Strategic investment under uncertainty: A synthesis

Investment is a central theme in economics, finance, and operational research. Traditionally, the focus of analysis has been either on assessing the value of flexibility (investment under uncertainty) or on describing commitment effects in competitive settings (industrial organization). Research contributions addressing the intersection of investment under uncertainty and industrial organization have become numerous in recent years. In this paper, we provide an overview aimed at categorizing and relating these research streams. We highlight managerial insights concerning the nature of competitive advantage (first- versus second-mover advantage), the manner in which information is revealed, firm heterogeneity, capital increment size, and the number of competing firms.     

Technology choice under several uncertainty sources

We analyze a model of irreversible investment with two sources of uncertainty. A risk-neutral decision maker has the choice between two mutually exclusive projects under input price and output price uncertainty. We propose a complete study of the shape of the rational investment region and we prove that it is never optimal to invest when the alternative investments generate the same payoff independently of its size. A key feature of this bidimensional degree of uncertainty is thus that the payoff generated by each project is not a sufficient statistic to make a rational investment. In this context, our analysis provides a new motive for waiting to invest: the benefits associated with the dominance of one project over the other. As an illustration, we apply our methodology to power generation under uncertainty.     

Optimal access pricing for natural monopoly networks when costs are sunk and revenues are uncertain

This paper studies optimal access pricing for natural monopoly networks with large sunk costs and uncertain revenues. Using techniques from the option pricing literature, we show that the optimal access price corresponds to a risk-free form of the Efficiency Component Pricing Rule (ECPR), that is, where the opportunity cost is based on the risk free rate of return. We also show that at levels of revenue above the optimal level that triggers entry, the entrant should pay a premium above risk-free ECPR that rewards the incumbent for relinquishing his rights to the risky cash flows at the higher revenue level.     

Optimal investment under operational flexibility, risk aversion, and uncertainty

Traditional real options analysis addresses the problem of investment under uncertainty assuming a risk-neutral decision maker and complete markets. In reality, however, decision makers are often risk averse and markets are incomplete. We confirm that risk aversion lowers the probability of investment and demonstrate how this effect can be mitigated by incorporating operational flexibility in the form of embedded suspension and resumption options. Although such options facilitate investment, we find that the likelihood of investing is still lower compared to the risk-neutral case. Risk aversion also increases the likelihood that the project will be abandoned, although this effect is less pronounced. Finally, we illustrate the impact of risk aversion on the optimal suspension and resumption thresholds and the interaction among risk aversion, volatility, and optimal decision thresholds under complete operational flexibility.     

Renewable energy investments under different support schemes: A real options approach

This paper adopts a real options approach to analyze investment timing and capacity choice for renewable energy projects under different support schemes. The main purpose is to examine investment behavior under the most extensively employed support schemes, namely, feed-in tariffs and renewable energy certificate trading. We consider both multiple sources of uncertainty under each support scheme and uncertainty with respect to any change of support scheme, and we obtain both analytical (when possible) and numerical solutions. In a Nordic case study based on wind power, we find that the feed-in tariff encourages earlier investment. Nevertheless, as investment has been undertaken, renewable energy certificate trading creates incentives for larger projects. In our baseline scenario and taking the fixed feed-in tariff as a base, the revenue required to trigger investments is 61% higher with renewable certificates. At the same time, investment capacity is 61% higher.     

Project options valuation with net present value and decision tree analysis

Real options analysis (ROA) has been developed to correctly value projects with inherent flexibility, including the possibility to abandon, defer, expand, contract or switch to a different project. ROA allows computing the correct discount rate using the replicating portfolio technique or risk-neutral probability method. We propose an alternative approach for valuing Real Options based on the certainty-equivalent version of the net present value formula, which eliminates the need to identify market-priced twin securities. In addition, our approach can be extended to the case of multinomial trees, a useful tool for modeling uncertainty in projects. We introduce within decision tree analysis (DTA) a method to derive the different discount rates that prevail at different chance nodes. We illustrate the valuation method with an application presented in “A Scenario Approach to Capacity Planning” [Eppen, G.D., Martin, R.K., Schrage, L.E., 1989. A scenario approach to capacity planning. Operations Research, 37 (4)], in which the authors state that for the capacity configuration investment decision studied at General Motors, “… there is no scientific way to determine the appropriate discount rate based on estimated demand.” Our method allows deriving the scientifically correct discount rates. A major result of the analysis is that the discount rates are endogenously derived from the project structure and its behavior in light of prevailing market conditions, instead of being exogenously imposed.     

