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Annual International Conference on Real Options: Theory Meets Practice

4th Annual Real Options Conference

University of Cambridge
Judge Institute of Managment

Valuing Natural Resource Investments | International Investment Flexibility | Keynote Address | Organizational Adoption and Implications | Practitioner Perspective from Consulting Firms | Empirical Evidence | Competition and Strategy | Theoretical Issues in Real Option Valuation | Academic Perspectives on Future Developments


Valuing Natural Resource Investments
Gordon Sick (U. Calgary)

Gonzalo Cortazar (Catholic U. of Chile), Eduardo Schwartz (UCLA), and F. Riera (Catholic U. of Chile), Market-based Forecasts of Commodity Prices Using Futures

Commodity prices are very volatile, with typical annual variations from 20 to 40%. This price uncertainty has a major impact on asset valuation and risk management issues and typically may be dealt with in several ways. For valuation purposes, for example, market prices that have already taken into account this risk may be used. Futures contracts markets provide these risk-free estimates. There is now a wide consensus that for valuing commodity contingent cash flows it is better to compute them using futures prices instead of expected spot prices. The virtue of this approach is twofold. First actual market prices can be used instead of private predictions that are subject to all sort of biases depending on who performs the prediction. Second, risk free interest rates can be used for discounting cash flows instead of having to add a risk premium, subject to great estimation error. One remaining implementation problem remains when the time-horizon of the commodity contingent cash flows exceeds the futures longest maturity that is traded in the market. In this case it is necessary to make an estimate of which would have been the current price for a futures
contract with a matching maturity, should there be one.

For risk management purposes futures markets may be used to hedge risk. Once the optimal exposure is defined, the hedging strategy must be designed in a way that it not only considers current futures prices but also their process. It is well known that hedging ratios critically
depend on volatility and factor correlation estimates. Thus a good model for explaining the stochastic movement of futures prices becomes critical for risk management purposes.

Sometimes expected cash flows (not only their present value) are relevant. Most of the academic literature and industry practice forecast commodity spot prices using econometric models that estimate short, medium and long-term equilibrium prices using expected demand and supply functions. Another common method is to use time series estimates
and base the forecast on past behavior of prices. We build on a different approach which models the stochastic behavior of prices for purposes of explaining futures prices, and use this stochastic process to obtain market-based forecasts of expected spot prices. We consider that expected spot prices should be the addition of a risk premium to the known (or estimated) futures price. Even though we recognize that we have rather noisy estimates of the risk premium, we think that by using futures prices to help predict expected prices is at the least a good additional source of information that should be taken into account when making expected price forecasts.

In this article we present two new models of the stochastic behavior of commodity prices, both of which accommodate mean reversion, use parameters which we believe are easier to interpret than those of most of the existing models, and do not require to specify the interest rate.

The first model has two factors, the spot price and the deviations from long term expected returns. Our second model introduces as its third risk factor a stochastic long-term drift on the logarithm of the spotprice. We estimate the models by implementing a simple procedure using the well-known Excel program. We apply this procedure to estimate the same model (and database) in Schwartz (97) and obtain similar results without resorting to the Kalman filter approach described there. Then, we estimate our new models on an updated data base that includes copper and oil futures prices traded at NYMEX until 1998, and compare futures
price estimates with those obtained by previous studies. Finally we use our futures price estimates to obtain market-based forecasts of expected spot prices for both commodities.

Murray Carlson, Zeigham Khokher, and Sheridan Titman (U. Texas-Austin),
An Equilibrium Analysis of Exhaustible Resource Investments

Contingent claims analysis is currently being used extensively in the energy industry. For example, energy traders often use models suggested by Black (1976), Brennan and Schwartz (1985), Schwartz (1997) and others for risk management as well as for valuing financial
contracts and real investments. These applications, which typical calibrate the models' parameters using some combination of historical prices and observed forward and option prices, have proven to be successful in valuing and hedging relatively short-term financial contracts.

There is, however, an inherent inconsistency in the application of these models that is likely to create a problem when the models are applied to value and hedge longer horizon investments. Specifically, although the models assume the parameters in the price process are constant, the calibration procedures that are used in practice typically provide for a more flexible specification by allowing the parameters to change with time. Although these procedures generally provide reasonably good approximations when the models are used to interpolate among prices in liquid markets, as we will show, they can generate biases when the methodology is used to extrapolate from observed derivative prices to value long term real
investments like the pipelines and other infrastructure needed to exploit oil and gas reserves.

