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What Do We Learn from the Price of Crude Oil Futures?” working paper
, 2007
"... Abstract: Based on a twocountry, multiperiod general equilibrium model of the spot and futures markets for crude oil, we show that there is no theoretical support for the common view that oil futures prices are accurate predictors of the spot price in the meansquared prediction error (MSPE) sense ..."
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Cited by 100 (27 self)
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Abstract: Based on a twocountry, multiperiod general equilibrium model of the spot and futures markets for crude oil, we show that there is no theoretical support for the common view that oil futures prices are accurate predictors of the spot price in the meansquared prediction error (MSPE) sense; yet under certain conditions there is support for the view that oil futures prices are unbiased predictors. Our empirical analysis documents that futuresbased forecasts typically are less accurate than the nochange forecast and biased, although the bias is small. Much of the MSPE is driven by the variability of the futures price about the expected spot price, as captured by the basis. Empirically, the fluctuations in the oil futures basis are larger and more persistent than fluctuations in the basis of foreign exchange futures. Within the context of our theoretical model, this anomaly can be explained by the marginal convenience yield of oil inventories. We show that increased uncertainty about future oil supply shortfalls under plausible assumptions causes the basis to decline and precautionary demand for crude oil to increase, resulting in an immediate increase in the real spot price that is not necessarily associated with an accumulation of oil inventories. Our main result is that the negative of the basis may be viewed as an index of fluctuations in the price of crude oil driven by precautionary demand for oil. An empirical analysis of this index provides independent evidence of how shifts in market expectations about future oil supply shortfalls affect the spot price of crude oil. Such expectation shifts have been difficult to quantify, yet have been shown to play an important role in explaining oil price fluctuations. Our empirical results are consistent with related evidence in the literature obtained by alternative methodologies.
Stochastic Models of Energy Commodity Prices and Their Applications: Meanreversion with Jumps and Spikes
, 2000
"... I propose several meanreversion jumpdi#usion models to describe spot prices of energy commodities that maybevery costly to store. I incorporate multiple jumps, regimeswitching and stochastic volatilityinto these models in order to capture the salient features of energy commodity prices due to phy ..."
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Cited by 88 (6 self)
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I propose several meanreversion jumpdi#usion models to describe spot prices of energy commodities that maybevery costly to store. I incorporate multiple jumps, regimeswitching and stochastic volatilityinto these models in order to capture the salient features of energy commodity prices due to physical characteristics of energy commodities. Prices of various energy commodity derivatives are derived under each model using the Fourier transform methods. In the context of deregulated electric power industry, I construct a real options approachtovalue physical assets such as generation and transmission facilities. The implications of modeling assumptions to the valuation of real assets are also examined.
Equilibrium Forward Curves for Commodities
 Journal of Finance
, 2000
"... We develop an equilibrium model of the term structure of forward prices for storable commodities. As a consequence of a nonnegativity constraint on inventory, the spot commodity has an embedded timing option that is absent in forward contracts. This option’s value changes over time due to both endog ..."
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Cited by 87 (2 self)
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We develop an equilibrium model of the term structure of forward prices for storable commodities. As a consequence of a nonnegativity constraint on inventory, the spot commodity has an embedded timing option that is absent in forward contracts. This option’s value changes over time due to both endogenous inventory and exogenous transitory shocks to supply and demand. Our model makes predictions about volatilities of forward prices at different horizons and shows how conditional violations of the “Samuelson effect ” occur. We extend the model to incorporate a permanent second factor and calibrate the model to crude oil futures data. COMMODITY MARKETS IN RECENT YEARS have experienced dramatic growth in trading volume, the variety of contracts, and the range of underlying commodities. Market participants are also increasingly sophisticated about recognizing and exercising operational contingencies embedded in delivery contracts. 1 For all of these reasons, there is a widespread interest in models for pricing and hedging commoditylinked contingent claims. In this paper we present an equilibrium model of commodity spot and forward prices. By explicitly incorporating the microeconomics of supply, demand, and storage, our model captures some fundamental differences between commodities and financial assets. Empirically, commodities are strikingly different from stocks, bonds and other conventional financial assets. Among these differences are:
Pricing Of Options On Commodity Futures With Stochastic Term Structures Of Convenience Yields And Interest Rates
 JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS
, 1999
"... We develop a model to value options on commodity futures in the presence of stochastic interest rates as well as stochastic convenience yields. In the development of the model, we distinguish between forward and future convenience yields, a distinction that has not been recognized in the literature. ..."
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Cited by 81 (7 self)
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We develop a model to value options on commodity futures in the presence of stochastic interest rates as well as stochastic convenience yields. In the development of the model, we distinguish between forward and future convenience yields, a distinction that has not been recognized in the literature. Assuming normality of continuously compounded forward interest rates and convenience yields and lognormality of the spot price of the underlying commodity, we obtain closedform solutions generalizing the BlackScholes/Merton's formulas. We provide numerical examples with realistic parameter values showing that both the effect of introducing stochastic convenience yields into the model and the effect of having a short time lag between the maturity of a European call option and the underlying futures contract have significant impact on the option prices.
