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This article studies the ability of an N-factor Gaussian model to explain the stochastic behavior of oil futures prices when estimated with the use of all available price information, as opposed to traditional approaches of aggregating data for a set of maturities. A Kalman filter estimation procedure that allows for a time-dependent number of daily observations is used to calibrate the model. When applied to all daily oil futures price transactions from 1992 to 2001, the model performs very well, requiring at least three factors to explain the term structure of futures prices, but four factors to fit the volatility term structure. The model also performs very well for daily copper futures transactions from 1992 to 2001 and for out-of-sample daily oil futures transactions from 2002 to 2004.

This article describes a new approach to the valuation of commodity-contingent claims. The approach uses all the information contained in the term structure ofcommodity futures prices in addition to the historical ,volatilities of futures returnsfor diferent maturities. It is based on the principle that no arbitrage opportunities shoullf exist when trading in futures contracts.The jiamework is applied to price copper-contingent claims. We analyze the daily returnsfor all copper futures contracts traded at the Commodity Exchange of New York between 1978 and. By applying principal components analysis to the data, we conclude that a three-factr model describes the stochastic movement of copper futures prices.Finally, as an illustration of the approach, we use the factor loadings obtained in the principal components analysis to price the publicly traded copper interest-indexed notes issued by Magma Copper Company in 1988. 5th the proliferation of financial instruments linked to the price of commodities, such as htures, options on futures, and commodity-linked bonds, the valuation of commodity-contingent claims is becoming an increasingly important problem in financial economics. It is particularly suited for the evaluation of natural resource investments.The first commodity-contingent claims models, following the tradition of Black and Scholes [1973] for equity-contingent claims, assumed that all the uncertainty could be summarized in one factor, the spot price of the commodity. Models, of this type include Schwartz [1982] and Gibson and Schwartz [I 991 J for pricing commodity-linked securities, and Brennan and Schwartz [1985], Paddock, Siegel, andSmith [1988], and Cortazar and Schwartz [1993] for valuing real assets.Looking at the variability of the cost of carry for most commodities, it soon became apparent that a second stochastic variable is needed to value commodity-contingent claims properly. In their two-factor model, Gibson and Schwartz [1990] assume that the spot price of the commodity and the convenience yield, defined as the difference between the interest rate and the cost of carry, follows a joint stochastic process.In this article we take a different approach to the valuation of commodity-contingent claims. Our starting point is the whole term structure of existing

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The paper presents a model that determines when (at which output price level) it is optimum for a firm to invest in environmental technologies and which are the main parameters that affect this decision. Our analysis shows that firms require high output price levels to be induced to invest in environmental technologies, because they optimally would not want to commit to a heavy irreversible investment that could turn out to be unprofitable in the event of a price fall. A comparative static analysis predicts that firms in industries with high output price volatility would be more reluctant to invest in environmental protection technologies and would be more willing to operate at low output levels (thus attaining low emission levels). Increases in the interest rate would also reduce optimal environmental investment levels.Real Options, Environmental Economics, Capital Budgeting, Natural Resources