To explore these issues in more detail we develop a general equilibrium model of an extractable resource market where both the prices and extraction choices are determined endogenously. As we show, with plausible parameters the model generates prices that are roughly consistent with observed forward and option prices as well as with the price processes that were calibrated in Schwartz (1997). However, the subtle differences between the endogenous price process determined within our general equilibrium model and the exogenous processes considered in earlier papers can generate significant differences in both financial and real option values.

Our model extends existing general equilibrium models that have appeared in both the finance and economics literature. The model is particularly close in spirit to the Pindyck (1980) model, which adds uncertainty to the seminal Hotelling (1931) model that describes how the price of exhaustible resources evolve through time. It is also related to the more
recent work of Litzenberger and Rabinowitz (1995), who argue that because the option to wait has value in an uncertain environment, resources will be extracted more slowly and prices will appreciate less rapidly than they would in the Hotelling certainty model. In contrast to the Pindyck (1980) and Litzenberger and Rabinowitz (1995) models, the endogenous price process that arises in our model exhibits mean reversion, which is consistent with the empirical data discussed by Schwartz (1997) and others. Moreover, our model is consistent with the observation that discounted futures prices may be both above and below the current spot price (i.e. futures curves can be in weak contango or backwardation). These results are not simply due to the stochastic nature of the exogenous state variables but arise endogenously from the assumed frictions associated with the supply responses.

Our model generates insights about the evolution of natural resource prices that can potentially have important implications on the valuation and hedging of long dated financial or real options. In particular, although the endogenous price process generated by our model is qualitatively similar to the price process assumed by Schwartz (1997), the functional form
of the drift is, in general, non-linear and generates equilibrium price paths with less extreme realizations than would be generated by Schwartz's model. As a result, options, whose payoffs are especially sensitive to these extreme realizations, are generally less valuable in our general equilibrium setting where the extreme realizations are observed less frequently.

Gonzalo Cortazar, Paulina Acosta and Manuel Osorio (Catholic U. of Chile),
Monte Carlo Evaluation of Natural Resource Investments

This paper presents valuation models of natural resource investments solved by a Montecarlo simulation approach. We solve two real options models: the investment of an undeveloped oil field as modeled by Cortazar and Schwartz (1998) and the production schedule of a copper mine as modeled by Brennan and Schwartz (1985). We analyze alternative Montecarlo simulation implementations and discuss their results.

Since Boyle (1977) proposed Montecarlo simulation for valuing financial European options, this approach has become increasingly attractive because of its easy handling of path-dependent cash flows and complex uncertainty models. However, standard Montecarlo simulation models, with their forward induction approach, have traditionally been considered inappropriate for valuing American-type options.

In the last decade there have been several efforts to extend Monte Carlo simulation techniques for solving American-type options. These methods attempt to combine the simplicity of forward induction with the ability of determining the optimal option exercise of backward induction. One of the simulation methods, proposed by Barraquand and Martineau (1995), show that it is possible to discretize and to reduce the dimensionality of the valuation problem, and still get reasonably good approximations. For example, if we assume a multi-factorial process for a state variable S, the procedure calls for making several thousand
Monte Carlo simulations on S and grouping the obtained values into a fixed set of "bins". Then, by making successive simulation runs it is possible to empirically determine the transition probabilities between successive bins and finally to solve backwards the valuation process using each bin as a decision unit.

One of the main issues in this methodology is the selection of the one-dimensional state variable that will represent all state variables in the problem. As Broadie and Glasserman (1997b) point out, this procedure does not ensure convergence when, for example, there are
disjoint optimal exercise sectors. In this case, further increases in the number of one-dimensional bins are not able to determine the optimal exercise policy. To reduce this problem, Raymar and Zwecher (1997) recommend adding a second dimension to the bin grouping process, so the state of the economy can be represented by more than one dimension. In one recent implementation of the Barraquand and Martineau (1995) method to solving a real option problem, Cortazar and Schwartz (1998) determine the optimal timing of an undeveloped oil field. They argue that given that there is no disjoint exercise region in the valuation of an undeveloped oil field, there probably is no need to implement this valuation model using a two-dimensional Raymar and Zwecher (1997) method, but it suffices to make a one dimensional implementation of the Barraquand and Martineau (1995) method.

