Real Option Problems Research Articles

An exposition of least square Monte Carlo approach for real options valuation

The least square Monte Carlo simulation (LSM) approach is a state-of-the-art approach built upon approximate dynamic programming for the selection of single or multiple exercise options, and it has been extensively used for sequential decision-making and real options valuation. Although it has been broadly discussed and employed in many real-world applications, relatively less attention has been given to some of its implementation details. This paper aims to contribute to an improved understanding of sequential decision-making and real options valuation using the LSM algorithm. In this paper, we illustrate and argue the impact of only including the in-the-money (ITM) paths and the choice of regression functions for a specific example. A simple oil production problem with two common embedded options (shrink versus expands) has been utilized for the analysis.The analyses conducted in this article for the considered decision situation confirm that when at least one of the options (decision alternatives) is relevant to the out-of-the-money (OOTM) paths, it is crucial to consider all the paths to benefit from all the flexibilities. Furthermore, the choice of regression function is shown to have minor effect on the optimal strategies and the expected project value as long as the options are deeply ITM or OOTM. However, when the options are poorly ITM or OOTM, we might reach a different solution than what would have been achieved had we used an exact dynamic programming approach. In addition, excluding OOTM paths from the analysis adversely affects the option valuation part of the LSM for the current application, leading to lower project values. In contrast, the impact of path exclusion on regression performance is less emphasized. This work also verifies the robustness of the LSM approach for the selection of the polynomial order used for tuning the regression function. While some of the findings herein are problem-specific, a similar methodology can be used to evaluate the implementation details and refine problem settings in other real options problems.

Mature offshore oil field development: Solving a real options problem using stochastic dual dynamic integer programming

Oil and gas companies are facing low output prices and are forced to focus on the development of mature fields. Relevant investment decisions for operators include lifetime-enhancing activities, such as drilling new wells or permanent shutdown. We study the problem of optimal timing of investments in mature oil and gas fields in the presence of price uncertainty, which is an example of a complex real options problem consisting of a portfolio of interdependent options. We formulate a multistage stochastic integer programming model that incorporates a detailed representation of the uncertain oil price, and demonstrate how such a complex real options problem can be efficiently solved using the Stochastic Dual Dynamic Integer Programming algorithm. The paper presents a numerical example based on realistic data and discusses our computational results. We find that only a small number of Markov states are required to represent the uncertain price process, while obtaining convergence of the lower and upper bounds of the objective function. The value of stochastic solution of 11% is considerable in this example. It is concluded that the shutdown decision tends to be postponed as a result of high decommissioning costs, high discount rates, high price uncertainty and low operational expenditures, while it generally is accelerated if the decommissioning costs increase over time.

Dynamic Evaluation of Microservice Granularity Adaptation

Microservices have gained acceptance in software industries as an emerging architectural style for autonomic, scalable, and more reliable computing. Among the critical microservice architecture design decisions is when to adapt the granularity of a microservice architecture by merging/decomposing microservices. No existing work investigates the following question: How can we reason about the trade-off between predicted benefits and cost of pursuing microservice granularity adaptation under uncertainty? To address this question, we provide a novel formulation of the decision problem to pursue granularity adaptation as a real options problem. We propose a novel evaluation process for dynamically evaluating granularity adaptation design decisions under uncertainty. Our process is based on a novel combination of real options and the concept of Bayesian surprises. We show the benefits of our evaluation process by comparing it to four representative industrial microservice runtime monitoring tools, which can be used for retrospective evaluation for granularity adaptation decisions. Our comparison shows that our process can supersede and/or complement these tools. We implement a microservice application—Filmflix—using Amazon Web Service Lambda and use this implementation as a case study to show the unique benefit of our process compared to traditional application of real options analysis.

