Real options valuation, also often termed real options analysis,(ROV or ROA) applies option valuation techniques to capital budgeting decisions. A real option itself, is the right—but not the obligation—to undertake certain business initiatives, such as deferring, abandoning, expanding, staging, or contracting a capital investment project. For example, the opportunity to invest in the expansion of a firm's factory, or alternatively to sell the factory, is a real call or put option, respectively.
Real options are generally distinguished from conventional financial options in that they are not typically traded as securities, and do not usually involve decisions on an underlying asset that is traded as a financial security.A further distinction is that option holders here, i.e. management, can directly influence the value of the option's underlying project; whereas this is not a consideration as regards the underlying security of a financial option. Moreover, management cannot measure uncertainty in terms of volatility, and must instead rely on their perceptions of uncertainty. Unlike financial options, management also have to create or discover real options, and such creation and discovery process comprises an entrepreneurial or business task. Real options are most valuable when uncertainty is high; management has significant flexibility to change the course of the project in a favorable direction and is willing to exercise the options.
Real options analysis, as a discipline, extends from its application in corporate finance, to decision making under uncertainty in general, adapting the techniques developed for financial options to "real-life" decisions. For example, R&D managers can use Real Options Valuation to help them allocate their R&D budget among diverse projects; a non business example might be the decision to join the work force, or rather, to forgo several years of income to attend graduate school.It, thus, forces decision makers to be explicit about the assumptions underlying their projections, and for this reason ROV is increasingly employed as a tool in business strategy formulation. This extension of real options to real-world projects often requires customized decision support systems, because otherwise the complex compound real options will become too intractable to handle.
This simple example shows the relevance of the real option to delay investment and wait for further information, and is adapted from "Investment Example"..
Consider a firm that has the option to invest in a new factory. It can invest this year or next year. The question is: when should the firm invest? If the firm invests this year, it has an income stream earlier. But, if it invests next year, the firm obtains further information about the state of the economy, which can prevent it from investing with losses.
The firm knows its discounted cash flows if it invests this year: 5M. If it invests next year, the discounted cash flows are 6M with a 66.7% probability, and 3M with a 33.3% probability. Assuming a risk neutral rate of 10%, future discounted cash flows are, in present terms, 5.45M and 2.73M, respectively. The investment cost is 4M. If the firm invests next year, the present value of the investment cost is 3.63M.
Following the net present value rule for investment, the firm should invest this year because the discounted cash flows (5M) are greater than the investment costs (4M) by 1M. Yet, if the firm waits for next year, it only invests if discounted cash flows do not decrease. If discounted cash flows decrease to 3M, then investment is no longer profitable. If, they grow to 6M, then the firm invests. This implies that the firm invests next year with a 66.7% probability and earns 5.45M - 3.63M if it does invest. Thus the value to invest next year is 1.21M. Given that the value to invest next year exceeds the value to invest this year, the firm should wait for further information to prevent losses. This simple example shows how the net present value may lead the firm to take unnecessary risk, which could be prevented by real options valuation.
The firm does not know how well its stores are accepted in a foreign country. If their stores have high demand, the discounted cash flows per store is 10M. If their stores have low demand, the discounted cash flows per store is 5M. Assuming that the probability of both events is 50%, the expected discounted cash flows per store is 7.5M. It is also known that if the store's demand is independent of the store: if one store has high demand, the other also has high demand. The risk neutral rate is 10%. The investment cost per store is 8M.
Should the firm invest in one store, two stores, or not invest? The net present value suggests the firm should not invest: the net present value is -0.5M per store. But is it the best alternative? Following real options valuation, it is not: the firm has the real option to open one store this year, wait a year to know its demand, and invest in the new store next year if demand is high.
By opening one store, the firm knows that the probability of high demand is 50%. The potential value gain to expand next year is thus 50%*(10M-8M)/1.1 = 0.91M. The value to open one store this year is 7.5M - 8M = -0.5. Thus the value of the real option to invest in one store, wait a year, and invest next year is 0.41M. Given this, the firm should opt by opening one store. This simple example shows that a negative net present value does not imply that the firm should not invest.