In Cortazar and Schwartz (1998), the Barraquand and Martineau (1995) method is used to obtain the optimal timing of an undeveloped oil field. Uncertainty is described using a two-factor model for oil spot prices and convenience yield (Schwartz (1997). Instead of using two state variables (in addition to time) the problem is reduced to a one dimensional model using the value of the developed oil field (for the optimization stage) as the only state variable for deciding when it is optimal to invest. By reducing the problem dimensionality the implementation of this method is argued to remain simple yet to obtain reasonably accurate value estimates.

In Section 2 of this paper we solve the same undeveloped oil field considered in Cortazar and Schwartz (1998) but using the two-dimensional Raymar and Zwecher (1997) method and compare it with the Barraquand and Martineau (1995) approach used earlier.

In Section 3 we analyze alternative solutions to Brennan and Schwartz (1985) classic mine model using both simulation methods. Section 4 concludes.

Robert Elliott (U. of Alberta), Gordon Sick (U. of Calgary) and Michael Stein (U. of Oregon),
Pricing Electricity Calls

In this paper we develop a general model of spot electricity price that encom- passes the stylized features of many of the emerging deregulated electricity pools around the world. We incorporate seasonality on an annual basis and a daily basis around a mean-reverting de-seasonalized intrinsic price. A unique feature of this paper is the treatment of jumps in the spot price as arising from supply shocks as large generators in the system come off-line and go on-line in a partially predictable manner. We model the number of large generators on line as a discrete Markov process. This feature is motivated by the Alberta electricity pool,which has 14 large base-load generators and very little excess capacity. We show how to estimate the diffusion process with a Kalman filter technique and the discrete Markov model with maximum likelihood model. The motivation for pricing calls on this price process is two-fold.First many electricity customers purchase call options to manage their risk.Sec- ond,generators are called into the system or turned on, according to whether their marginal price is less than or greater than the system marginal price (spot price).The revenue stream to a company that builds a new generator that is not part of base load will be a strip of call options.Thus,this is a real option valuation model.

International Investment Flexibility
Chairperson: Blake Johnson (
Stanford U.)

Arun S.Muralidhar (J.P. Morgan),
Valuing the Financial Flexibility of a Multinational
Paper, Slides

This chapter argues that when corporate tax obligations are variable, a multinational firm has financial flexibility (the option to shift profits to favorable tax regions in every period and lower the global tax liability), and that traditional NPV analyses of foreign projects may not capture the value of this flexibility. It introduces an options pricing model to value the flexibility that internalizing tax management provides, and offers an adjusted NPV calculation that incorporates this portfolio of options into the investment decision. While national firms may find certain projects unattractive, a multinational firm is shown to acquire projects once they value the flexibility. Corporate tax rate data are used to compare potential projects in different countries for a U.S.-based MNE. The chapter concludes by discussing the implications of these results for MNEs and governments.

Greg Bell (Charles River Associates),
Exports and Flexible Production Technologies in Volatile International Markets

This paper considers the role of production technology in export oriented, irreversible investments made in a regime of volatile exchange rates. In this relatively simple model, technologies are characterized by their flexibility. More specialized technologies incur larger sunk costs in return for a cost advantage at the expected level of output. By reducing sunk costs and offering the firm a broader array of responses to changes in the exchange rate, flexibility reduces the cost of regret incurred by an investment. Accordingly, more flexible technologies enter the foreign markets at less favorable exchange rates and with higher scale. Where the firm has a choice of technology, increases in volatility lead to the selection of less specialized technologies, the sacrifice of cost advantages for flexibility.

Hiroshi Yamaguchi, Nobuya Takezawa, Ushio Sumita and Ted Azami (International University of Japan),
The Real Option Premium in Japanese Land Prices

The present paper examines the empirical implications of the real option pricing model developed in Quigg (1993). The present value of cash flows generated from developed property less the development costs gives us the value of the vacant plot of land. The owner of vacant plot of land, however, has the right to exercise the option of developing the property or can simply defer development. It is this real option to wait to develop vacant plots of land that we empirically investigate.

The study focuses on a sample of 754 transactions in the residential areas of Nerima-ward of Tokyo. We estimate the option premium during the late 1980's to be at 18.04% and the premium during our early 1990's sample at 18.52%. This is substantially larger than the premiums documented for residential areas in Seattle (Quigg).