Valuing Real Options in the Volatile Real World

Motivated by the real‐world challenges of real options evaluation faced by many companies when commodity prices exhibit dramatic volatility and project values can become negative, this study presents a framework for solving a multifactor real options problem by approximating the underlying stochastic process of project value with a generalized implied binomial tree. The proposed approach allows a flexible structure for stochastic processes with fat tail distributions, such as jump diffusion, regime switch or mean reversion and provides a more accurate estimate of the extreme downside risk by allowing negative values for the underlying project values. Our illustrative example shows that the value of a real option estimated by the proposed approach is more accurate and stable than the alternative lattice‐based approaches in the literature under a wide variety of underlying commodity process, which makes this a more robust approach for valuing complex real options under multiple sources of uncertainty in the volatile real world.

Real Options with Debt Renegotiation of Permanent Coupon Deduction

This paper addresses a classical real options problem taking debt renegotiation into account. Shareholders have a permanent American renegotiation option for a permanent coupon deduction. We provide explicit formulas for the pricing and timing of the option to start a project, optimal capital structure and optimal debt renegotiation strategy. We produce an analytical proof for a widely-used but unverified assertion that the optimal renegotiation time is just the common default time. We provide an explicit post-renegotiation coupon rate. We show that debt renegotiation increases investment option value and accelerates investment. The renegotiation surplus increases with project risk and decreases with sunk cost. The investment thresholds and the acceleration extent of investment increase with the project risk and sunk cost. For a low renegotiation cost and a low debtholders' bargaining power, shareholders tend to invest in high-risk projects. The leverage is increasing in tax rate and decreasing in bankruptcy cost. When tax rate is at a medium or low level, the leverage with renegotiation is greater than that without renegotiation. When tax rate is very high, the opposite holds. The leverage is increasing in debtholders' bargaining power. The coupon deduction ratio decreases with debtholders' bargaining power. The surplus of shareholders due to the renegotiation is decreasing in debtholders' bargaining power and renegotiation cost. For high-risk projects, the surplus of debtholders and that of shareholders are more sensitive to renegotiation cost and debtholders' bargaining power.

Pricing real options based on linear loss functions and conditional value at risk

The main purpose of this paper is to expand real option analysis out of the realm of pure financial option pricing techniques. To overcome many of the well-known concerns by adopting the financial option pricing techniques for modeling real options problems such as replicating portfolio concept, geometric Brownian motion as underlying stochastic process, and estimating project volatility, we propose an alternative real option valuation based on the loss function approach. The option value determined by the loss function approach is equivalent to the expected value of perfect information (EVPI) in decision analysis. It basically sets the upper bound of risk premium to pay in retaining the options. In practice, many firms utilize the concept of Value at Risk to manage their portfolio risk. If a firm sets a target VAR, then we may be able to link this VAR in refining the actual risk premium to pay in hedging the risk embedded in the investment. With this practice in mind, we present a logic to figure out an appropriate amount of real option premium to pay for a given level of risk tolerance. A comprehensive example is presented to demonstrate the computational procedures as well as economic interpretations on the outcomes.

Real Options Problem with Non-Smooth Obstacle

We consider a real options problem, which is posed as a stochastic optimal control problem. The investment strategy, which plays the role of control, involves a one-time option to expand (invest) and a one-time option to abandon (terminate) the project. The timing and amount of the investment and the termination time are parameters to be optimized in order to maximize the expected value of the profit. This stochastic optimization problem amounts to solving a deterministic variational inequality in dimension one, with the associated obstacle problem. Because we consider both cessation and expansion options and fixed and variable costs of expansion, the obstacle is non-smooth. Due to the lack of smoothness, we use the concept of a weak solution. However, such solutions may not lead to a straightforward investment strategy. Therefore, we further consider strong ($C^1$) solutions based on thresholds. We propose sufficient conditions for the existence of such solutions to the variational inequality with a non-smooth obstacle in dimension one. When applied to the real options problem, these sufficient conditions yield a simple optimal investment strategy with the stopping times defined in terms of the thresholds.

