The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging

In this article we compare three models of the stochastic behavior of commodity prices that take into account mean reversion, in terms of their ability to price existing futures contracts, and their implication with respect to the valuation of other financial and real assets. The first model is a simple one-factor model in which the logarithm of the spot price of the commodity is assumed to follow a mean reverting process. The second model takes into account a second stochastic factor, the convenience yield of the commodity, which is assumed to follow a mean reverting process. Finally, the third model also includes stochastic interest rates. The Kalman filter methodology is used to estimate the parameters of the three models for two commercial commodities, copper and oil, and one precious metal, gold. The analysis reveals strong mean reversion in the commercial commodity prices. Using the estimated parameters, we analyze the implications of the models for the term structure of futures prices and volatilities beyond the observed contracts, and for hedging contracts for future delivery. Finally, we analyze the implications of the models for capital budgeting decisions.     

REAL OPTIONS: STATE OF THE PRACTICE

In the mid‐1980s, financial economists began building option‐based models to value corporate investments in real assets, laying the foundation for an extensive academic literature in this area. The 1990s saw several books, numerous conferences, and many articles aimed at corporate practitioners, who began to experiment with these techniques. Now, as we approach the end of 2001, the real options approach to valuing real investments has established a solid, albeit limited, foothold in the corporate world. Based on their recent interviews with 39 individuals from 34 companies in seven different industries, the authors of this article attempt to answer the question, “How is real options being practiced, and what impact is it having in the corporate setting?” The article identifies three main corporate uses of real options—as a strategic way of thinking, an analytical valuation tool, and an organization‐wide process for evaluating, monitoring, and managing capital investments. For example, in some companies, real options is used as an input into an M&A process in which rigorous numerical analysis plays only a small role. In such cases, real options contributes as a qualitative way of thinking, with little formality either in terms of analytical rigor or organizational procedure. In other firms, real options is used in a commodity trading environment where options are clearly specified in contracts and simply need to be valued. In this case, real options functions as an analytical tool, though generally only in specialized areas of the firm and not on an organization‐wide basis. In still other companies, real options is used in a technology or R&D context where the firm's success is driven by identifying and managing potential sources of flexibility. In such cases, real options functions as an organization‐wide process with both a broad conceptual and analytical core. The companies that have shown the greatest interest in real options generally operate in industries where large investments with uncertain returns are commonplace, such as oil and gas, and life sciences. Major applications include the evaluation of exploration and production investments in oil and gas firms, generation plant investments in power firms, R&D portfolios in pharmaceutical and biotech firms, and technology investment portfolios in high‐tech firms. While the approaches to implementation are quite varied, there appears to be a common path to the successful adoption of real options. The key steps of the adoption process are: (1) conducting pilot projects; (2) getting buy‐in from senior‐level and rank‐and‐file managers; (3) codifying real options through expert working groups, specialist training, and customization; and (4) institutionalizing and integrating real options firm‐wide. After citing best practices for each of these four steps, the authors close by predicting that a “network” effect and acceptance by Wall Street will serve as catalysts for more widespread corporate use of real options.     

Managing Operational Flexibility in Investment Decisions: The Case of Intel

Significant attention has been paid to how real options analysis can help in valuing operating flexibility when making major capital investment decisions. But there has been far less study of how to manage such flexibility, particularly in cases where a decision to defer, contract, or expand any one investment program affects a range of other programs, including those outside the firm. Such interrelated investments are increasingly common in a "connected" economy where products and technologies are designed across firms and industries.
Based on a field study at Intel, this paper describes and analyzes one set of practices for coordinating such diverse systems of investments. It shows how information about interrelated investments is communicated within and between companies so that coherent changes can be made at the level of an overall system. The authors argue that studies of investment appraisal need to move beyond the predominant focus on valuation to encompass the wider organizational processes by which operational flexibility is exercised in the modern economy.     