The flexibility available to management – i.e. the actual "real options" – generically, will relate to project size, project timing, and the operation of the project once established. In all cases, any (non-recoverable) upfront expenditure related to this flexibility is the option premium. Real options are also commonly applied to stock valuation - see Business valuation #Option pricing approaches - as well as to various other "Applications" referenced below.
Where the project's scope is uncertain, flexibility as to the size of the relevant facilities is valuable, and constitutes optionality.
Where there is uncertainty as to when, and how, business or other conditions will eventuate, flexibility as to the timing of the relevant project(s) is valuable, and constitutes optionality. Growth options are perhaps the most generic in this category – these entail the option to exercise only those projects that appear to be profitable at the time of initiation.
Management may have flexibility relating to the product produced and /or the process used in manufacture. This flexibility constitutes optionality.
Given the above, it is clear that there is an analogy between real options and financial options,and we would therefore expect options-based modelling and analysis to be applied here. At the same time, it is nevertheless important to understand why the more standard valuation techniques may not be applicable for ROV.
ROV is often contrasted with more standard techniques of capital budgeting, such as discounted cash flow (DCF) analysis / net present value (NPV).Under this "standard" NPV approach, future expected cash flows are present valued under the empirical probability measure at a discount rate that reflects the embedded risk in the project; see CAPM, APT, WACC. Here, only the expected cash flows are considered, and the "flexibility" to alter corporate strategy in view of actual market realizations is "ignored"; see below as well as Corporate finance#Valuing flexibility. The NPV framework (implicitly) assumes that management is "passive" with regard to their Capital Investment once committed. Some analysts account for this uncertainty by (i) adjusting the discount rate, e.g. by increasing the cost of capital, or (ii) adjusting the cash flows, e.g. using certainty equivalents, or (iii) applying (subjective) "haircuts" to the forecast numbers, or (iv) via probability-weighting these as in rNPV. Even when employed, however, these latter methods do not normally properly account for changes in risk over the project's lifecycle and hence fail to appropriately adapt the risk adjustment.
By contrast, ROV assumes that management is "active" and can "continuously" respond to market changes. Real options consider "all" scenarios (or "states") and indicate the best corporate action in each of these contingent events.Because management adapts to each negative outcome by decreasing its exposure and to positive scenarios by scaling up, the firm benefits from uncertainty in the underlying market, achieving a lower variability of profits than under the commitment/NPV stance. The contingent nature of future profits in real option models is captured by employing the techniques developed for financial options in the literature on contingent claims analysis. Here the approach, known as risk-neutral valuation, consists in adjusting the probability distribution for risk consideration, while discounting at the risk-free rate. This technique is also known as the "martingale" approach, and uses a risk-neutral measure. For technical considerations here, see below.
Given these different treatments, the real options value of a project is typically higher than the NPV – and the difference will be most marked in projects with major flexibility, contingency, and volatility. As for financial options higher volatility of the underlying leads to higher value. (An application of Real Options Valuation in the Philippine banking industry exhibited that increased levels of income volatility may adversely affect option values on the loan portfolio, when the presence of information asymmetry is considered. In this case, increased volatility may limit the value of an option. ) Part of the criticism (and subsequently slow adoption) of Real Options Valuation in practice and academe stems from the generally higher values for underlying assets these functions generate. However, studies have shown that these models are reliable estimators of underlying asset value, when input values are properly identified.
Although there is much similarity between the modelling of real options and financial options,ROV is distinguished from the latter, in that it takes into account uncertainty about the future evolution of the parameters that determine the value of the project, coupled with management's ability to respond to the evolution of these parameters. It is the combined effect of these that makes ROV technically more challenging than its alternatives.
