making though this solution was, it solves only one exceedingly special case of the general problem of valuing a derivative (including a real option). It is vital that users of real options should understand that the valuation problem in its most general form consists of a Black-Scholes PDE, plus suitable boundary conditions, plus some solution method. In the most demanding real options problems, that solution method has to be a discrete numerical method (as in engineering and physics).

There is one theoretical advantage to an emphasis on numerical methods, namely that in some cases the analytic solution does not model the true behaviour of the option across all the possible states of S and t, but only within boundaries. For example, in the case of a perpetual American call on a dividend-paying asset, if the stock price is ever observed to be above the optimal exercise price S*, the option's value V(S,t) is less than its intrinsic value P(S,T) (and the option should, and could, have been exercised earlier, if trading and value reporting had been truly continuous). However, the analytic solution is of course tangent to P(S,T) at S* (by the smooth pasting condition). In fact, above S* the analytic solution still exists, though it should not be used because it rises above P(S,T). Hence although the analytic solution still exists above S* (the free boundary up to which the solution is defined), it no longer models the value of the option, nor guides decisions. In contrast, a suitably designed numerical method can reflect the fact that the option's time value is declining progressively below zero as S rises above S*. In this example, a numerical solution can be made a more fundamentally and universally 'true' model of an option's behaviour than an analytical solution which is meaningful only within a given domain.

We have striven to avoid a 'worst case' outcome, in which the reader is unable to formulate or to solve a problem in more general ways and is therefore tempted to simplify any actual problem into some unsuitable format, merely because that format happens to have an analytic solution. Of course, even experts can and must use analytical approximate solutions from time to time, in order to gain improved insight, and in order to cross-check a numerical method. For example, a European option valuation sets a lower bound to an American option's value, and a valid numerical solution to the American option should converge to the analytical solution for the European option if the rate of dividend is set to zero; likewise a perpetual option's value sets an upper bound to the value of an option which has a finite time to expiry, and in this case also a necessary but not a sufficient condition for a numerical solution to be valid is that it should converge to the analytical (here perpetual) solution if time to expiry is set large.

The editor is grateful to the authors for all their contributions and for detecting many errors, but the errors that remain are his own, particularly those that arise in the introductions to the work of the rest of the team. I hope to be forgiven for any distortions of their ideas that have been unwittingly introduced.

Sydney Howell
Real Options Group
Manchester Business School

Edition details

• Publisher: FT Press
• Publication date: 2001
• Language: English
• ISBN 10: 0273653024
• ISBN 13: 9780273653028
• Binding: Hardcover
• Edition number: 1
• Number of pages: 304