Valuation and systemic risk consequences of bank opacity

We examine the effects of opacity on bank valuation and synchronicity in bank equity returns over the years 2000–2006 prior to the 2007 financial crisis. As expected, investments in opaque assets are more profitable than investments in transparent assets, and taking profitability into account, have larger valuation discounts relative to transparent assets. The valuation discounts on opaque asset investments decline over the 2000–2006 period only to be followed by a sharp reversal in 2007. The decline is coincident with a rise in bank equity share prices, decrease in transparent asset holdings by banks, and greater return synchronicity – evidence consistent with a feedback effect.     

The impact of strategic interaction on earnings expectations associated with corporate product strategies

We examine how strategic interaction in an industry influences the earnings expectations of financial analysts with regard to new product strategies. We find that following announcement of new products, analysts revise earnings forecasts upward more for announcing firms competing in low-strategic interaction industries than for firms competing in high-strategic interaction industries. For value-enhancing (value-reducing) product strategies, earnings forecast revisions are more favorable for rivals competing under a high (low) degree of strategic interaction than for rivals competing under a low (high) degree of strategic interaction. Overall empirical evidence indicates that the nature of strategic competition within the industry is important in assessing the market expectations of earnings for new product announcers and their rivals.     

Price dispersion in OTC markets: A new measure of liquidity

In this paper, we model price dispersion effects in over-the-counter (OTC) markets to show that, in the presence of inventory risk for dealers and search costs for investors, traded prices may deviate from the expected market valuation of an asset. We interpret this deviation as a liquidity effect and develop a new liquidity measure quantifying the price dispersion in the context of the US corporate bond market. This market offers a unique opportunity to study liquidity effects since, from October 2004 onwards, all OTC transactions in this market have to be reported to a common database known as the Trade Reporting and Compliance Engine (TRACE). Furthermore, market-wide average price quotes are available from Markit Group Limited, a financial information provider. Thus, it is possible, for the first time, to directly observe deviations between transaction prices and the expected market valuation of securities. We quantify and analyze our new liquidity measure for this market and find significant price dispersion effects that cannot be simply captured by bid-ask spreads. We show that our new measure is indeed related to liquidity by regressing it on commonly-used liquidity proxies and find a strong relation between our proposed liquidity measure and bond characteristics, as well as trading activity variables. Furthermore, we evaluate the reliability of end-of-day marks that traders use to value their positions. Our evidence suggests that the price deviations from expected market valuations are significantly larger and more volatile than previously assumed. Overall, the results presented here improve our understanding of the drivers of liquidity and are important for many applications in OTC markets, in general.     

A Reduced‐Form Model for Warrant Valuation

This paper studies warrant valuation using a reduced‐form model. Analogous to the credit risk literature, structural models require complete information about the asset value process and the firm’s liabilities. In contrast, reduced‐form models require only information about the firm’s stock price process. We introduce a reduced‐form model where the warrant holder is a price taker, and we relate our model to structural models appearing in the literature.     

Oil price dynamics,macro-finance interactions and the role of financial speculation

What is the role of financial speculation in determining the real oil price? We find that while macroeconomic shocks have been the main real oil price upward driver since mid-1980s, financial shocks have sizably contributed since early 2000s as well, and at a much larger extent since mid-2000s. Even though financial shocks contribute 44% out of the 65% real oil price increase over the period 2004–2010, the third oil price shock is a macro-finance episode: macroeconomic shocks actually largely account for the 2007–2008 oil price swing. While we then find support to the demand side view of real oil price determination, we however also find a much larger role for financial shocks than previously noted in the literature.     