|“||First, you must figure out the full range of possible values for the underlying asset.... This involves estimating what the asset's value would be if it existed today and forecasting to see the full set of possible future values... [These] calculations provide you with numbers for all the possible future values of the option at the various points where a decision is needed on whether to continue with the project...||”|
When valuing the real option, the analyst must therefore consider the inputs to the valuation, the valuation method employed, and whether any technical limitations may apply. Conceptually, valuing a real option looks at the premium between inflows and outlays for a particular project. Inputs to the value of a real option (time, discount rates, volatility, cash inflows and outflows) are each affected by the terms of business, and external environmental factors that a project exists in. Terms of business as information regarding ownership, data collection costs, and patents, are formed in relation to political, environmental, socio-cultural, technological, environmental and legal factors that affect an industry. Just as terms of business are affected by external environmental factors, these same circumstances affect the volatility of returns, as well as the discount rate (as firm or project specific risk). Furthermore, the external environmental influences that affect an industry affect projections on expected inflows and outlays.
Given the similarity in valuation approach, the inputs required for modelling the real option correspond, generically, to those required for a financial option valuation.The specific application, though, is as follows:
The valuation methods usually employed, likewise, are adapted from techniques developed for valuing financial options.Note though that, in general, while most "real" problems allow for American style exercise at any point (many points) in the project's life and are impacted by multiple underlying variables, the standard methods are limited either with regard to dimensionality, to early exercise, or to both. In selecting a model, therefore, analysts must make a trade off between these considerations; see Option (finance) #Model implementation. The model must also be flexible enough to allow for the relevant decision rule to be coded appropriately at each decision point.
Various other methods, aimed mainly at practitioners, have been developed for real option valuation. These typically use cash-flow scenarios for the projection of the future pay-off distribution, and are not based on restricting assumptions similar to those that underlie the closed form (or even numeric) solutions discussed. The most recent additions include the Datar–Mathews methodand the fuzzy pay-off method.
The relevance of Real options, even as a thought framework, may be limited due to market, organizational and / or technical considerations.When the framework is employed, therefore, the analyst must first ensure that ROV is relevant to the project in question. These considerations are as follows.
As discussed above, the market and environment underlying the project must be one where "change is most evident", and the "source, trends and evolution" in product demand and supply, create the "flexibility, contingency, and volatility"which result in optionality. Without this, the NPV framework would be more relevant.
Real options are "particularly important for businesses with a few key characteristics",and may be less relevant otherwise. In overview, it is important to consider the following in determining that the RO framework is applicable:
Limitations as to the use of these models arise due to the contrast between Real Options and financial options, for which these were originally developed. The main difference is that the underlying is often not tradable – e.g. the factory owner cannot easily sell the factory upon which he has the option. Additionally, the real option itself may also not be tradeable – e.g. the factory owner cannot sell the right to extend his factory to another party, only he can make this decision (some real options, however, can be sold, e.g., ownership of a vacant lot of land is a real option to develop that land in the future). Even where a market exists – for the underlying or for the option – in most cases there is limited (or no) market liquidity. Finally, even if the firm can actively adapt to market changes, it remains to determine the right paradigm to discount future claims
The difficulties, are then:
These issues are addressed via several interrelated assumptions:
Whereas business managers have been making capital investment decisions for centuries, the term "real option" is relatively new, and was coined by Professor Stewart Myers of the MIT Sloan School of Management in 1977. In 1930, Irving Fisher wrote explicitly of the "options" available to a business owner ( The Theory of Interest , II.VIII). The description of such opportunities as "real options", however, followed on the development of analytical techniques for financial options, such as Black–Scholes in 1973. As such, the term "real option" is closely tied to these option methods.
Real options are today an active field of academic research. Professor Lenos Trigeorgis has been a leading name for many years, publishing several influential books and academic articles. Other pioneering academics in the field include Professors Michael Brennan, Eduardo Schwartz, Graham Davis, Gonzalo Cortazar, Han Smit, Avinash Dixit and Robert Pindyck (the latter two, authoring the pioneering text in the discipline). An academic conference on real options is organized yearly (Annual International Conference on Real Options).
Amongst others, the concept was "popularized" by Michael J. Mauboussin, then chief U.S. investment strategist for Credit Suisse First Boston.He uses real options to explain the gap between how the stock market prices some businesses and the "intrinsic value" for those businesses. Trigeorgis also has broadened exposure to real options through layman articles in publications such as The Wall Street Journal. This popularization is such that ROV is now a standard offering in postgraduate finance degrees, and often, even in MBA curricula at many Business Schools.
