Urban Spatial Development: a Real Options Approach

We investigate urban spatial development assuming that landowners irreversibly develop property in an uncertain environment. Unlike the standard monocentric city model, we assume that bid rents for houses are not monotonically decreasing with the distance from the central business district (CBD) because there exist subcenters that are subsidiary to the CBD. As a result, land is initially developed outward from the CBD. Leapfrog development may happen, i.e., distant land from the CBD may be developed prior to nearby land; however, land that is developed later will be more densely developed because it is developed at a better state of nature. We further find that the development patterns of at least four large cities are consistent with that predicted by our model.     

Product Development and Market Expansion: A Real Options Model

We create a model that values complementary and substitute products with potentially correlated revenues, which must be developed sequentially. The model also incorporates the effects of changing market conditions. We find that the value of a combined project increases in correlation, but the probability of investing in the initial product is a decreasing function of correlation. These results are reversed if the products are substitutes. Regardless of the correlation level, higher levels of substitutability reduce the value of the combined projects and increase the probability of investing. Despite greater uncertainty during the phase of limited competition, the firm is more likely to invest early than to postpone investment.     

A Bayesian Approach to Real Options: The Case of Distinguishing between Temporary and Permanent Shocks

Traditional real options models demonstrate the importance of the “option to wait” due to uncertainty over future shocks to project cash flows. However, there is often another important source of uncertainty: uncertainty over the permanence of past shocks. Adding Bayesian uncertainty over the permanence of past shocks augments the traditional option to wait with an additional “option to learn.” The implied investment behavior differs significantly from that in standard models. For example, investment may occur at a time of stable or decreasing cash flows, respond sluggishly to cash flow shocks, and depend on the timing of project cash flows.     

Real Options: Experimental Evidence

Empirical testing of the real options theory has been very limited. This is primarily due to various inherent problems with obtaining field data for many components of real options theory. This paper utilizes experimental methodology to generate the data. The advantage of the experimental approach is that it enables the investigator to generate reliable and replicable data in a controlled environment. The results of the experiment indicate that fundamental insights of real options theory are not evident to individual investors. The majority invested too early and thus failed to recognize the benefit of the option to wait. However, when the investors had to compete with others for the right to invest, their bids generally reflected the value of the embedded option. Furthermore, as predicted by the theory, their bids increased with greater uncertainty about future cash flows from the investment.     

Laboratory Evidence on How Managers Intuitively Value Real Growth Options

We asked 82 experienced managers to value, in effect, a set of real options, by taking decisions on invented case studies. The classic Black Scholes model should set an upper bound for rational valuations of these options (since it assumes a risk neutral discount rate, which may be optimistic). The managers valued their options erratically, and generally optimistically, though their responses to changes in moneyness, volatility and maturity tended to be in the 'correct' directions. Oil industry managers over-valued least, relative to Black-Scholes, and Brewery managers most. Questionnaires explored managers' perceptions of the real option parameters encountered in their workplaces.     

Valuing Assets Using Real Options: An Application to Deregulated Electricity Markets

This paper provides a detailed case of the application of real options valuation techniques to value a contract for the use of a power generation facility. The authors' aim is not primarily to offer a valuation "recipe" for a specific type of asset, but to show how the real options framework can be actually made to work in a variety of situations.
The case illustrates how minor adaptations that take into account the ways in which actual settings differ from the assumptions of standard formulas like Black-Scholes can be used to increase the precision and realism of results. By introducing relatively simple changes to a standard options valuation model, the authors obtain results that are reasonably close to those reported for actual transactions involving similar types of assets. Despite the industry-specific context of the analysis, the applicability of the techniques discussed in the paper should extend beyond the energy industry to other contexts characterized by similar types of uncertainty and production process, particularly those associated with minerals and other commodities.     

The Value of Embedded Real Options: Evidence from Consumer Automobile Lease Contracts

Under the common assumption of constant interest rates, we show that penalties for early termination of a lease are often structured in such a way that the cancellation option embedded in consumer automotive leases has little value. Furthermore, our estimates drawn from a sample of three popular car models over 1990 to 2000 indicate that the stand‐alone value of the lease‐end purchase option is, on average, about 16% of the market value of underlying used vehicles, or about $1,462 per contract. Finally, we examine the sensitivity of our option value estimates to model parameters and default risk.     

Pricing Exotic Options and American Options: A Multidimensional Asymptotic Expansion Approach

This paper introduces a new method for pricing exotic options whose payoff functions depend on several stochastic indices and American options in multidimensional models. This method is based on two ideas. One is an application of the asymptotic expansion method for the law of a multidimensional diffusion process. The other is the combination of the asymptotic expansion method and the method called backward induction. The author applies the method to the problems of pricing call options on the maximum of two assets in the CEV model, average strike options in the Black–Scholes model and American options in the Heston model. Numerical examples show practical effectiveness of the proposed method.     

The Real Options Component and Market Value of Taiwan Technological Companies

Real options valuation has been applied in real investment extensively. However the empirical researches of real options components’ value are seldom studied. This study uses the panel data model to test whether the stock prices of Taiwan listed companies reflect investor’s expectations regarding the value of real options. This article demonstrates that investors cannot ignore the real options components when evaluating stock market value. The results also confirm that the proportion of a firm’s market value not due to assets-in-place is significantly and positively related to the variables of stock beta, skewness of stock returns, size, capital stock, and research and development. In addition, firms with lower firm life cycle have a higher real options value.     