Log-gamma motion as flexible model for generalized interest rates

Negative, oscillating, and near zero interest rates are changing financial modeling completely. To address this situation, we introduce novel, flexible, and estimable model of interest rate. This model is based on recent developments of so-called Inv-Log-Gamma process. This model is much easier to be estimated as the continuous time models for interest rates with dampings, where interest rate r_t possesses a martingale property. Even though the estimation of continuous time interest rates is a difficult task. Therefore, more flexible and estimable model for interest rate is needed, which motivates our developments. Simulation and real data examples illustrate usefulness of our development.     

Duopolistic competition under risk aversion and uncertainty

A monopolist typically defers entry into an industry as both price uncertainty and the level of risk aversion increase. By contrast, the presence of a rival typically hastens entry under risk neutrality. Here, we examine these two opposing effects in a duopoly setting. We demonstrate that the value of a firm and its entry decision behave differently with risk aversion and uncertainty depending on the type of competition. Interestingly, if the leader’s role is defined endogenously, then higher uncertainty makes her relatively better off, whereas with the roles exogenously defined, the impact of uncertainty is ambiguous.     

Generalised soft binomial American real option pricing model (fuzzy–stochastic approach)

The stochastic discrete binomial models and continuous models are usually applied in option valuation. Valuation of the real American options is solved usually by the numerical procedures. Therefore, binomial model is suitable approach for appraising the options of American type. However, there is not in several situations especially in real option methodology application at to disposal input data of required quality. Two aspects of input data uncertainty should be distinguished; risk (stochastic) and vagueness (fuzzy). Traditionally, input data are in a form of real (crisp) numbers or crisp-stochastic distribution function. Therefore, hybrid models, combination of risk and vagueness could be useful approach in option valuation. Generalised hybrid fuzzy–stochastic binomial American real option model under fuzzy numbers (T-numbers) and Decomposition principle is proposed and described. Input data (up index, down index, growth rate, initial underlying asset price, exercise price and risk-free rate) are in a form of fuzzy numbers and result, possibility-expected option value is also determined vaguely as a fuzzy set. Illustrative example of equity valuation as an American real call option is presented.     

The pricing of Asian options under stochastic interest rates

The purpose of this paper is to analyse the effect of stochastic interest rates on the pricing of Asian options. It is shown that a stochastic, in contrast to a deterministic, development of the term structure of interest rates has a significant influence. The price of the underlying asset, e.g. a stock or oil, and the prices of bonds are assumed to follow correlated two-dimensional Itô processes. The averages considered in the Asian options are calculated on a discrete time grid, e.g. all closing prices on Wednesdays during the lifetime of the contract. The value of an Asian option will be obtained through the application of Monte Carlo simulation, and for this purpose the stochastic processes for the basic assets need not be severely restricted. However, to make comparison with published results originating from models with deterministic interest rates, we will stay within the setting of a Gaussian framework.     

Valuing the option to invest in an incomplete market

This paper considers the impact of entrepreneurial risk aversion and incompleteness on investment timing and the value of the option to invest. A risk averse entrepreneur faces the irreversible decision of when to pay a cost in order to receive a one-off investment payoff. The uncertainty associated with the investment payoff can be partly offset by hedging, but the remaining unhedgeable risk is idiosyncratic. Nested within our incomplete set-up is the complete model of McDonald and Siegel (Q J Econ 101:707–727, 1986) which assumes investment payoffs are perfectly spanned by traded assets. We find risk aversion and idiosyncratic risk erode option value and lower the investment threshold. Our main finding is that there is a parameter region within which the complete and incomplete models give differing investment signals. In this region, the option is never exercised (and investment never occurs) in the complete model, whereas the entrepreneur exercises the option in the incomplete setting. Strikingly, this parameter region corresponds to a negative implicit dividend yield on the payoff, and so this exercise behavior contrasts with conventional wisdom of Merton (Bell J Econ Manage 4:141–183, 1973) for complete markets. Finally, in this parameter region, increased volatility speeds-up investment and option values are not strictly convex in project value, in sharp contrast to the conclusion of standard real options models. The author thanks George Constantinides, Graham Davis, Jerome Detemple, Avinash Dixit, David Hobson, Stewart Hodges, Bart Lambrecht, Andrew Lyasoff, Robert McDonald, Pierre Mella-Barral, Jianjun Miao, Bob Nau (ES discussant), Gordon Sick, James Smith, Stathis Tompaidis, Elizabeth Whalley and Zvi Wiener for their comments. The author also thanks seminar participants at the University of Texas at Austin (2004), Kings College London, the Cornell Finance Workshop, the Oxford-Princeton Finance Workshop, the BIRS Finance Workshop (2004), the Eighth Annual Real Options conference, the Bachelier Finance Society Third World Congress (2004), Princeton University, Boston University, the Fields Institute Toronto, QMF 2004, Warwick Business School, and the Econometric Society Winter Meetings (2006). First version: July, 2004.     