Recently, real options have been employed in business strategy, both for valuation purposes and as a conceptual framework.The idea of treating strategic investments as options was popularized by Timothy Luehrman in two HBR articles: "In financial terms, a business strategy is much more like a series of options, than a series of static cash flows". Investment opportunities are plotted in an "option space" with dimensions "volatility" & value-to-cost ("NPVq").
Luehrman also co-authored with William Teichner a Harvard Business School case study, Arundel Partners: The Sequel Project, in 1992, which may have been the first business school case study to teach ROV.Reflecting the "mainstreaming" of ROV, Professor Robert C. Merton discussed the essential points of Arundel in his Nobel Prize Lecture in 1997. Arundel involves a group of investors that is considering acquiring the sequel rights to a portfolio of yet-to-be released feature films. In particular, the investors must determine the value of the sequel rights before any of the first films are produced. Here, the investors face two main choices. They can produce an original movie and sequel at the same time or they can wait to decide on a sequel after the original film is released. The second approach, he states, provides the option not to make a sequel in the event the original movie is not successful. This real option has economic worth and can be valued monetarily using an option-pricing model. See Option (filmmaking).
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In finance, a bond option is an option to buy or sell a bond at a certain price on or before the option expiry date. These instruments are typically traded OTC.
In mathematical finance, a Monte Carlo option model uses Monte Carlo methods to calculate the value of an option with multiple sources of uncertainty or with complicated features. The first application to option pricing was by Phelim Boyle in 1977. In 1996, M. Broadie and P. Glasserman showed how to price Asian options by Monte Carlo. In 2001 F. A. Longstaff and E. S. Schwartz developed a practical Monte Carlo method for pricing American-style options.
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Financial modeling is the task of building an abstract representation of a real world financial situation. This is a mathematical model designed to represent the performance of a financial asset or portfolio of a business, project, or any other investment.
In finance, a lattice model is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option, where a decision as to option exercise is required at "all" times before and including maturity. A continuous model, on the other hand, such as Black–Scholes, would only allow for the valuation of European options, where exercise is on the option's maturity date. For interest rate derivatives lattices are additionally useful in that they address many of the issues encountered with continuous models, such as pull to par. The method is also used for valuing certain exotic options, where because of path dependence in the payoff, Monte Carlo methods for option pricing fail to account for optimal decisions to terminate the derivative by early exercise., though methods now exist for solving this problem.
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The following outline is provided as an overview of and topical guide to finance:
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The fuzzy pay-off method for real option valuation is a method for valuing real options, developed by Mikael Collan, Robert Fullér, and József Mezei; and published in 2009. It is based on the use of fuzzy logic and fuzzy numbers for the creation of the possible pay-off distribution of a project. The structure of the method is similar to the probability theory based Datar–Mathews method for real option valuation, but the method is not based on probability theory and uses fuzzy numbers and possibility theory in framing the real option valuation problem.
Eduardo Saul Schwartz is a professor of finance at the Anderson School of Management, University of California, Los Angeles, where he holds the California Chair in Real Estate & Land Economics. He is known for pioneering research in several areas of finance, particularly derivatives. His major contributions include: the real options method of pricing investments under uncertainty; the Longstaff–Schwartz model - a multi-factor short-rate model; the Longstaff-Schwartz method for valuing American options by Monte Carlo Simulation; the use of Finite difference methods for option pricing.
The Datar–Mathews Method is a method for real options valuation. The method provides an easy way to determine the real option value of a project simply by using the average of positive outcomes for the project. The method can be understood as an extension of the net present value (NPV) multi-scenario Monte Carlo model with an adjustment for risk aversion and economic decision-making. The method uses information that arises naturally in a standard discounted cash flow (DCF), or NPV, project financial valuation. It was created in 2000 by Vinay Datar, professor at Seattle University; and Scott H. Mathews, Technical Fellow at The Boeing Company.
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