Interest Tax Shields: A Barrier Options Approach

There is a link between barrier options and tax shields of interest expense. We combine this link with a traditional valuation approach, to present practical valuation formulas for interest tax shields in three debt scenarios with risk of default: (1) constant debt, (2) delayed debt, and (3) debt refinancing. In all cases, default and refinancing are contingent on the random evolution of the income of the firm. For each scenario, we work out sensitivity analysis of the value of tax shields with respect to income, growth, systematic and business risk, risk-free interest rate, interest coverage ratio covenant, and the firm??s refinancing strategy.     

Fundamental Real Estate Prices: An Empirical Estimation with International Data

We propose two alternative models to estimate fundamental prices on real estate markets. The first model is based on a no-arbitrage condition between renting and buying. The second model interprets the period costs as the result of market equilibrium between housing demand and supply. We estimate both models for the USA, the UK, Japan, Switzerland, and the Netherlands. We find that observed prices deviate substantially and for long periods from their estimated fundamental values. However, we find some evidence that, in the long-run, actual prices tend to return to their fundamental values progressively. This result is due to both impulse–response functions and forecast analyses. In particular, we find that using the fundamental price significantly increases the accuracy of out-of-sample long-term forecasts of the price.

Real Options: Meeting the Georgetown Challange

In response to the demand for a single, generally accepted real options methodology, this article proposes a four‐step process leading to a practical solution to most applications of real option analysis. The first step is familiar: calculate the standard net present value of the project assuming no managerial flexibility, which results in a value estimate (and a “branch” of a decision tree) for each year of the project's life. The second step estimates the volatility of the value of the project and produces a value tree designed to capture the main sources of uncertainty. Note that the authors focus on the uncertainty about overall project value, which is driven by uncertainty in revenue growth, operating margins, operating leverage, input costs, and technology. The key point here is that, in contrast to many real options approaches, none of these variables taken alone is assumed to be a reliable surrogate for the uncertainty of the project itself. For example, in assessing the option value of a proven oil reserve, the relevant measure of volatility is the volatility not of oil prices, but of the value of the operating entity—that is, the project value without leverage. The third step attempts to capture managerial flexibility using a decision “tree” that illustrates the decisions to be made, their possible outcomes, and their corresponding probabilities. The article illustrate various kinds of applications, including a phased investment in a chemical plant (which is treated as a compound option) and an investment in a peak‐load power plant (a switching option with changing variance, which precludes the use of constant risk‐neutral probabilities as in standard decision tree analysis). The fourth and final step uses a “no‐arbitrage” approach to form a replicating portfolio with the same payouts as the real option. For most corporate investment projects, it is impossible to locate a “twin security” that trades in the market. In the absence of such a security, the conventional NPV of a project (again, without flexibility) is the best candidate for a perfectly correlated underlying asset because it represents management's best estimate of value based on the expected cash flows of the project.     

The Real Options Component of Firm Market Value: The Case of the Technological Corporation

Abstract:   This paper tests whether stock prices reflect investor's expectations regarding the value of real options. The analysis is implemented based on a sample of 391 high‐tech companies listed on main OECD stock markets during the period December 1994 through December 2000. Results confirm the predicted relation between the fraction of a firm's market value not accounted for by its assets‐in‐place, and a series of variables that are assumed to disclose its real options value, variables such as research and development activity, risk and skewness of stock returns, and size. The results are robust even after controlling for valuation date, sub‐industry, country, and alternative measures of risk.     

实物期权研究述评

实物期权思想是Wcisbrod（1974）和Arrow（1974）等人研究在给定不可逆条件下政府投资决策时首先提出的。随后,实物期权被广泛运用于资本预算和价值评估领域,相比传统的资本预算模型（DCF）具有无比优越性。而将实物期权理论用于解释企业存在与效率边际则为企业理论提供了一个动态的观察角度,必将对企业理论的发展产生深远影响。     

A Fuzzy Set Approach for Generalized CRR Model: An Empirical Analysis of S&;P 500 Index Options

This paper applies fuzzy set theory to the Cox, Ross and Rubinstein (CRR) model to set up the fuzzy binomial option pricing model (OPM). The model can provide reasonable ranges of option prices, which many investors can use it for arbitrage or hedge. Because of the CRR model can provide only theoretical reference values for a generalized CRR model in this article we use fuzzy volatility and fuzzy riskless interest rate to replace the corresponding crisp values. In the fuzzy binomial OPM, investors can correct their portfolio strategy according to the right and left value of triangular fuzzy number and they can interpret the optimal difference, according to their individual risk preferences. Finally, in this study an empirical analysis of S&P 500 index options is used to find that the fuzzy binomial OPM is much closer to the reality than the generalized CRR model.This project has been supported by NSC 93-2416-H-009-024.JEL Classification:     

Pricing Options under Stochastic Interest Rates: A New Approach

We will generalize the Black-Scholes option pricing formula by incorporating stochastic interest rates. Although the existing literature has obtained some formulae for stock options under stochastic interest rates, the closed-form solutions have been known only under the Gaussian (Merton type) interest rate processes. We will show that an explicit solution, which is an extended Black-Scholes formula under stochastic interest rates in certain asymptotic sense, can be obtained by extending the asymptotic expansion approach when the interest rate volatility is small. This method, called the small-disturbance asymptotics for Itô processes, has recently been developed by Kunitomo and Takahashi (1995, 1998) and Takahashi (1997). We found that the extended Black-Scholes formula is decomposed into the original Black-Scholes formula under the deterministic interest rates and the adjustment term driven by the volatility of interest rates. We will illustrate the numerical accuracy of our new formula by using the Cox–Ingersoll–Ross model for the interest rates.