Pricing in Electricity Markets: a mean reverting jump diffusion model with seasonality”, Applied Mathematical Finance
 Markov Switching”, WP 97, Banco central do Brasil
, 2005
"... irk be ck W or ki ng P ap er s in E co no m ic ..."
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Exotic electricity options and the valuation of electricity generation and transmission assets
 PROCEEDINGS OF THE CHICAGO RISK MANAGEMENT CONFERENCE
, 2001
"... This paper presents and applies a methodology for valuing electricity derivatives by constructing replicating portfolios from electricity futures and the risk free asset. Futures based replication is argued to be made necessary by the nonstorable nature of electricity, which rules out the tradition ..."
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Cited by 63 (3 self)
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This paper presents and applies a methodology for valuing electricity derivatives by constructing replicating portfolios from electricity futures and the risk free asset. Futures based replication is argued to be made necessary by the nonstorable nature of electricity, which rules out the traditional spot market, storagebased method of valuing commodity derivatives. Using the futures based approach, valuation formulae are derived for both spark and locational spread options for both geometric Brownian motion and mean reverting price processes. These valuation results are in turn used to construct real options based valuation formulae for generation and transmission assets. Finally, the valuation formula derived for generation assets is used to value a sample of
Pricing and Hedging Spread Options
 SIAM Review
, 2003
"... Abstract. We survey theoretical and computational problems associated with the pricing and hedging of spread options. These options are ubiquitous in the financial markets, whether they be equity, fixed income, foreign exchange, commodities, or energy markets. As a matter of introduction, we present ..."
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Cited by 59 (8 self)
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Abstract. We survey theoretical and computational problems associated with the pricing and hedging of spread options. These options are ubiquitous in the financial markets, whether they be equity, fixed income, foreign exchange, commodities, or energy markets. As a matter of introduction, we present a general overview of the common features of all spread options by discussing in detail their roles as speculation devices and risk management tools. We describe the mathematical framework used to model them, and we review the numerical algorithms actually used to price and hedge them. There is already extensive literature on the pricing of spread options in the equity and fixed income markets, and our contribution is mostly to put together material scattered across a wide spectrum of recent textbooks and journal articles. On the other hand, information about the various numerical procedures that can be used to price and hedge spread options on physical commodities is more difficult to find. For this reason, we make a systematic effort to choose examples from the energy markets in order to illustrate the numerical challenges associated with these instruments. This gives us a chance to discuss an interesting application of spread options to an asset valuation problem after it is recast in the framework of real options. This approach is currently the object of intense mathematical research. In this spirit, we review the two major avenues to modeling energy price dynamics. We explain how the pricing and hedging algorithms can be implemented in the framework of models for both the spot price dynamics and the forward curve dynamics.
Stochastic Convenience Yield Implied from Commodity Futures and Interest Rates
 Journal of Finance
, 2005
"... We characterize an econometrically identifiable threefactor Gaussian model of commodity spot prices, convenience yields and interest rates, which nests many existing specifications. The model allows convenience yields to be a function of spot prices and interest rates. It also allows for timevaryi ..."
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Cited by 41 (3 self)
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We characterize an econometrically identifiable threefactor Gaussian model of commodity spot prices, convenience yields and interest rates, which nests many existing specifications. The model allows convenience yields to be a function of spot prices and interest rates. It also allows for timevarying riskpremia, and thus disentangles two different sources of meanreversion in spot prices. Empirical results show strong evidence for spotprice level dependence in convenience yields for Crude oil and copper, which implies meanreversion in prices under the riskneutral measure. Silver, gold and copper exhibit timevarying riskpremia, which implies meanreversion of prices under the physical measure. The price dependence in convenience yields has a substantial impact on option prices, while the timevariation in riskpremia affects risk management decisions.
The dynamics of commodity spot and futures markets: A primer
 Energy Journal
"... I discuss the shortrun dynamics of commodity prices, production, and inventories, as well as the sources and effects of market volatility. I explain how prices, rates of production, ana ’ inventory levels are interrelated, and are determined via equilibrium in two interconnected markets: a cash mar ..."
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Cited by 36 (0 self)
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I discuss the shortrun dynamics of commodity prices, production, and inventories, as well as the sources and effects of market volatility. I explain how prices, rates of production, ana ’ inventory levels are interrelated, and are determined via equilibrium in two interconnected markets: a cash market for spot purchases and sales of the commodity, and a market for storage. I show how equilibrium in these markets affects and is affected by changes in the level qf price volatility. I also explain the role and behavior of commodity futures markets, and the relationship between spot prices, futures prices, and inventoql behavior. I illustrate these ideas with data for the petroleum complex crude oil, heating oil, and gasoline over the past two decades.
Bidbased stochastic model for electricity prices: the impact of fundamental drivers on market dynamics
 Energy Laboratory Publications MIT EL 00004, Massachusetts Institute of Technology
, 2000
"... For further information please contact Marija Ilic at 6172534682 or via ..."
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Cited by 31 (5 self)
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For further information please contact Marija Ilic at 6172534682 or via