New evidence on the price and liquidity effects of the FTSE 100 index revisions

We study the price and liquidity effects following the FTSE 100 index revisions. We employ the standard GARCH(1,1) model to allow the residual variance of the single index model (SIM) to vary systematically over time and use a Kalman filter approach to model SIM coefficients as a random walk process. We show that the observed price effect depends on the abnormal return estimation methods. Specifically, the OLS-based abnormal returns indicate that the price effect associated with the index revision is temporary, whereas both SIM with random coefficients and GARCH(1,1) model suggest that both additions and deletions experience permanent price change. Added (removed) stocks exhibit permanent (temporary) change in trading volume and bid-ask spread. The analysis of the spread components suggests that the permanent change associated with additions is a result of non-information-related liquidity. We interpret the permanent price effect of additions and deletions combined with the permanent (temporary) shift in liquidity of added (removed) stocks as evidence in favour of the imperfect substitution hypothesis with some non-information-related liquidity effects in the case of additions.     

Loss aversion and the asymmetric transmission of monetary policy

There is widespread evidence that monetary policy exerts asymmetric effects on output over contractions and expansions in economic activity, while price responses display no sizeable asymmetry. To rationalize these facts we develop a dynamic general equilibrium model where households’ utility depends on consumption deviations from a reference level below which loss aversion is displayed. State-dependent degrees of real rigidity and elasticity of intertemporal substitution in consumption generate competing effects on output and inflation. Contractions face the Central Bank with higher responsiveness of output to interest rate changes, as well as a flatter aggregate supply schedule.     

Valuation of Internet Stocks—An IPO Perspective

We empirically investigate valuations of Internet firms at various stages of the initial public offering (IPO) from two perspectives. First, we examine the association between the valuation of Internet IPOs and a set of financial and nonfinancial variables, which prior anecdotal or empirical evidence suggests may serve as value drivers. Second, we document differences in IPO valuations between Internet and non-Internet firms as well as across different stages in the IPO process—i.e., initial prospectus price, final offer price, and first trading day price—within each set of firms. Our primary two conclusions are as follows. First, there are noticeable differences between valuations of Internet and non-Internet firms, especially at the prospectus and final IPO stage. Specifically, the valuation of non-Internet firms generally follows the conventional wisdom regarding valuation: positive earnings and cash flows are priced, while negative earnings and negative cash flows are not. The valuation of Internet firms, however, departs from conventional wisdom, with earnings not being priced, and negative cash flows being priced perhaps because they are viewed as investments. This difference between the two classes of firms may be expected, given the age and unique nature of the Internet industry. Second, there are significant differences between the initial valuation of firms at the prospectus and IPO stage and their valuation by the stock market at the end of the first trading day. For non-Internet firms, the difference is largely ascribed to the relative offering size. For Internet firms, however, the differences are with respect to positive cash flows, sales growth, R&D, and high-risk warnings, in addition to the relative offering size.     

Revisiting the Tourinho real options model: outstanding issues 30 years later

This article presents and extends the first known model in real options, proposed in Tourinho (1979), and provides thoughts on addressing issues that are still outstanding 30 years later. It discusses the need to ensure the existence of market equilibrium when applying real options valuation to price assets, once all agents behave as suggested by the solution to the pricing equation. It argues that this can be achieved by using a stochastic process for the price that is sufficiently general to respond to supply and demand imbalances in the market for the resource. Once the individual decision rules are derived, the parameters of the process must be determined to ensure market equilibrium exists. For reserves of natural resources, this can be done by using a mean-reverting process for the price of the commodity and ensuring that the long-term price to which it reverts equals the trigger price for development of the marginal reserve.     

Forecasting trends with asset prices

The question of interest in this paper is the estimation of the trend of a financial asset, and the impact of its misspecification on investment strategies. The setting we consider is that of a stochastic asset price model where the trend follows an unobservable Ornstein–Uhlenbeck process. Motivated by the use of Kalman filtering as a forecasting tool, we address the problem of parameter estimation, and measure the effect of parameter misspecification. Numerical examples illustrate the difficulty of trend forecasting in financial time series.     