The empirical approach taken in this paper involves estimating a hedonic regression so that we can obtain forecasted values of developed property. Our regression specification takes into account features of importance in the Japanese real estate market.

Our findings are also consistent with the notion of a building cycle where the property prices in a given area are highly correlated. When it is profitable to exercise the option to develop a plot of land in one area, it should be profitable to develop property in adjacent areas as well. This then leads to a construction booms such as that witnessed in Tokyo during the second half of the 1980's.


Keynote Luncheon Address
Risk and Options

Dr. Myron S. Scholes
Stanford University

Professor Scholes is the Frank E. Buck Professor of Finance Emeritus at Stanford Universityīs Graduate School of Business and a partner in Oak Hill Capital Management. Prior to that he taught at MIT and the University of Chicago, and has been a Senior Research Fellow at the Hoover Institution. He received a Ph.D. in 1969 from the University of Chicago. Professor Scholes is a member of the Econometric Society and was President of the American Finance Association.

Professor Scholes is widely known for his seminal work in options pricing, capital markets, tax policies and the financial services industry. He is co-originator of the Black-Scholes options pricing model and risk-neutral valuation, which are the basis of the pricing and risk-management technology that is used to value and manage the risk of derivative instruments around the world and for much of real options valuation. For this work, he was awarded the Nobel Prize in Economic Sciences in 1997.

On the practitioner side, Dr. Scholes has been a principal and Limited Partner at Long-Term Capital Management from 1993-1998. Between 1991 ≠ 1993, he was a Managing Director at Salomon Brothers, a member of Salomon's risk management committee and Co-Head of its Fixed Income Derivatives Sales and Trading Department.

Organizational Adoption & Implications
Chairperson: Soussan Faiz (Texaco Inc.)

Andrew Stark (Manchester Business School),
Successfully Integrating the Real Options Approach into your Corporate Decision Making


David Houldridge (Smith & Nephew),
Adopting Real Options as an Assessible and User Friendly Tool Within Your Organization


Michael E. Raynor (Deloitte Consulting),
Real Organizations for Real Options: Administrative Implications of Creating and Exercising Real Options Through Corporate Diversification

Diversified corporations competing in industries characterized by uncertain and rapidly changing structures can enhance their competitiveness by increasing their level of strategic flexibility, i.e., their ability to reconfigure divisional relationships to exploit shifting industry-level complementarities.

The value of this kind of strategic flexibility can be understood using a real options framework. Specifically, part of the value of a diversified portfolio of operating assets is a function of the present value of future synergies between currently unrelated businesses that are subject to market convergence. By diversifying and acquiring assets in industries subject to increasing complementarity, firms acquire the right, but not the obligation, to pursue interdivisional synergies when and as appropriate. In other words, under particular circumstances, diversification creates real options on the integration of currently separate operating units.

This paper investigates the administrative implications of attempting to create and exercise real options on future synergies through diversification. For whereas an investor can acquire and exercise a financial option simply by issuing the appropriate žbuyÓ orders, creating and exercising a real option on future synergies has potentially significant organizational ramifications. Using a case study methodology, this paper examines the implications of a real options approach to diversification on the nature and quality of corporate-divisional and
interdivisional relationships and proposes an administrative theory of real options diversification.

Panel Discussion: Current Status and Future Prospects I
(Practitioner Perspectives from Consulting Firms)
Moderator: Gregg Bell (
Charles River Associates)

Panelists include:
Remy Schosmann (Ernst & Young)
Mike Kaye (Andersen Consulting)
Yann Bonduelle (Pricewaterhouse Coopers)
Gunnar Pritsch (McKinsey & Co.)
Ravi Bulchandani (Morgan Stanley Dean Witter)
Laura Martin (Credit Suisse First
Alberto Micalizzi (Real Options Group)


Empirical Evidence
Chairperson: Bhagwan Choundhry (UCLA)

Han Smit (Erasmus U. Rotterdam, Netherlands),
Option Characteristics of Growth Stocks


A. Al-Horani (Manchester Business School), Peter Pope (Lancaster University) and Andrew Stark (Manchester Business School),
Research and Development Expenditures, Real Options and the Book-to-Market Effect on Expected Returns


Antonio Bernardo (UCLA), Bhagwan Chowdhry (UCLA), Darius Palia (Columbia U.), and Elena Sernova.
Real Options and the Diversification Discount