Closed-form solution to a real option problem with regime switching

I investigate the optimal investment timing model in which investment is feasible in only one of the two regimes, which shift at Poisson jump times. I derive the option value and investment threshold in closed forms. I also prove that some solutions in previous models are obtained as the limits of the solution. The closed-form solution can be useful as a new framework to study real option problems with the illiquidity of option exercise opportunities.

Airline investments in exclusive airport facilities: Timing decisions under demand ambiguity

In this paper, we study the timing decision of airlines’ investments in exclusive airport facilities in the presence of demand ambiguity and competition. We model the investment decision as a real options problem under ambiguity. An airline's ambiguity-averse preferences are modeled using the multiple prior expected utility form. We obtain the optimal investment timing rule for the airline and find that it requires the airline's expected present value of its future incremental profit from investing to exceed the investment cost by the option value multiplier. We then compare the airline's optimal investment timing rule to the social optimum and discuss two possible subsidy policies, a lump-sum subsidy and a per-unit subsidy, with which the government can align the airline's investment timing rule with the social optimum. We characterize the stepwise structure of both subsidy policies, in which the optimal time to invest in an exclusive terminal depends on three thresholds: the social optimum, the airline's break-even point, and a combination of the social optimum and the airline optimum. We conclude that the two subsidy policies have equivalent effects when the government and the airline have the same ambiguity levels, as they lead to the same investment timing and require the same amount of government funds.

Optimal regulation of energy network expansion when costs are stochastic

We analyze optimal regulation of the gradual investments in energy networks necessary to accommodate the energy transition. We focus on a real option problem where costs of new network technology are stochastic and not observable to the regulator. We solve for the regulatory scheme that optimally balances timely investments with rent extraction in this dynamic agency context. We then apply this methodology to a situation in which investment can be either in traditional network technology, with observable costs, or using an innovative network technology for which there is asymmetric information on costs. The optimal choice trades off the potential benefits of cheaper expansion with the costs of overcoming information frictions.

Real options, ambiguity, and dynamic consistency — A technical note

Recent research on real options does not only consider optimal investment decisions under risk, but also under ambiguity. However, most models that allow for ambiguity are generally not dynamically consistent. Examples are, among others, the α-MEU model, the imprecision aversion model, or the NMEU model. Dynamic consistency is however required to solve optimal stopping real options problems analytically or in closed-form. This paper highlights the resulting difficulties, which are often overlooked, exemplarily for the NMEU model.

Real Options, Ambiguity, and Dynamic Consistency - A Comment on 'ambiguity Aversion in Buyer-Seller Relationships: A Contingent-Claims and Social Network Explanation'

Recent research on real options does not only consider optimal investment decisions under risk, but also under ambiguity. However, most models that allow for ambiguity are generally not dynamically consistent. Examples are, among others, the $\alpha$-MEU model, the imprecision aversion model, or the NMEU model. Dynamic consistency is however required to solve optimal stopping real options problems analytically or in closed-form. This paper highlights the resulting difficulties, which are often overlooked, exemplarily for the NMEU model.

The optimal stopping problem revisited

We consider an optimal stopping time problem, related with many models found in real options problems. We present analytical solutions for a broad class of gain functions, considering quite general assumptions over the model. Also, an extensive and general sensitivity analysis is provided.

Valuing Real Options in the Volatile Real World - A Generalized Implied Binomial Tree Approach

Motivated by the real-world challenges of real options evaluation faced by many companies when commodity prices exhibit dramatic volatility and project values can become negative, this paper presents a generalized framework for solving a multifactor real options problem by approximating the underlying stochastic process of project value with a displaced implied binomial tree. The proposed approach allows a flexible structure for stochastic processes with fat tail distributions such as jump diffusion or regime switch, and provides a more accurate estimate of the extreme downside risk by allowing negative values for the underlying project values. The value of a real option by the proposed approach is more accurate and stable than the alternative lattice-based approaches in the literature regardless of the underlying commodity process, which makes this a general and robust approach for valuing complex real options under multiple sources of uncertainty in the volatile real world.