Impact of sourcing flexibility on the outsourcing of services under demand uncertainty

This paper investigates the relationship between market conditions and the value and use of sourcing flexibility for service processes. We develop and analyze a series of models, and we derive expressions for the optimal switching decision, the value of the option to outsource, the value of the option to backsource, and the probability and timing of switches between the alternative sources.     

Modeling the dynamics of interest rate volatility with skewed fat-tailed distributions

This paper proposes generalized parametric models of the short-term interest rate that nest one-factor CEV and discrete time GARCH models. The paper estimates the generalized and nested models with skewed fat-tailed distributions to determine the correct specification of the conditional distribution of interest rates. The results indicate that the discrete time models that incorporate the level and GARCH effects into the diffusion function and that accommodate the tail-thickness of the interest rate distribution perform much better than the CEV model in forecasting the future volatility of interest rates. The results also show that the significance of nonlinearity in the drift function relies crucially on the specification of the volatility function.     

Capacity switching options under rivalry and uncertainty

Deregulated infrastructure industries exhibit stiff competition for market share. Firms may be able to limit the effects of competition by launching new projects in stages. Using a two-stage real options model, we explore the value of such flexibility. We first demonstrate that the value of investing in a sequential manner for a monopolist is positive but decreases with uncertainty. Next, we find that a typical duopoly firm’s value relative to a monopolist’s decreases with uncertainty as long as the loss in market share is high. Intriguingly, this result is reversed for a low loss in market share. We finally show that this loss in value is reduced if a firm invests in a sequential manner and specify the conditions under which sequential capacity expansion is more valuable for a duopolist firm than for a monopolist.     

Option pricing under joint dynamics of interest rates, dividends, and stock prices

This paper proposes a unified framework for option pricing, which integrates the stochastic dynamics of interest rates, dividends, and stock prices under the transversality condition. Using the Vasicek model for the spot rate dynamics, I compare the framework with two existing option pricing models. The main implication is that the stochastic spot rate affects options not only directly but also via an endogenously determined dividend yield and return volatility; consequently, call prices can be decreasing with respect to interest rates.     

Mean–variance efficiency with extended CIR interest rates

We study a mean–variance investment problem in a continuous‐time framework where the interest rates follow Cox–Ingersoll–Ross dynamics. We construct a mean–variance efficient portfolio through the solutions of backward stochastic differential equations. We also give sufficient conditions under which an explicit analytic expression is available for the mean–variance optimal wealth of the investor. Copyright © 2009 John Wiley & Sons, Ltd.     

风险项目的投资期权分析

本文讨论了风险投资家向企业主融资时的投资期权,求出了投资期权的表达式,并对其中的一些参数进行了分析.     

The impacts of uncertainties in a real options model under incomplete information

This paper examines the impact with respect to the uncertainty of the underlying state variable, profit uncertainty, on the real options model in a situation of incomplete information. Profit uncertainty has not incorporated into the real options model under incomplete information, in that the underlying state variable is not formulated as the stochastic process (see, e.g., Bernardo, A. E., Chowdhry, E. B., 2002. Resources, real options, and corporate strategy. Journal of Financial Economics, 63, 211–234). We extend the model developed by Bernardo and Chowdhry to formulate the underlying state variable as the stochastic process. We conclude that profit uncertainty has the same type of impact on the real options value and its triggers, both under complete and incomplete information.     

Volatility estimation for stochastic project value models

One of the key parameters in modeling capital budgeting decisions for investments with embedded options is the project volatility. Most often, however, there is no market or historical data available to provide an accurate estimate for this parameter. A common approach to estimating the project volatility in such instances is to use a Monte Carlo simulation where one or more sources of uncertainty are consolidated into a single stochastic process for the project cash flows, from which the volatility parameter can be determined. Nonetheless, the simulation estimation method originally suggested for this purpose systematically overstates the project volatility, which can result in incorrect option values and non-optimal investment decisions. Examples that illustrate this issue numerically have appeared in several recent papers, along with revised estimation methods that address this problem. In this article, we extend that work by showing analytically the source of the overestimation bias and the adjustment necessary to remove it. We then generalize this development for the cases of levered cash flows and non-constant volatility. In each case, we use an example problem to show how a revised estimation methodology can be applied.     

随机利率下亚式期权的定价模型

§1Introduction Asianoptionpayoffdependsontheaverageofassetpricesoverthelifeofoptions.Theirpopularityistoavoidthepossiblepricemanipulationatthematuritydatefor ordinaryoptions.ItturnsouttobedifficulttoderiveBlack-Scholes-likeclosed-form formulaforAsianoptionsbecausethedistributionofarithmetic-averageassetpricesdoes nothavestandardexpression.AlotofworkhasbeendoneonpricingAsianoptionssince KemmaandVorst(1990).Manytreatmentsdealwiththecaseofgeometricaverageforthe firststepeitherasanapproximatio…