Mimicking repurchases

We study the tendency of firms to mimic the repurchase announcements of their industry counterparts. We argue that a firm, by repurchasing its shares, sends a positive signal about itself and a negative one about its competitors. This induces the competing firms to mimic the behavior of the repurchasing firm by repurchasing themselves. Using a broad sample of US firms from the period 1984–2002, we show that, in concentrated industries, a repurchase announcement lowers the stock price of the other firms in the same industry. The other firms react by repurchasing themselves to undo these negative effects. Repurchases are chosen as a strategic reaction to other firms’ repurchase decisions and are not motivated by the desire to time the market, i.e., to take advantage of a significantly undervalued stock price. Therefore, repurchasing firms in more concentrated industries experience a lower increase in value in comparison with their counterparts in less concentrated industries in the post-announcement era. Alternative methodologies used to estimate long-term performance confirm that it is only the repurchasing firms in low concentration industries that outperform the market, their non-repurchasing peers, and their counterparts in more concentrated industries by amounts that are economically and statistically significant.     

Competition and the cost of debt

This paper empirically shows that the cost of bank debt is systematically higher for firms that operate in competitive product markets. Using various proxies for product market competition, and reductions of import tariff rates to capture exogenous changes to a firm's competitive environment, I find that competition has a significantly positive effect on the cost of bank debt. Moreover, the analysis reveals that the effect of competition is greater in industries in which small firms face financially strong rivals, in industries with intense strategic interactions between firms, and in illiquid industries. Overall, these findings suggest that banks price financial contracts by taking into account the risk that arises from product market competition.     

SUBORDINATED BINOMIAL OPTION PRICING

We extend the binomial option pricing model to allow for more accurate price dynamics while retaining computational simplicity. The asset price in each binomial period evolves according to two independent and successive Bernoulli trials on trade occurrence/nonoccurrence and up/down price movement. Subordination leads to a trinomial tree with stochastic volatility in calendar time. We derive utility‐dependent valuation results incorporating the leverage effect and test the model empirically.     

Accounting rules,equity valuation,and growth options

In a model with irreversible capacity investments, we show that financial statements prepared under replacement cost accounting provide investors with sufficient information for equity valuation purposes. Under alternative accounting rules, including historical cost and value in use accounting, investors will generally not be able to value precisely a firm’s growth options and therefore its equity. For these accounting rules, we describe the range of valuations that is consistent with the firm’s financial statements. We further show that replacement cost accounting preserves all value-relevant information if the firm’s investments are reversible. However, the directional relation between the value of the firm’s equity and the replacement cost of its assets is different from that in the setting with irreversible investments.     

Pricing Dynamic Insurance Risks Using the Principle of Equivalent Utility

We introduce an expected utility approach to price insurance risks in a dynamic financial market setting. The valuation method is based on comparing the maximal expected utility functions with and without incorporating the insurance product, as in the classical principle of equivalent utility. The pricing mechanism relies heavily on risk preferences and yields two reservation prices - one each for the underwriter and buyer of the contract. The framework is rather general and applies to a number of applications that we extensively analyze.     

Pricing discretely monitored Asian options under Lévy processes

We present methodologies to price discretely monitored Asian options when the underlying evolves according to a generic Lévy process. For geometric Asian options we provide closed-form solutions in terms of the Fourier transform and we study in particular these formulas in the Lévy-stable case. For arithmetic Asian options we solve the valuation problem by recursive integration and derive a recursive theoretical formula for the moments to check the accuracy of the results. We compare the implementation of our method to Monte Carlo simulation implemented with control variates and using different parametric Lévy processes. We also discuss model risk issues.     

Evaluating Real Estate Valuation Systems

A framework for comparing real estate valuation systems (including automated valuation models (AVMs) and current appraisal methods) is proposed. The density estimation and profit simulation (DEPS) method measures quality of a valuation system by simulating benefits to the mortgage lender who uses this method in mortgage underwriting to limit mortgage portfolio losses due to default. Related simple measures relevant to the selection of a valuation system are also discussed: skewness of the distribution of errors, correlation of valuation errors with current selling price errors, correlation of errors of the valuation system with errors of valuation systems used by competing mortgage lenders, and other measures.