Real options in the laboratory: An experimental study of sequential investment decisions

Many real-life risky decisions in finance and management are dynamic and decision policies can be adapted as uncertainty is reduced by the arrival of new information. In this type of situation, called a real options problem, a decision maker must choose how much of his finite resources to invest in a dynamic risky environment. In two laboratory experiments, we test a well-defined decision problem with the central characteristics of a real options framework and do so in such a way that it is amendable to formal modeling. We find that people choose differently than the expected value maximizing policy, consistent with risk aversion and non-linear probability weighting. We conclude that although real options analysis is useful as a normative valuation method, its recommendations are sometimes contrary to people’s innate tendencies when making risky choices and this counterintuitiveness should be considered when implementing real options analysis in training and practice.

Considering real options in short-term decision making

Option-like situations in non-financial markets, often referred to as real options, are usually discussed and analyzed in the context of investment decisions. In spite of the real options literature’s focus on investment decisions, option-like situations are also frequently encountered in operating decisions. For instance, decisions on the operating mode of a flexible machine in the presence of switching costs can be characterized as complex real options problems with multiple compound options. For an optimal long-term solution, short-term decision rules must consider the value of these options. In this paper we first show how a fully rational decision rule that takes the long-term consequences of short-term decisions into account can be derived within the real options framework. We contrast the outcomes of decisions according to this benchmark rule with the outcomes of decisions according to the traditional decision rule based on current contribution margin and illustrate our findings with a simulation analysis providing for a rich set of environments characterized by different levels of uncertainty and different switching costs. A major drawback of the options-based rule is the necessity to estimate option values at every decision point drawing on information from all future periods. We therefore analyze how a simplified options-based decision rule that looks ahead only one period performs against the benchmark rule. In an extension of the simulation analysis we find that the simplified decision rule serves as a good heuristic and improves decision-making similar to the benchmark rule while at the same time being much more likely to be implemented in practice.

A cash flow view of real options

ABSTRACTThis article gives a cash flow view of real options in distinction from the majority of the literature on real options. Via a cash flow view, the article shows that real options can fit within conventional engineering investment analysis, in particular the usual discounted cash flow analysis familiar to most engineers, and there is no need to go looking for answers to real options problems in other disciplines. No mathematical sophistication is needed in order to understand the approach. All real options problems can be reduced to one plain option approach or, in the case of compound options, to a collection of plain options. There is no need to distinguish option type; for example, between expand or contract.

Real options decision framework: Strategic operating policies for open pit mine planning

This paper presents a first approach towards the development of a dynamics decision-making tool (DDMT) for open pit mine planning projects. In this paper, a decision framework, the so-called real option decision framework (RODF), is developed based on a real-options approach with practical applicability to a mining investment project. Four strategic operating options namely, deferral options, maintain options, expand options, and shutdown options, are assumed for mining operations. We illustrated the proposed framework and developed methods for a hypothetical gold mine. The standard discounted cash flow (DCF) method was carried out to analyze the project values without options. The real option valuation (ROV) approach was calculated for the deferral and expand options. We used a system dynamics (SD) modeling method to solve real options problems and the discrete-event simulations were used to simulate the potential values of the projects. The findings are that investors are prone to lose an opportunity to invest if relying on traditional DCF-NPV rules as they suggest accepting the project if and only if NPV is greater than zero. However, results obtained from real options suggest that the project has a value to an investor across different time horizons. The insight is that it is of paramount importance to find an optimal time to exercise a strategic option. It is indicated that strategic options such as the deferral option may yield a higher value than the base case (DCF-NPV) mine option because project risks can be hedged, whereas the expand option may also offer additional value to mine operators. However, such extra-additional values can only be captured through managerial flexibility.

FUZZY GROUPING VARIABLES IN ECONOMIC ANALYSIS. A PILOT STUDY OF A VERIFICATION OF A NORMATIVE MODEL FOR R and D ALLIANCES

(ProQuest: ... denotes formulae omitted.)1.INTRODUCTIONMany investments decisions in presence of uncertainty can be characterized as real options problems [9, 19]. Consequently, in the last decade, the development of normative techniques to evaluate real options investments, summarized by the seminal book by Dixit and Pyndyck [11], has significantly shaped the research on sequential investments and created a fruitful paradigm for its treatment [17].More recently real options analysis (ROA) has been used also to evaluate R&D alliances established between firms [8,15,16,17,25]. These agreements not only generate stochastic benefits (which suggest the existence of uncertainty) but also bring sunk costs (which imply irreversibility). In addition, a key element in these agreements is flexibility: firms have the opportunity, but not the obligation to sign an alliance, or sometimes the right to renew an existing one. In other words, they can postpone their decisions to form an alliance when more information is available. Therefore, the study of R&D alliances in a real options framework per se includes these important three aspects [23]. Despite the normative work on real option valuation, only recently some researches have started analysing behavioral aspects [19]. These studies highlight that individuals exhibit systematic deviations from the predictions derived using normative models [22].This research attempts to extend the boundaries of real options analysis to environments where people have biases in their decision-making, especially in the context of R&D alliances and merger and acquisitions as well as to provide tools for appropriate validation of the relevant models. Consistent with neoclassical rational theory, prior studies show that mergers are driven by rational expectations of growth options, synergies or reallocation of assets in a response to industry shocks. The rational view also includes real options models, where decisions such as acquisitions waves are driven by growth opportunities [30]. However, contrary to rational theory, decision makers may act irrationally when making choices under uncertainty [18,28]. Individuals exhibit systematic deviations from the predictions derived using normative models - i.e. models assuming that individuals are risk neutral expected value maximizing agents [22]. Investors' exuberance, positive sentiments of boards as well as cognitive biases - such as overconfidence - influence companies' behavior under uncertainty. To use Smit and Lovallo's [28] words, acquisition strategy is vulnerable to the way managers perceive risk and losses, judgment biases in their strategy, the bidding behavior of rivals and mispricing in financial markets. Note, that these assumptions need to be reflected also in the design of the validation instruments and in the collection of validation data. Such data need to be gathered in a way that allows for the identification of specific subgroups in the validation sample that meet the assumptions of the models. Standard grouping variables may not be applied in the analysis of the sample, since the definition of the subgroups may not be crisp (e.g. rationality, risk-aversion, etc. can manifest themselves in a particular respondent to a certain degree, not necessarily fully). The requirement of full satisfaction of certain assumptions (full rationality, full information, etc.) may render the applicable part of the validation sample too small to be still relevant. On the other hand the use of the full sample without any knowledge concerning their fulfilment of the assumptions of the model that is being validated is methodologically incorrect. This calls for two things - first, the tools for the assessment of the degree of fulfilment of the assumptions of the model in the participants (and the data they provide) need to be available (or at least built-in the data gathering procedure), and second, data analysis tools capable of dealing with fuzzy subsets of the validation sample need to be used. …

A practical analytical model for valuing early stage investments using real options

In this work, we build on a previous real options approach that utilises managerial cash-flow estimates to value early stage project investments. Through a simplifying assumption, where we assume that the managerial cash-flow estimates are normally distributed, we derive a closed-form solution to the real option problem. The model is developed through the introduction of a market sector indicator, which is assumed to be correlated to a tradeable market index and drives the project's cash-flow estimates. In this way we can model a cash-flow process that is partially correlated to a traded market index. This provides the mechanism for valuing real options of the cash-flow in a financially consistent manner under the risk-neutral minimum martingale measure. The method requires minimal subjective input of model parameters and is very easy to implement.